39 files changed, 9586 insertions, 0 deletions

diff --git a/3rd_party/Makefile.am b/3rd_party/Makefile.am
new file mode 100644
index 0000000..a196ea3
--- /dev/null
+++ b/3rd_party/Makefile.am
@@ -0,0 +1,6 @@
+AUTOMAKE_OPTIONS = foreign
+ACLOCAL_AMFLAGS = -I m4
+SUBDIRS =
+if HAVE_WIRELESS_PAIRING
+SUBDIRS += ed25519 libsrp6a-sha512
+endif
diff --git a/3rd_party/README.md b/3rd_party/README.md
new file mode 100644
index 0000000..0bec640
--- /dev/null
+++ b/3rd_party/README.md
@@ -0,0 +1,36 @@
+# Third party components/libraries
+
+This folder contains  third party components or libraries  that are used
+within the  libimobiledevice project.  They have been bundled since they
+are either not readily available on the intended target platforms and/or
+have been modified.
+
+Their respective licenses are provided in each corresponding folder in a
+file called LICENSE.
+
+
+## ed25519
+
+Source: https://github.com/orlp/ed25519
+Based on commit 7fa6712ef5d581a6981ec2b08ee623314cd1d1c4.
+[LICENCE](ed25519/LICENSE)
+
+The original source has not been modified, except that the file `test.c`
+and the contained DLL files have been removed. To allow building within
+libimobiledevice, a `Makefile.am` has been added.
+
+
+## libsrp6a-sha512
+
+Source: https://github.com/secure-remote-password/stanford-srp
+Based on commit 587900d32777348f98477cb25123d5761fbe3725.
+[LICENCE](libsrp6a-sha512/LICENSE)
+
+For the usage within libimobiledevice, only [libsrp](https://github.com/secure-remote-password/stanford-srp/tree/master/libsrp)
+has been used as a basis.
+It has been adapted to the needs of the libimobiledevice project, and
+contains just a part of the original code; it only supports the SRP6a
+client method which has been modified to use SHA512 instead of SHA1,
+hence the name was changed to `libsrp6a-sha512`.
+More details about the modifications can be found in [libsrp6a-sha512/README.md](libsrp6a-sha512/README.md).
+
diff --git a/3rd_party/ed25519/LICENSE b/3rd_party/ed25519/LICENSE
new file mode 100644
index 0000000..c1503f9
--- /dev/null
+++ b/3rd_party/ed25519/LICENSE
@@ -0,0 +1,16 @@
+Copyright (c) 2015 Orson Peters <orsonpeters@gmail.com>
+
+This software is provided 'as-is', without any express or implied warranty. In no event will the
+authors be held liable for any damages arising from the use of this software.
+
+Permission is granted to anyone to use this software for any purpose, including commercial
+applications, and to alter it and redistribute it freely, subject to the following restrictions:
+
+1. The origin of this software must not be misrepresented; you must not claim that you wrote the
+   original software. If you use this software in a product, an acknowledgment in the product
+   documentation would be appreciated but is not required.
+
+2. Altered source versions must be plainly marked as such, and must not be misrepresented as
+   being the original software.
+
+3. This notice may not be removed or altered from any source distribution.
diff --git a/3rd_party/ed25519/Makefile.am b/3rd_party/ed25519/Makefile.am
new file mode 100644
index 0000000..d8e4e04
--- /dev/null
+++ b/3rd_party/ed25519/Makefile.am
@@ -0,0 +1,26 @@
+AUTOMAKE_OPTIONS = foreign no-dependencies
+
+AM_CPPFLAGS = \
+        -I$(top_srcdir)/include \
+        -I$(top_srcdir)
+
+AM_CFLAGS = \
+        $(GLOBAL_CFLAGS) \
+        $(ssl_lib_CFLAGS)
+
+AM_LDFLAGS =
+
+noinst_LTLIBRARIES = libed25519.la
+libed25519_la_LIBADD = 
+libed25519_la_LDFLAGS = $(AM_LDFLAGS) -no-undefined
+libed25519_la_SOURCES = \
+        add_scalar.c \
+        fe.c \
+        ge.c \
+        keypair.c \
+        key_exchange.c \
+        sc.c \
+        seed.c \
+        sign.c \
+        sha512.c \
+        verify.c
diff --git a/3rd_party/ed25519/README.md b/3rd_party/ed25519/README.md
new file mode 100644
index 0000000..2c431c2
--- /dev/null
+++ b/3rd_party/ed25519/README.md
@@ -0,0 +1,165 @@
+Ed25519
+=======
+
+This is a portable implementation of [Ed25519](http://ed25519.cr.yp.to/) based
+on the SUPERCOP "ref10" implementation. Additionally there is key exchanging
+and scalar addition included to further aid building a PKI using Ed25519. All
+code is licensed under the permissive zlib license.
+
+All code is pure ANSI C without any dependencies, except for the random seed
+generation which uses standard OS cryptography APIs (`CryptGenRandom` on
+Windows, `/dev/urandom` on nix). If you wish to be entirely portable define
+`ED25519_NO_SEED`. This disables the `ed25519_create_seed` function, so if your
+application requires key generation you must supply your own seeding function
+(which is simply a 256 bit (32 byte) cryptographic random number generator).
+
+
+Performance
+-----------
+
+On a Windows machine with an Intel Pentium B970 @ 2.3GHz I got the following
+speeds (running on only one a single core):
+
+    Seed generation: 64us (15625 per second)
+    Key generation: 88us (11364 per second)
+    Message signing (short message): 87us (11494 per second)
+    Message verifying (short message): 228us (4386 per second)
+    Scalar addition: 100us (10000 per second)
+    Key exchange: 220us (4545 per second)
+
+The speeds on other machines may vary. Sign/verify times will be higher with
+longer messages. The implementation significantly benefits from 64 bit
+architectures, if possible compile as 64 bit.
+
+
+Usage
+-----
+
+Simply add all .c and .h files in the `src/` folder to your project and include
+`ed25519.h` in any file you want to use the API. If you prefer to use a shared
+library, only copy `ed25519.h` and define `ED25519_DLL` before importing.
+
+There are no defined types for seeds, private keys, public keys, shared secrets
+or signatures. Instead simple `unsigned char` buffers are used with the
+following sizes:
+
+```c
+unsigned char seed[32];
+unsigned char signature[64];
+unsigned char public_key[32];
+unsigned char private_key[64];
+unsigned char scalar[32];
+unsigned char shared_secret[32];
+```
+
+API
+---
+
+```c
+int ed25519_create_seed(unsigned char *seed);
+```
+
+Creates a 32 byte random seed in `seed` for key generation. `seed` must be a
+writable 32 byte buffer. Returns 0 on success, and nonzero on failure.
+
+```c
+void ed25519_create_keypair(unsigned char *public_key, unsigned char *private_key,
+                            const unsigned char *seed);
+```
+
+Creates a new key pair from the given seed. `public_key` must be a writable 32
+byte buffer, `private_key` must be a writable 64 byte buffer and `seed` must be
+a 32 byte buffer.
+
+```c
+void ed25519_sign(unsigned char *signature,
+                  const unsigned char *message, size_t message_len,
+                  const unsigned char *public_key, const unsigned char *private_key);
+```
+
+Creates a signature of the given message with the given key pair. `signature`
+must be a writable 64 byte buffer. `message` must have at least `message_len`
+bytes to be read. 
+
+```c
+int ed25519_verify(const unsigned char *signature,
+                   const unsigned char *message, size_t message_len,
+                   const unsigned char *public_key);
+```
+
+Verifies the signature on the given message using `public_key`. `signature`
+must be a readable 64 byte buffer. `message` must have at least `message_len`
+bytes to be read. Returns 1 if the signature matches, 0 otherwise.
+
+```c
+void ed25519_add_scalar(unsigned char *public_key, unsigned char *private_key,
+                        const unsigned char *scalar);
+```
+
+Adds `scalar` to the given key pair where scalar is a 32 byte buffer (possibly
+generated with `ed25519_create_seed`), generating a new key pair. You can
+calculate the public key sum without knowing the private key and vice versa by
+passing in `NULL` for the key you don't know. This is useful for enforcing
+randomness on a key pair by a third party while only knowing the public key,
+among other things.  Warning: the last bit of the scalar is ignored - if
+comparing scalars make sure to clear it with `scalar[31] &= 127`.
+
+
+```c
+void ed25519_key_exchange(unsigned char *shared_secret,
+                          const unsigned char *public_key, const unsigned char *private_key);
+```
+
+Performs a key exchange on the given public key and private key, producing a
+shared secret. It is recommended to hash the shared secret before using it.
+`shared_secret` must be a 32 byte writable buffer where the shared secret will
+be stored.
+
+Example
+-------
+
+```c
+unsigned char seed[32], public_key[32], private_key[64], signature[64];
+unsigned char other_public_key[32], other_private_key[64], shared_secret[32];
+const unsigned char message[] = "TEST MESSAGE";
+
+/* create a random seed, and a key pair out of that seed */
+if (ed25519_create_seed(seed)) {
+    printf("error while generating seed\n");
+    exit(1);
+}
+
+ed25519_create_keypair(public_key, private_key, seed);
+
+/* create signature on the message with the key pair */
+ed25519_sign(signature, message, strlen(message), public_key, private_key);
+
+/* verify the signature */
+if (ed25519_verify(signature, message, strlen(message), public_key)) {
+    printf("valid signature\n");
+} else {
+    printf("invalid signature\n");
+}
+
+/* create a dummy keypair to use for a key exchange, normally you'd only have
+the public key and receive it through some communication channel */
+if (ed25519_create_seed(seed)) {
+    printf("error while generating seed\n");
+    exit(1);
+}
+
+ed25519_create_keypair(other_public_key, other_private_key, seed);
+
+/* do a key exchange with other_public_key */
+ed25519_key_exchange(shared_secret, other_public_key, private_key);
+
+/* 
+    the magic here is that ed25519_key_exchange(shared_secret, public_key,
+    other_private_key); would result in the same shared_secret
+*/
+
+```
+
+License
+-------
+All code is released under the zlib license. See LICENSE for details.
diff --git a/3rd_party/ed25519/add_scalar.c b/3rd_party/ed25519/add_scalar.c
new file mode 100644
index 0000000..7528a7a
--- /dev/null
+++ b/3rd_party/ed25519/add_scalar.c
@@ -0,0 +1,69 @@
+#include "ed25519.h"
+#include "ge.h"
+#include "sc.h"
+#include "sha512.h"
+
+
+/* see http://crypto.stackexchange.com/a/6215/4697 */
+void ed25519_add_scalar(unsigned char *public_key, unsigned char *private_key, const unsigned char *scalar) {
+    const unsigned char SC_1[32] = {1}; /* scalar with value 1 */
+    
+    unsigned char n[32]; 
+    ge_p3 nB;
+    ge_p1p1 A_p1p1;
+    ge_p3 A;
+    ge_p3 public_key_unpacked;
+    ge_cached T;
+
+    sha512_context hash;
+    unsigned char hashbuf[64];
+
+    int i;
+
+    /* copy the scalar and clear highest bit */
+    for (i = 0; i < 31; ++i) {
+        n[i] = scalar[i];
+    }
+    n[31] = scalar[31] & 127;
+
+    /* private key: a = n + t */
+    if (private_key) {
+        sc_muladd(private_key, SC_1, n, private_key);
+
+        // https://github.com/orlp/ed25519/issues/3
+        sha512_init(&hash);
+        sha512_update(&hash, private_key + 32, 32);
+        sha512_update(&hash, scalar, 32);
+        sha512_final(&hash, hashbuf);
+        for (i = 0; i < 32; ++i) {
+            private_key[32 + i] = hashbuf[i];
+        }
+    }
+
+    /* public key: A = nB + T */
+    if (public_key) {
+        /* if we know the private key we don't need a point addition, which is faster */
+        /* using a "timing attack" you could find out wether or not we know the private
+           key, but this information seems rather useless - if this is important pass
+           public_key and private_key seperately in 2 function calls */
+        if (private_key) {
+            ge_scalarmult_base(&A, private_key);
+        } else {
+            /* unpack public key into T */
+            ge_frombytes_negate_vartime(&public_key_unpacked, public_key);
+            fe_neg(public_key_unpacked.X, public_key_unpacked.X); /* undo negate */
+            fe_neg(public_key_unpacked.T, public_key_unpacked.T); /* undo negate */
+            ge_p3_to_cached(&T, &public_key_unpacked);
+
+            /* calculate n*B */
+            ge_scalarmult_base(&nB, n);
+
+            /* A = n*B + T */
+            ge_add(&A_p1p1, &nB, &T);
+            ge_p1p1_to_p3(&A, &A_p1p1);
+        }
+            
+        /* pack public key */
+        ge_p3_tobytes(public_key, &A);
+    }
+}
diff --git a/3rd_party/ed25519/ed25519.h b/3rd_party/ed25519/ed25519.h
new file mode 100644
index 0000000..8924659
--- /dev/null
+++ b/3rd_party/ed25519/ed25519.h
@@ -0,0 +1,38 @@
+#ifndef ED25519_H
+#define ED25519_H
+
+#include <stddef.h>
+
+#if defined(_WIN32)
+    #if defined(ED25519_BUILD_DLL)
+        #define ED25519_DECLSPEC __declspec(dllexport)
+    #elif defined(ED25519_DLL)
+        #define ED25519_DECLSPEC __declspec(dllimport)
+    #else
+        #define ED25519_DECLSPEC
+    #endif
+#else
+    #define ED25519_DECLSPEC
+#endif
+
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+#ifndef ED25519_NO_SEED
+int ED25519_DECLSPEC ed25519_create_seed(unsigned char *seed);
+#endif
+
+void ED25519_DECLSPEC ed25519_create_keypair(unsigned char *public_key, unsigned char *private_key, const unsigned char *seed);
+void ED25519_DECLSPEC ed25519_sign(unsigned char *signature, const unsigned char *message, size_t message_len, const unsigned char *public_key, const unsigned char *private_key);
+int ED25519_DECLSPEC ed25519_verify(const unsigned char *signature, const unsigned char *message, size_t message_len, const unsigned char *public_key);
+void ED25519_DECLSPEC ed25519_add_scalar(unsigned char *public_key, unsigned char *private_key, const unsigned char *scalar);
+void ED25519_DECLSPEC ed25519_key_exchange(unsigned char *shared_secret, const unsigned char *public_key, const unsigned char *private_key);
+
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif
diff --git a/3rd_party/ed25519/fe.c b/3rd_party/ed25519/fe.c
new file mode 100644
index 0000000..2105eb7
--- /dev/null
+++ b/3rd_party/ed25519/fe.c
@@ -0,0 +1,1491 @@
+#include "fixedint.h"
+#include "fe.h"
+
+
+/*
+    helper functions
+*/
+static uint64_t load_3(const unsigned char *in) {
+    uint64_t result;
+
+    result = (uint64_t) in[0];
+    result |= ((uint64_t) in[1]) << 8;
+    result |= ((uint64_t) in[2]) << 16;
+
+    return result;
+}
+
+static uint64_t load_4(const unsigned char *in) {
+    uint64_t result;
+
+    result = (uint64_t) in[0];
+    result |= ((uint64_t) in[1]) << 8;
+    result |= ((uint64_t) in[2]) << 16;
+    result |= ((uint64_t) in[3]) << 24;
+    
+    return result;
+}
+
+
+
+/*
+    h = 0
+*/
+
+void fe_0(fe h) {
+    h[0] = 0;
+    h[1] = 0;
+    h[2] = 0;
+    h[3] = 0;
+    h[4] = 0;
+    h[5] = 0;
+    h[6] = 0;
+    h[7] = 0;
+    h[8] = 0;
+    h[9] = 0;
+}
+
+
+
+/*
+    h = 1
+*/
+
+void fe_1(fe h) {
+    h[0] = 1;
+    h[1] = 0;
+    h[2] = 0;
+    h[3] = 0;
+    h[4] = 0;
+    h[5] = 0;
+    h[6] = 0;
+    h[7] = 0;
+    h[8] = 0;
+    h[9] = 0;
+}
+
+
+
+/*
+    h = f + g
+    Can overlap h with f or g.
+
+    Preconditions:
+       |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+       |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+
+    Postconditions:
+       |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+*/
+
+void fe_add(fe h, const fe f, const fe g) {
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    int32_t g0 = g[0];
+    int32_t g1 = g[1];
+    int32_t g2 = g[2];
+    int32_t g3 = g[3];
+    int32_t g4 = g[4];
+    int32_t g5 = g[5];
+    int32_t g6 = g[6];
+    int32_t g7 = g[7];
+    int32_t g8 = g[8];
+    int32_t g9 = g[9];
+    int32_t h0 = f0 + g0;
+    int32_t h1 = f1 + g1;
+    int32_t h2 = f2 + g2;
+    int32_t h3 = f3 + g3;
+    int32_t h4 = f4 + g4;
+    int32_t h5 = f5 + g5;
+    int32_t h6 = f6 + g6;
+    int32_t h7 = f7 + g7;
+    int32_t h8 = f8 + g8;
+    int32_t h9 = f9 + g9;
+    
+    h[0] = h0;
+    h[1] = h1;
+    h[2] = h2;
+    h[3] = h3;
+    h[4] = h4;
+    h[5] = h5;
+    h[6] = h6;
+    h[7] = h7;
+    h[8] = h8;
+    h[9] = h9;
+}
+
+
+
+/*
+    Replace (f,g) with (g,g) if b == 1;
+    replace (f,g) with (f,g) if b == 0.
+
+    Preconditions: b in {0,1}.
+*/
+
+void fe_cmov(fe f, const fe g, unsigned int b) {
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    int32_t g0 = g[0];
+    int32_t g1 = g[1];
+    int32_t g2 = g[2];
+    int32_t g3 = g[3];
+    int32_t g4 = g[4];
+    int32_t g5 = g[5];
+    int32_t g6 = g[6];
+    int32_t g7 = g[7];
+    int32_t g8 = g[8];
+    int32_t g9 = g[9];
+    int32_t x0 = f0 ^ g0;
+    int32_t x1 = f1 ^ g1;
+    int32_t x2 = f2 ^ g2;
+    int32_t x3 = f3 ^ g3;
+    int32_t x4 = f4 ^ g4;
+    int32_t x5 = f5 ^ g5;
+    int32_t x6 = f6 ^ g6;
+    int32_t x7 = f7 ^ g7;
+    int32_t x8 = f8 ^ g8;
+    int32_t x9 = f9 ^ g9;
+
+    b = (unsigned int) (- (int) b); /* silence warning */
+    x0 &= b;
+    x1 &= b;
+    x2 &= b;
+    x3 &= b;
+    x4 &= b;
+    x5 &= b;
+    x6 &= b;
+    x7 &= b;
+    x8 &= b;
+    x9 &= b;
+    
+    f[0] = f0 ^ x0;
+    f[1] = f1 ^ x1;
+    f[2] = f2 ^ x2;
+    f[3] = f3 ^ x3;
+    f[4] = f4 ^ x4;
+    f[5] = f5 ^ x5;
+    f[6] = f6 ^ x6;
+    f[7] = f7 ^ x7;
+    f[8] = f8 ^ x8;
+    f[9] = f9 ^ x9;
+}
+
+/*
+    Replace (f,g) with (g,f) if b == 1;
+    replace (f,g) with (f,g) if b == 0.
+
+    Preconditions: b in {0,1}.
+*/
+
+void fe_cswap(fe f,fe g,unsigned int b) {
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    int32_t g0 = g[0];
+    int32_t g1 = g[1];
+    int32_t g2 = g[2];
+    int32_t g3 = g[3];
+    int32_t g4 = g[4];
+    int32_t g5 = g[5];
+    int32_t g6 = g[6];
+    int32_t g7 = g[7];
+    int32_t g8 = g[8];
+    int32_t g9 = g[9];
+    int32_t x0 = f0 ^ g0;
+    int32_t x1 = f1 ^ g1;
+    int32_t x2 = f2 ^ g2;
+    int32_t x3 = f3 ^ g3;
+    int32_t x4 = f4 ^ g4;
+    int32_t x5 = f5 ^ g5;
+    int32_t x6 = f6 ^ g6;
+    int32_t x7 = f7 ^ g7;
+    int32_t x8 = f8 ^ g8;
+    int32_t x9 = f9 ^ g9;
+    b = (unsigned int) (- (int) b); /* silence warning */
+    x0 &= b;
+    x1 &= b;
+    x2 &= b;
+    x3 &= b;
+    x4 &= b;
+    x5 &= b;
+    x6 &= b;
+    x7 &= b;
+    x8 &= b;
+    x9 &= b;
+    f[0] = f0 ^ x0;
+    f[1] = f1 ^ x1;
+    f[2] = f2 ^ x2;
+    f[3] = f3 ^ x3;
+    f[4] = f4 ^ x4;
+    f[5] = f5 ^ x5;
+    f[6] = f6 ^ x6;
+    f[7] = f7 ^ x7;
+    f[8] = f8 ^ x8;
+    f[9] = f9 ^ x9;
+    g[0] = g0 ^ x0;
+    g[1] = g1 ^ x1;
+    g[2] = g2 ^ x2;
+    g[3] = g3 ^ x3;
+    g[4] = g4 ^ x4;
+    g[5] = g5 ^ x5;
+    g[6] = g6 ^ x6;
+    g[7] = g7 ^ x7;
+    g[8] = g8 ^ x8;
+    g[9] = g9 ^ x9;
+}
+
+
+
+/*
+    h = f
+*/
+
+void fe_copy(fe h, const fe f) {
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    
+    h[0] = f0;
+    h[1] = f1;
+    h[2] = f2;
+    h[3] = f3;
+    h[4] = f4;
+    h[5] = f5;
+    h[6] = f6;
+    h[7] = f7;
+    h[8] = f8;
+    h[9] = f9;
+}
+
+
+
+/*
+    Ignores top bit of h.
+*/
+
+void fe_frombytes(fe h, const unsigned char *s) {
+    int64_t h0 = load_4(s);
+    int64_t h1 = load_3(s + 4) << 6;
+    int64_t h2 = load_3(s + 7) << 5;
+    int64_t h3 = load_3(s + 10) << 3;
+    int64_t h4 = load_3(s + 13) << 2;
+    int64_t h5 = load_4(s + 16);
+    int64_t h6 = load_3(s + 20) << 7;
+    int64_t h7 = load_3(s + 23) << 5;
+    int64_t h8 = load_3(s + 26) << 4;
+    int64_t h9 = (load_3(s + 29) & 8388607) << 2;
+    int64_t carry0;
+    int64_t carry1;
+    int64_t carry2;
+    int64_t carry3;
+    int64_t carry4;
+    int64_t carry5;
+    int64_t carry6;
+    int64_t carry7;
+    int64_t carry8;
+    int64_t carry9;
+
+    carry9 = (h9 + (int64_t) (1 << 24)) >> 25;
+    h0 += carry9 * 19;
+    h9 -= carry9 << 25;
+    carry1 = (h1 + (int64_t) (1 << 24)) >> 25;
+    h2 += carry1;
+    h1 -= carry1 << 25;
+    carry3 = (h3 + (int64_t) (1 << 24)) >> 25;
+    h4 += carry3;
+    h3 -= carry3 << 25;
+    carry5 = (h5 + (int64_t) (1 << 24)) >> 25;
+    h6 += carry5;
+    h5 -= carry5 << 25;
+    carry7 = (h7 + (int64_t) (1 << 24)) >> 25;
+    h8 += carry7;
+    h7 -= carry7 << 25;
+    carry0 = (h0 + (int64_t) (1 << 25)) >> 26;
+    h1 += carry0;
+    h0 -= carry0 << 26;
+    carry2 = (h2 + (int64_t) (1 << 25)) >> 26;
+    h3 += carry2;
+    h2 -= carry2 << 26;
+    carry4 = (h4 + (int64_t) (1 << 25)) >> 26;
+    h5 += carry4;
+    h4 -= carry4 << 26;
+    carry6 = (h6 + (int64_t) (1 << 25)) >> 26;
+    h7 += carry6;
+    h6 -= carry6 << 26;
+    carry8 = (h8 + (int64_t) (1 << 25)) >> 26;
+    h9 += carry8;
+    h8 -= carry8 << 26;
+
+    h[0] = (int32_t) h0;
+    h[1] = (int32_t) h1;
+    h[2] = (int32_t) h2;
+    h[3] = (int32_t) h3;
+    h[4] = (int32_t) h4;
+    h[5] = (int32_t) h5;
+    h[6] = (int32_t) h6;
+    h[7] = (int32_t) h7;
+    h[8] = (int32_t) h8;
+    h[9] = (int32_t) h9;
+}
+
+
+
+void fe_invert(fe out, const fe z) {
+    fe t0;
+    fe t1;
+    fe t2;
+    fe t3;
+    int i;
+
+    fe_sq(t0, z);
+
+    for (i = 1; i < 1; ++i) {
+        fe_sq(t0, t0);
+    }
+
+    fe_sq(t1, t0);
+
+    for (i = 1; i < 2; ++i) {
+        fe_sq(t1, t1);
+    }
+
+    fe_mul(t1, z, t1);
+    fe_mul(t0, t0, t1);
+    fe_sq(t2, t0);
+
+    for (i = 1; i < 1; ++i) {
+        fe_sq(t2, t2);
+    }
+
+    fe_mul(t1, t1, t2);
+    fe_sq(t2, t1);
+
+    for (i = 1; i < 5; ++i) {
+        fe_sq(t2, t2);
+    }
+
+    fe_mul(t1, t2, t1);
+    fe_sq(t2, t1);
+
+    for (i = 1; i < 10; ++i) {
+        fe_sq(t2, t2);
+    }
+
+    fe_mul(t2, t2, t1);
+    fe_sq(t3, t2);
+
+    for (i = 1; i < 20; ++i) {
+        fe_sq(t3, t3);
+    }
+
+    fe_mul(t2, t3, t2);
+    fe_sq(t2, t2);
+
+    for (i = 1; i < 10; ++i) {
+        fe_sq(t2, t2);
+    }
+
+    fe_mul(t1, t2, t1);
+    fe_sq(t2, t1);
+
+    for (i = 1; i < 50; ++i) {
+        fe_sq(t2, t2);
+    }
+
+    fe_mul(t2, t2, t1);
+    fe_sq(t3, t2);
+
+    for (i = 1; i < 100; ++i) {
+        fe_sq(t3, t3);
+    }
+
+    fe_mul(t2, t3, t2);
+    fe_sq(t2, t2);
+
+    for (i = 1; i < 50; ++i) {
+        fe_sq(t2, t2);
+    }
+
+    fe_mul(t1, t2, t1);
+    fe_sq(t1, t1);
+
+    for (i = 1; i < 5; ++i) {
+        fe_sq(t1, t1);
+    }
+
+    fe_mul(out, t1, t0);
+}
+
+
+
+/*
+    return 1 if f is in {1,3,5,...,q-2}
+    return 0 if f is in {0,2,4,...,q-1}
+
+    Preconditions:
+       |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+*/
+
+int fe_isnegative(const fe f) {
+    unsigned char s[32];
+
+    fe_tobytes(s, f);
+    
+    return s[0] & 1;
+}
+
+
+
+/*
+    return 1 if f == 0
+    return 0 if f != 0
+
+    Preconditions:
+       |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+*/
+
+int fe_isnonzero(const fe f) {
+    unsigned char s[32];
+    unsigned char r;
+
+    fe_tobytes(s, f);
+
+    r = s[0];
+    #define F(i) r |= s[i]
+    F(1);
+    F(2);
+    F(3);
+    F(4);
+    F(5);
+    F(6);
+    F(7);
+    F(8);
+    F(9);
+    F(10);
+    F(11);
+    F(12);
+    F(13);
+    F(14);
+    F(15);
+    F(16);
+    F(17);
+    F(18);
+    F(19);
+    F(20);
+    F(21);
+    F(22);
+    F(23);
+    F(24);
+    F(25);
+    F(26);
+    F(27);
+    F(28);
+    F(29);
+    F(30);
+    F(31);
+    #undef F
+
+    return r != 0;
+}
+
+
+
+/*
+    h = f * g
+    Can overlap h with f or g.
+
+    Preconditions:
+       |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
+       |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
+
+    Postconditions:
+       |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
+    */
+
+    /*
+    Notes on implementation strategy:
+
+    Using schoolbook multiplication.
+    Karatsuba would save a little in some cost models.
+
+    Most multiplications by 2 and 19 are 32-bit precomputations;
+    cheaper than 64-bit postcomputations.
+
+    There is one remaining multiplication by 19 in the carry chain;
+    one *19 precomputation can be merged into this,
+    but the resulting data flow is considerably less clean.
+
+    There are 12 carries below.
+    10 of them are 2-way parallelizable and vectorizable.
+    Can get away with 11 carries, but then data flow is much deeper.
+
+    With tighter constraints on inputs can squeeze carries into int32.
+*/
+
+void fe_mul(fe h, const fe f, const fe g) {
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    int32_t g0 = g[0];
+    int32_t g1 = g[1];
+    int32_t g2 = g[2];
+    int32_t g3 = g[3];
+    int32_t g4 = g[4];
+    int32_t g5 = g[5];
+    int32_t g6 = g[6];
+    int32_t g7 = g[7];
+    int32_t g8 = g[8];
+    int32_t g9 = g[9];
+    int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */
+    int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */
+    int32_t g3_19 = 19 * g3;
+    int32_t g4_19 = 19 * g4;
+    int32_t g5_19 = 19 * g5;
+    int32_t g6_19 = 19 * g6;
+    int32_t g7_19 = 19 * g7;
+    int32_t g8_19 = 19 * g8;
+    int32_t g9_19 = 19 * g9;
+    int32_t f1_2 = 2 * f1;
+    int32_t f3_2 = 2 * f3;
+    int32_t f5_2 = 2 * f5;
+    int32_t f7_2 = 2 * f7;
+    int32_t f9_2 = 2 * f9;
+    int64_t f0g0    = f0   * (int64_t) g0;
+    int64_t f0g1    = f0   * (int64_t) g1;
+    int64_t f0g2    = f0   * (int64_t) g2;
+    int64_t f0g3    = f0   * (int64_t) g3;
+    int64_t f0g4    = f0   * (int64_t) g4;
+    int64_t f0g5    = f0   * (int64_t) g5;
+    int64_t f0g6    = f0   * (int64_t) g6;
+    int64_t f0g7    = f0   * (int64_t) g7;
+    int64_t f0g8    = f0   * (int64_t) g8;
+    int64_t f0g9    = f0   * (int64_t) g9;
+    int64_t f1g0    = f1   * (int64_t) g0;
+    int64_t f1g1_2  = f1_2 * (int64_t) g1;
+    int64_t f1g2    = f1   * (int64_t) g2;
+    int64_t f1g3_2  = f1_2 * (int64_t) g3;
+    int64_t f1g4    = f1   * (int64_t) g4;
+    int64_t f1g5_2  = f1_2 * (int64_t) g5;
+    int64_t f1g6    = f1   * (int64_t) g6;
+    int64_t f1g7_2  = f1_2 * (int64_t) g7;
+    int64_t f1g8    = f1   * (int64_t) g8;
+    int64_t f1g9_38 = f1_2 * (int64_t) g9_19;
+    int64_t f2g0    = f2   * (int64_t) g0;
+    int64_t f2g1    = f2   * (int64_t) g1;
+    int64_t f2g2    = f2   * (int64_t) g2;
+    int64_t f2g3    = f2   * (int64_t) g3;
+    int64_t f2g4    = f2   * (int64_t) g4;
+    int64_t f2g5    = f2   * (int64_t) g5;
+    int64_t f2g6    = f2   * (int64_t) g6;
+    int64_t f2g7    = f2   * (int64_t) g7;
+    int64_t f2g8_19 = f2   * (int64_t) g8_19;
+    int64_t f2g9_19 = f2   * (int64_t) g9_19;
+    int64_t f3g0    = f3   * (int64_t) g0;
+    int64_t f3g1_2  = f3_2 * (int64_t) g1;
+    int64_t f3g2    = f3   * (int64_t) g2;
+    int64_t f3g3_2  = f3_2 * (int64_t) g3;
+    int64_t f3g4    = f3   * (int64_t) g4;
+    int64_t f3g5_2  = f3_2 * (int64_t) g5;
+    int64_t f3g6    = f3   * (int64_t) g6;
+    int64_t f3g7_38 = f3_2 * (int64_t) g7_19;
+    int64_t f3g8_19 = f3   * (int64_t) g8_19;
+    int64_t f3g9_38 = f3_2 * (int64_t) g9_19;
+    int64_t f4g0    = f4   * (int64_t) g0;
+    int64_t f4g1    = f4   * (int64_t) g1;
+    int64_t f4g2    = f4   * (int64_t) g2;
+    int64_t f4g3    = f4   * (int64_t) g3;
+    int64_t f4g4    = f4   * (int64_t) g4;
+    int64_t f4g5    = f4   * (int64_t) g5;
+    int64_t f4g6_19 = f4   * (int64_t) g6_19;
+    int64_t f4g7_19 = f4   * (int64_t) g7_19;
+    int64_t f4g8_19 = f4   * (int64_t) g8_19;
+    int64_t f4g9_19 = f4   * (int64_t) g9_19;
+    int64_t f5g0    = f5   * (int64_t) g0;
+    int64_t f5g1_2  = f5_2 * (int64_t) g1;
+    int64_t f5g2    = f5   * (int64_t) g2;
+    int64_t f5g3_2  = f5_2 * (int64_t) g3;
+    int64_t f5g4    = f5   * (int64_t) g4;
+    int64_t f5g5_38 = f5_2 * (int64_t) g5_19;
+    int64_t f5g6_19 = f5   * (int64_t) g6_19;
+    int64_t f5g7_38 = f5_2 * (int64_t) g7_19;
+    int64_t f5g8_19 = f5   * (int64_t) g8_19;
+    int64_t f5g9_38 = f5_2 * (int64_t) g9_19;
+    int64_t f6g0    = f6   * (int64_t) g0;
+    int64_t f6g1    = f6   * (int64_t) g1;
+    int64_t f6g2    = f6   * (int64_t) g2;
+    int64_t f6g3    = f6   * (int64_t) g3;
+    int64_t f6g4_19 = f6   * (int64_t) g4_19;
+    int64_t f6g5_19 = f6   * (int64_t) g5_19;
+    int64_t f6g6_19 = f6   * (int64_t) g6_19;
+    int64_t f6g7_19 = f6   * (int64_t) g7_19;
+    int64_t f6g8_19 = f6   * (int64_t) g8_19;
+    int64_t f6g9_19 = f6   * (int64_t) g9_19;
+    int64_t f7g0    = f7   * (int64_t) g0;
+    int64_t f7g1_2  = f7_2 * (int64_t) g1;
+    int64_t f7g2    = f7   * (int64_t) g2;
+    int64_t f7g3_38 = f7_2 * (int64_t) g3_19;
+    int64_t f7g4_19 = f7   * (int64_t) g4_19;
+    int64_t f7g5_38 = f7_2 * (int64_t) g5_19;
+    int64_t f7g6_19 = f7   * (int64_t) g6_19;
+    int64_t f7g7_38 = f7_2 * (int64_t) g7_19;
+    int64_t f7g8_19 = f7   * (int64_t) g8_19;
+    int64_t f7g9_38 = f7_2 * (int64_t) g9_19;
+    int64_t f8g0    = f8   * (int64_t) g0;
+    int64_t f8g1    = f8   * (int64_t) g1;
+    int64_t f8g2_19 = f8   * (int64_t) g2_19;
+    int64_t f8g3_19 = f8   * (int64_t) g3_19;
+    int64_t f8g4_19 = f8   * (int64_t) g4_19;
+    int64_t f8g5_19 = f8   * (int64_t) g5_19;
+    int64_t f8g6_19 = f8   * (int64_t) g6_19;
+    int64_t f8g7_19 = f8   * (int64_t) g7_19;
+    int64_t f8g8_19 = f8   * (int64_t) g8_19;
+    int64_t f8g9_19 = f8   * (int64_t) g9_19;
+    int64_t f9g0    = f9   * (int64_t) g0;
+    int64_t f9g1_38 = f9_2 * (int64_t) g1_19;
+    int64_t f9g2_19 = f9   * (int64_t) g2_19;
+    int64_t f9g3_38 = f9_2 * (int64_t) g3_19;
+    int64_t f9g4_19 = f9   * (int64_t) g4_19;
+    int64_t f9g5_38 = f9_2 * (int64_t) g5_19;
+    int64_t f9g6_19 = f9   * (int64_t) g6_19;
+    int64_t f9g7_38 = f9_2 * (int64_t) g7_19;
+    int64_t f9g8_19 = f9   * (int64_t) g8_19;
+    int64_t f9g9_38 = f9_2 * (int64_t) g9_19;
+    int64_t h0 = f0g0 + f1g9_38 + f2g8_19 + f3g7_38 + f4g6_19 + f5g5_38 + f6g4_19 + f7g3_38 + f8g2_19 + f9g1_38;
+    int64_t h1 = f0g1 + f1g0   + f2g9_19 + f3g8_19 + f4g7_19 + f5g6_19 + f6g5_19 + f7g4_19 + f8g3_19 + f9g2_19;
+    int64_t h2 = f0g2 + f1g1_2 + f2g0   + f3g9_38 + f4g8_19 + f5g7_38 + f6g6_19 + f7g5_38 + f8g4_19 + f9g3_38;
+    int64_t h3 = f0g3 + f1g2   + f2g1   + f3g0   + f4g9_19 + f5g8_19 + f6g7_19 + f7g6_19 + f8g5_19 + f9g4_19;
+    int64_t h4 = f0g4 + f1g3_2 + f2g2   + f3g1_2 + f4g0   + f5g9_38 + f6g8_19 + f7g7_38 + f8g6_19 + f9g5_38;
+    int64_t h5 = f0g5 + f1g4   + f2g3   + f3g2   + f4g1   + f5g0   + f6g9_19 + f7g8_19 + f8g7_19 + f9g6_19;
+    int64_t h6 = f0g6 + f1g5_2 + f2g4   + f3g3_2 + f4g2   + f5g1_2 + f6g0   + f7g9_38 + f8g8_19 + f9g7_38;
+    int64_t h7 = f0g7 + f1g6   + f2g5   + f3g4   + f4g3   + f5g2   + f6g1   + f7g0   + f8g9_19 + f9g8_19;
+    int64_t h8 = f0g8 + f1g7_2 + f2g6   + f3g5_2 + f4g4   + f5g3_2 + f6g2   + f7g1_2 + f8g0   + f9g9_38;
+    int64_t h9 = f0g9 + f1g8   + f2g7   + f3g6   + f4g5   + f5g4   + f6g3   + f7g2   + f8g1   + f9g0   ;
+    int64_t carry0;
+    int64_t carry1;
+    int64_t carry2;
+    int64_t carry3;
+    int64_t carry4;
+    int64_t carry5;
+    int64_t carry6;
+    int64_t carry7;
+    int64_t carry8;
+    int64_t carry9;
+
+    carry0 = (h0 + (int64_t) (1 << 25)) >> 26;
+    h1 += carry0;
+    h0 -= carry0 << 26;
+    carry4 = (h4 + (int64_t) (1 << 25)) >> 26;
+    h5 += carry4;
+    h4 -= carry4 << 26;
+
+    carry1 = (h1 + (int64_t) (1 << 24)) >> 25;
+    h2 += carry1;
+    h1 -= carry1 << 25;
+    carry5 = (h5 + (int64_t) (1 << 24)) >> 25;
+    h6 += carry5;
+    h5 -= carry5 << 25;
+
+    carry2 = (h2 + (int64_t) (1 << 25)) >> 26;
+    h3 += carry2;
+    h2 -= carry2 << 26;
+    carry6 = (h6 + (int64_t) (1 << 25)) >> 26;
+    h7 += carry6;
+    h6 -= carry6 << 26;
+
+    carry3 = (h3 + (int64_t) (1 << 24)) >> 25;
+    h4 += carry3;
+    h3 -= carry3 << 25;
+    carry7 = (h7 + (int64_t) (1 << 24)) >> 25;
+    h8 += carry7;
+    h7 -= carry7 << 25;
+
+    carry4 = (h4 + (int64_t) (1 << 25)) >> 26;
+    h5 += carry4;
+    h4 -= carry4 << 26;
+    carry8 = (h8 + (int64_t) (1 << 25)) >> 26;
+    h9 += carry8;
+    h8 -= carry8 << 26;
+
+    carry9 = (h9 + (int64_t) (1 << 24)) >> 25;
+    h0 += carry9 * 19;
+    h9 -= carry9 << 25;
+
+    carry0 = (h0 + (int64_t) (1 << 25)) >> 26;
+    h1 += carry0;
+    h0 -= carry0 << 26;
+
+    h[0] = (int32_t) h0;
+    h[1] = (int32_t) h1;
+    h[2] = (int32_t) h2;
+    h[3] = (int32_t) h3;
+    h[4] = (int32_t) h4;
+    h[5] = (int32_t) h5;
+    h[6] = (int32_t) h6;
+    h[7] = (int32_t) h7;
+    h[8] = (int32_t) h8;
+    h[9] = (int32_t) h9;
+}
+
+
+/*
+h = f * 121666
+Can overlap h with f.
+
+Preconditions:
+   |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+
+Postconditions:
+   |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+*/
+
+void fe_mul121666(fe h, fe f) {
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    int64_t h0 = f0 * (int64_t) 121666;
+    int64_t h1 = f1 * (int64_t) 121666;
+    int64_t h2 = f2 * (int64_t) 121666;
+    int64_t h3 = f3 * (int64_t) 121666;
+    int64_t h4 = f4 * (int64_t) 121666;
+    int64_t h5 = f5 * (int64_t) 121666;
+    int64_t h6 = f6 * (int64_t) 121666;
+    int64_t h7 = f7 * (int64_t) 121666;
+    int64_t h8 = f8 * (int64_t) 121666;
+    int64_t h9 = f9 * (int64_t) 121666;
+    int64_t carry0;
+    int64_t carry1;
+    int64_t carry2;
+    int64_t carry3;
+    int64_t carry4;
+    int64_t carry5;
+    int64_t carry6;
+    int64_t carry7;
+    int64_t carry8;
+    int64_t carry9;
+
+    carry9 = (h9 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
+    carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
+    carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
+    carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
+    carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
+
+    carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+    carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
+    carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+    carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
+    carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
+
+    h[0] = (int32_t) h0;
+    h[1] = (int32_t) h1;
+    h[2] = (int32_t) h2;
+    h[3] = (int32_t) h3;
+    h[4] = (int32_t) h4;
+    h[5] = (int32_t) h5;
+    h[6] = (int32_t) h6;
+    h[7] = (int32_t) h7;
+    h[8] = (int32_t) h8;
+    h[9] = (int32_t) h9;
+}
+
+
+/*
+h = -f
+
+Preconditions:
+   |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+
+Postconditions:
+   |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+*/
+
+void fe_neg(fe h, const fe f) {
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    int32_t h0 = -f0;
+    int32_t h1 = -f1;
+    int32_t h2 = -f2;
+    int32_t h3 = -f3;
+    int32_t h4 = -f4;
+    int32_t h5 = -f5;
+    int32_t h6 = -f6;
+    int32_t h7 = -f7;
+    int32_t h8 = -f8;
+    int32_t h9 = -f9;
+
+    h[0] = h0;
+    h[1] = h1;
+    h[2] = h2;
+    h[3] = h3;
+    h[4] = h4;
+    h[5] = h5;
+    h[6] = h6;
+    h[7] = h7;
+    h[8] = h8;
+    h[9] = h9;
+}
+
+
+void fe_pow22523(fe out, const fe z) {
+    fe t0;
+    fe t1;
+    fe t2;
+    int i;
+    fe_sq(t0, z);
+
+    for (i = 1; i < 1; ++i) {
+        fe_sq(t0, t0);
+    }
+
+    fe_sq(t1, t0);
+
+    for (i = 1; i < 2; ++i) {
+        fe_sq(t1, t1);
+    }
+
+    fe_mul(t1, z, t1);
+    fe_mul(t0, t0, t1);
+    fe_sq(t0, t0);
+
+    for (i = 1; i < 1; ++i) {
+        fe_sq(t0, t0);
+    }
+
+    fe_mul(t0, t1, t0);
+    fe_sq(t1, t0);
+
+    for (i = 1; i < 5; ++i) {
+        fe_sq(t1, t1);
+    }
+
+    fe_mul(t0, t1, t0);
+    fe_sq(t1, t0);
+
+    for (i = 1; i < 10; ++i) {
+        fe_sq(t1, t1);
+    }
+
+    fe_mul(t1, t1, t0);
+    fe_sq(t2, t1);
+
+    for (i = 1; i < 20; ++i) {
+        fe_sq(t2, t2);
+    }
+
+    fe_mul(t1, t2, t1);
+    fe_sq(t1, t1);
+
+    for (i = 1; i < 10; ++i) {
+        fe_sq(t1, t1);
+    }
+
+    fe_mul(t0, t1, t0);
+    fe_sq(t1, t0);
+
+    for (i = 1; i < 50; ++i) {
+        fe_sq(t1, t1);
+    }
+
+    fe_mul(t1, t1, t0);
+    fe_sq(t2, t1);
+
+    for (i = 1; i < 100; ++i) {
+        fe_sq(t2, t2);
+    }
+
+    fe_mul(t1, t2, t1);
+    fe_sq(t1, t1);
+
+    for (i = 1; i < 50; ++i) {
+        fe_sq(t1, t1);
+    }
+
+    fe_mul(t0, t1, t0);
+    fe_sq(t0, t0);
+
+    for (i = 1; i < 2; ++i) {
+        fe_sq(t0, t0);
+    }
+
+    fe_mul(out, t0, z);
+    return;
+}
+
+
+/*
+h = f * f
+Can overlap h with f.
+
+Preconditions:
+   |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
+
+Postconditions:
+   |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
+*/
+
+/*
+See fe_mul.c for discussion of implementation strategy.
+*/
+
+void fe_sq(fe h, const fe f) {
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    int32_t f0_2 = 2 * f0;
+    int32_t f1_2 = 2 * f1;
+    int32_t f2_2 = 2 * f2;
+    int32_t f3_2 = 2 * f3;
+    int32_t f4_2 = 2 * f4;
+    int32_t f5_2 = 2 * f5;
+    int32_t f6_2 = 2 * f6;
+    int32_t f7_2 = 2 * f7;
+    int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
+    int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
+    int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
+    int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
+    int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
+    int64_t f0f0    = f0   * (int64_t) f0;
+    int64_t f0f1_2  = f0_2 * (int64_t) f1;
+    int64_t f0f2_2  = f0_2 * (int64_t) f2;
+    int64_t f0f3_2  = f0_2 * (int64_t) f3;
+    int64_t f0f4_2  = f0_2 * (int64_t) f4;
+    int64_t f0f5_2  = f0_2 * (int64_t) f5;
+    int64_t f0f6_2  = f0_2 * (int64_t) f6;
+    int64_t f0f7_2  = f0_2 * (int64_t) f7;
+    int64_t f0f8_2  = f0_2 * (int64_t) f8;
+    int64_t f0f9_2  = f0_2 * (int64_t) f9;
+    int64_t f1f1_2  = f1_2 * (int64_t) f1;
+    int64_t f1f2_2  = f1_2 * (int64_t) f2;
+    int64_t f1f3_4  = f1_2 * (int64_t) f3_2;
+    int64_t f1f4_2  = f1_2 * (int64_t) f4;
+    int64_t f1f5_4  = f1_2 * (int64_t) f5_2;
+    int64_t f1f6_2  = f1_2 * (int64_t) f6;
+    int64_t f1f7_4  = f1_2 * (int64_t) f7_2;
+    int64_t f1f8_2  = f1_2 * (int64_t) f8;
+    int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
+    int64_t f2f2    = f2   * (int64_t) f2;
+    int64_t f2f3_2  = f2_2 * (int64_t) f3;
+    int64_t f2f4_2  = f2_2 * (int64_t) f4;
+    int64_t f2f5_2  = f2_2 * (int64_t) f5;
+    int64_t f2f6_2  = f2_2 * (int64_t) f6;
+    int64_t f2f7_2  = f2_2 * (int64_t) f7;
+    int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
+    int64_t f2f9_38 = f2   * (int64_t) f9_38;
+    int64_t f3f3_2  = f3_2 * (int64_t) f3;
+    int64_t f3f4_2  = f3_2 * (int64_t) f4;
+    int64_t f3f5_4  = f3_2 * (int64_t) f5_2;
+    int64_t f3f6_2  = f3_2 * (int64_t) f6;
+    int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
+    int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
+    int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
+    int64_t f4f4    = f4   * (int64_t) f4;
+    int64_t f4f5_2  = f4_2 * (int64_t) f5;
+    int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
+    int64_t f4f7_38 = f4   * (int64_t) f7_38;
+    int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
+    int64_t f4f9_38 = f4   * (int64_t) f9_38;
+    int64_t f5f5_38 = f5   * (int64_t) f5_38;
+    int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
+    int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
+    int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
+    int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
+    int64_t f6f6_19 = f6   * (int64_t) f6_19;
+    int64_t f6f7_38 = f6   * (int64_t) f7_38;
+    int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
+    int64_t f6f9_38 = f6   * (int64_t) f9_38;
+    int64_t f7f7_38 = f7   * (int64_t) f7_38;
+    int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
+    int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
+    int64_t f8f8_19 = f8   * (int64_t) f8_19;
+    int64_t f8f9_38 = f8   * (int64_t) f9_38;
+    int64_t f9f9_38 = f9   * (int64_t) f9_38;
+    int64_t h0 = f0f0  + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
+    int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
+    int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
+    int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38;
+    int64_t h4 = f0f4_2 + f1f3_4 + f2f2   + f5f9_76 + f6f8_38 + f7f7_38;
+    int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38;
+    int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19;
+    int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38;
+    int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4   + f9f9_38;
+    int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2;
+    int64_t carry0;
+    int64_t carry1;
+    int64_t carry2;
+    int64_t carry3;
+    int64_t carry4;
+    int64_t carry5;
+    int64_t carry6;
+    int64_t carry7;
+    int64_t carry8;
+    int64_t carry9;
+    carry0 = (h0 + (int64_t) (1 << 25)) >> 26;
+    h1 += carry0;
+    h0 -= carry0 << 26;
+    carry4 = (h4 + (int64_t) (1 << 25)) >> 26;
+    h5 += carry4;
+    h4 -= carry4 << 26;
+    carry1 = (h1 + (int64_t) (1 << 24)) >> 25;
+    h2 += carry1;
+    h1 -= carry1 << 25;
+    carry5 = (h5 + (int64_t) (1 << 24)) >> 25;
+    h6 += carry5;
+    h5 -= carry5 << 25;
+    carry2 = (h2 + (int64_t) (1 << 25)) >> 26;
+    h3 += carry2;
+    h2 -= carry2 << 26;
+    carry6 = (h6 + (int64_t) (1 << 25)) >> 26;
+    h7 += carry6;
+    h6 -= carry6 << 26;
+    carry3 = (h3 + (int64_t) (1 << 24)) >> 25;
+    h4 += carry3;
+    h3 -= carry3 << 25;
+    carry7 = (h7 + (int64_t) (1 << 24)) >> 25;
+    h8 += carry7;
+    h7 -= carry7 << 25;
+    carry4 = (h4 + (int64_t) (1 << 25)) >> 26;
+    h5 += carry4;
+    h4 -= carry4 << 26;
+    carry8 = (h8 + (int64_t) (1 << 25)) >> 26;
+    h9 += carry8;
+    h8 -= carry8 << 26;
+    carry9 = (h9 + (int64_t) (1 << 24)) >> 25;
+    h0 += carry9 * 19;
+    h9 -= carry9 << 25;
+    carry0 = (h0 + (int64_t) (1 << 25)) >> 26;
+    h1 += carry0;
+    h0 -= carry0 << 26;
+    h[0] = (int32_t) h0;
+    h[1] = (int32_t) h1;
+    h[2] = (int32_t) h2;
+    h[3] = (int32_t) h3;
+    h[4] = (int32_t) h4;
+    h[5] = (int32_t) h5;
+    h[6] = (int32_t) h6;
+    h[7] = (int32_t) h7;
+    h[8] = (int32_t) h8;
+    h[9] = (int32_t) h9;
+}
+
+
+/*
+h = 2 * f * f
+Can overlap h with f.
+
+Preconditions:
+   |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
+
+Postconditions:
+   |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
+*/
+
+/*
+See fe_mul.c for discussion of implementation strategy.
+*/
+
+void fe_sq2(fe h, const fe f) {
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    int32_t f0_2 = 2 * f0;
+    int32_t f1_2 = 2 * f1;
+    int32_t f2_2 = 2 * f2;
+    int32_t f3_2 = 2 * f3;
+    int32_t f4_2 = 2 * f4;
+    int32_t f5_2 = 2 * f5;
+    int32_t f6_2 = 2 * f6;
+    int32_t f7_2 = 2 * f7;
+    int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
+    int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
+    int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
+    int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
+    int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
+    int64_t f0f0    = f0   * (int64_t) f0;
+    int64_t f0f1_2  = f0_2 * (int64_t) f1;
+    int64_t f0f2_2  = f0_2 * (int64_t) f2;
+    int64_t f0f3_2  = f0_2 * (int64_t) f3;
+    int64_t f0f4_2  = f0_2 * (int64_t) f4;
+    int64_t f0f5_2  = f0_2 * (int64_t) f5;
+    int64_t f0f6_2  = f0_2 * (int64_t) f6;
+    int64_t f0f7_2  = f0_2 * (int64_t) f7;
+    int64_t f0f8_2  = f0_2 * (int64_t) f8;
+    int64_t f0f9_2  = f0_2 * (int64_t) f9;
+    int64_t f1f1_2  = f1_2 * (int64_t) f1;
+    int64_t f1f2_2  = f1_2 * (int64_t) f2;
+    int64_t f1f3_4  = f1_2 * (int64_t) f3_2;
+    int64_t f1f4_2  = f1_2 * (int64_t) f4;
+    int64_t f1f5_4  = f1_2 * (int64_t) f5_2;
+    int64_t f1f6_2  = f1_2 * (int64_t) f6;
+    int64_t f1f7_4  = f1_2 * (int64_t) f7_2;
+    int64_t f1f8_2  = f1_2 * (int64_t) f8;
+    int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
+    int64_t f2f2    = f2   * (int64_t) f2;
+    int64_t f2f3_2  = f2_2 * (int64_t) f3;
+    int64_t f2f4_2  = f2_2 * (int64_t) f4;
+    int64_t f2f5_2  = f2_2 * (int64_t) f5;
+    int64_t f2f6_2  = f2_2 * (int64_t) f6;
+    int64_t f2f7_2  = f2_2 * (int64_t) f7;
+    int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
+    int64_t f2f9_38 = f2   * (int64_t) f9_38;
+    int64_t f3f3_2  = f3_2 * (int64_t) f3;
+    int64_t f3f4_2  = f3_2 * (int64_t) f4;
+    int64_t f3f5_4  = f3_2 * (int64_t) f5_2;
+    int64_t f3f6_2  = f3_2 * (int64_t) f6;
+    int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
+    int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
+    int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
+    int64_t f4f4    = f4   * (int64_t) f4;
+    int64_t f4f5_2  = f4_2 * (int64_t) f5;
+    int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
+    int64_t f4f7_38 = f4   * (int64_t) f7_38;
+    int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
+    int64_t f4f9_38 = f4   * (int64_t) f9_38;
+    int64_t f5f5_38 = f5   * (int64_t) f5_38;
+    int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
+    int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
+    int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
+    int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
+    int64_t f6f6_19 = f6   * (int64_t) f6_19;
+    int64_t f6f7_38 = f6   * (int64_t) f7_38;
+    int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
+    int64_t f6f9_38 = f6   * (int64_t) f9_38;
+    int64_t f7f7_38 = f7   * (int64_t) f7_38;
+    int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
+    int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
+    int64_t f8f8_19 = f8   * (int64_t) f8_19;
+    int64_t f8f9_38 = f8   * (int64_t) f9_38;
+    int64_t f9f9_38 = f9   * (int64_t) f9_38;
+    int64_t h0 = f0f0  + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
+    int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
+    int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
+    int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38;
+    int64_t h4 = f0f4_2 + f1f3_4 + f2f2   + f5f9_76 + f6f8_38 + f7f7_38;
+    int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38;
+    int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19;
+    int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38;
+    int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4   + f9f9_38;
+    int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2;
+    int64_t carry0;
+    int64_t carry1;
+    int64_t carry2;
+    int64_t carry3;
+    int64_t carry4;
+    int64_t carry5;
+    int64_t carry6;
+    int64_t carry7;
+    int64_t carry8;
+    int64_t carry9;
+    h0 += h0;
+    h1 += h1;
+    h2 += h2;
+    h3 += h3;
+    h4 += h4;
+    h5 += h5;
+    h6 += h6;
+    h7 += h7;
+    h8 += h8;
+    h9 += h9;
+    carry0 = (h0 + (int64_t) (1 << 25)) >> 26;
+    h1 += carry0;
+    h0 -= carry0 << 26;
+    carry4 = (h4 + (int64_t) (1 << 25)) >> 26;
+    h5 += carry4;
+    h4 -= carry4 << 26;
+    carry1 = (h1 + (int64_t) (1 << 24)) >> 25;
+    h2 += carry1;
+    h1 -= carry1 << 25;
+    carry5 = (h5 + (int64_t) (1 << 24)) >> 25;
+    h6 += carry5;
+    h5 -= carry5 << 25;
+    carry2 = (h2 + (int64_t) (1 << 25)) >> 26;
+    h3 += carry2;
+    h2 -= carry2 << 26;
+    carry6 = (h6 + (int64_t) (1 << 25)) >> 26;
+    h7 += carry6;
+    h6 -= carry6 << 26;
+    carry3 = (h3 + (int64_t) (1 << 24)) >> 25;
+    h4 += carry3;
+    h3 -= carry3 << 25;
+    carry7 = (h7 + (int64_t) (1 << 24)) >> 25;
+    h8 += carry7;
+    h7 -= carry7 << 25;
+    carry4 = (h4 + (int64_t) (1 << 25)) >> 26;
+    h5 += carry4;
+    h4 -= carry4 << 26;
+    carry8 = (h8 + (int64_t) (1 << 25)) >> 26;
+    h9 += carry8;
+    h8 -= carry8 << 26;
+    carry9 = (h9 + (int64_t) (1 << 24)) >> 25;
+    h0 += carry9 * 19;
+    h9 -= carry9 << 25;
+    carry0 = (h0 + (int64_t) (1 << 25)) >> 26;
+    h1 += carry0;
+    h0 -= carry0 << 26;
+    h[0] = (int32_t) h0;
+    h[1] = (int32_t) h1;
+    h[2] = (int32_t) h2;
+    h[3] = (int32_t) h3;
+    h[4] = (int32_t) h4;
+    h[5] = (int32_t) h5;
+    h[6] = (int32_t) h6;
+    h[7] = (int32_t) h7;
+    h[8] = (int32_t) h8;
+    h[9] = (int32_t) h9;
+}
+
+
+/*
+h = f - g
+Can overlap h with f or g.
+
+Preconditions:
+   |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+   |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+
+Postconditions:
+   |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+*/
+
+void fe_sub(fe h, const fe f, const fe g) {
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    int32_t g0 = g[0];
+    int32_t g1 = g[1];
+    int32_t g2 = g[2];
+    int32_t g3 = g[3];
+    int32_t g4 = g[4];
+    int32_t g5 = g[5];
+    int32_t g6 = g[6];
+    int32_t g7 = g[7];
+    int32_t g8 = g[8];
+    int32_t g9 = g[9];
+    int32_t h0 = f0 - g0;
+    int32_t h1 = f1 - g1;
+    int32_t h2 = f2 - g2;
+    int32_t h3 = f3 - g3;
+    int32_t h4 = f4 - g4;
+    int32_t h5 = f5 - g5;
+    int32_t h6 = f6 - g6;
+    int32_t h7 = f7 - g7;
+    int32_t h8 = f8 - g8;
+    int32_t h9 = f9 - g9;
+
+    h[0] = h0;
+    h[1] = h1;
+    h[2] = h2;
+    h[3] = h3;
+    h[4] = h4;
+    h[5] = h5;
+    h[6] = h6;
+    h[7] = h7;
+    h[8] = h8;
+    h[9] = h9;
+}
+
+
+
+/*
+Preconditions:
+  |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+
+Write p=2^255-19; q=floor(h/p).
+Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
+
+Proof:
+  Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
+  Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4.
+
+  Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
+  Then 0<y<1.
+
+  Write r=h-pq.
+  Have 0<=r<=p-1=2^255-20.
+  Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
+
+  Write x=r+19(2^-255)r+y.
+  Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
+
+  Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
+  so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
+*/
+
+void fe_tobytes(unsigned char *s, const fe h) {
+    int32_t h0 = h[0];
+    int32_t h1 = h[1];
+    int32_t h2 = h[2];
+    int32_t h3 = h[3];
+    int32_t h4 = h[4];
+    int32_t h5 = h[5];
+    int32_t h6 = h[6];
+    int32_t h7 = h[7];
+    int32_t h8 = h[8];
+    int32_t h9 = h[9];
+    int32_t q;
+    int32_t carry0;
+    int32_t carry1;
+    int32_t carry2;
+    int32_t carry3;
+    int32_t carry4;
+    int32_t carry5;
+    int32_t carry6;
+    int32_t carry7;
+    int32_t carry8;
+    int32_t carry9;
+    q = (19 * h9 + (((int32_t) 1) << 24)) >> 25;
+    q = (h0 + q) >> 26;
+    q = (h1 + q) >> 25;
+    q = (h2 + q) >> 26;
+    q = (h3 + q) >> 25;
+    q = (h4 + q) >> 26;
+    q = (h5 + q) >> 25;
+    q = (h6 + q) >> 26;
+    q = (h7 + q) >> 25;
+    q = (h8 + q) >> 26;
+    q = (h9 + q) >> 25;
+    /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
+    h0 += 19 * q;
+    /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
+    carry0 = h0 >> 26;
+    h1 += carry0;
+    h0 -= carry0 << 26;
+    carry1 = h1 >> 25;
+    h2 += carry1;
+    h1 -= carry1 << 25;
+    carry2 = h2 >> 26;
+    h3 += carry2;
+    h2 -= carry2 << 26;
+    carry3 = h3 >> 25;
+    h4 += carry3;
+    h3 -= carry3 << 25;
+    carry4 = h4 >> 26;
+    h5 += carry4;
+    h4 -= carry4 << 26;
+    carry5 = h5 >> 25;
+    h6 += carry5;
+    h5 -= carry5 << 25;
+    carry6 = h6 >> 26;
+    h7 += carry6;
+    h6 -= carry6 << 26;
+    carry7 = h7 >> 25;
+    h8 += carry7;
+    h7 -= carry7 << 25;
+    carry8 = h8 >> 26;
+    h9 += carry8;
+    h8 -= carry8 << 26;
+    carry9 = h9 >> 25;
+    h9 -= carry9 << 25;
+
+    /* h10 = carry9 */
+    /*
+    Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
+    Have h0+...+2^230 h9 between 0 and 2^255-1;
+    evidently 2^255 h10-2^255 q = 0.
+    Goal: Output h0+...+2^230 h9.
+    */
+    s[0] = (unsigned char) (h0 >> 0);
+    s[1] = (unsigned char) (h0 >> 8);
+    s[2] = (unsigned char) (h0 >> 16);
+    s[3] = (unsigned char) ((h0 >> 24) | (h1 << 2));
+    s[4] = (unsigned char) (h1 >> 6);
+    s[5] = (unsigned char) (h1 >> 14);
+    s[6] = (unsigned char) ((h1 >> 22) | (h2 << 3));
+    s[7] = (unsigned char) (h2 >> 5);
+    s[8] = (unsigned char) (h2 >> 13);
+    s[9] = (unsigned char) ((h2 >> 21) | (h3 << 5));
+    s[10] = (unsigned char) (h3 >> 3);
+    s[11] = (unsigned char) (h3 >> 11);
+    s[12] = (unsigned char) ((h3 >> 19) | (h4 << 6));
+    s[13] = (unsigned char) (h4 >> 2);
+    s[14] = (unsigned char) (h4 >> 10);
+    s[15] = (unsigned char) (h4 >> 18);
+    s[16] = (unsigned char) (h5 >> 0);
+    s[17] = (unsigned char) (h5 >> 8);
+    s[18] = (unsigned char) (h5 >> 16);
+    s[19] = (unsigned char) ((h5 >> 24) | (h6 << 1));
+    s[20] = (unsigned char) (h6 >> 7);
+    s[21] = (unsigned char) (h6 >> 15);
+    s[22] = (unsigned char) ((h6 >> 23) | (h7 << 3));
+    s[23] = (unsigned char) (h7 >> 5);
+    s[24] = (unsigned char) (h7 >> 13);
+    s[25] = (unsigned char) ((h7 >> 21) | (h8 << 4));
+    s[26] = (unsigned char) (h8 >> 4);
+    s[27] = (unsigned char) (h8 >> 12);
+    s[28] = (unsigned char) ((h8 >> 20) | (h9 << 6));
+    s[29] = (unsigned char) (h9 >> 2);
+    s[30] = (unsigned char) (h9 >> 10);
+    s[31] = (unsigned char) (h9 >> 18);
+}
diff --git a/3rd_party/ed25519/fe.h b/3rd_party/ed25519/fe.h
new file mode 100644
index 0000000..b4b62d2
--- /dev/null
+++ b/3rd_party/ed25519/fe.h
@@ -0,0 +1,41 @@
+#ifndef FE_H
+#define FE_H
+
+#include "fixedint.h"
+
+
+/*
+    fe means field element.
+    Here the field is \Z/(2^255-19).
+    An element t, entries t[0]...t[9], represents the integer
+    t[0]+2^26 t[1]+2^51 t[2]+2^77 t[3]+2^102 t[4]+...+2^230 t[9].
+    Bounds on each t[i] vary depending on context.
+*/
+
+
+typedef int32_t fe[10];
+
+
+void fe_0(fe h);
+void fe_1(fe h);
+
+void fe_frombytes(fe h, const unsigned char *s);
+void fe_tobytes(unsigned char *s, const fe h);
+
+void fe_copy(fe h, const fe f);
+int fe_isnegative(const fe f);
+int fe_isnonzero(const fe f);
+void fe_cmov(fe f, const fe g, unsigned int b);
+void fe_cswap(fe f, fe g, unsigned int b);
+
+void fe_neg(fe h, const fe f);
+void fe_add(fe h, const fe f, const fe g);
+void fe_invert(fe out, const fe z);
+void fe_sq(fe h, const fe f);
+void fe_sq2(fe h, const fe f);
+void fe_mul(fe h, const fe f, const fe g);
+void fe_mul121666(fe h, fe f);
+void fe_pow22523(fe out, const fe z);
+void fe_sub(fe h, const fe f, const fe g);
+
+#endif
diff --git a/3rd_party/ed25519/fixedint.h b/3rd_party/ed25519/fixedint.h
new file mode 100644
index 0000000..1a8745b
--- /dev/null
+++ b/3rd_party/ed25519/fixedint.h
@@ -0,0 +1,72 @@
+/*
+    Portable header to provide the 32 and 64 bits type.
+
+    Not a compatible replacement for <stdint.h>, do not blindly use it as such.
+*/
+
+#if ((defined(__STDC__) && __STDC__ && __STDC_VERSION__ >= 199901L) || (defined(__WATCOMC__) && (defined(_STDINT_H_INCLUDED) || __WATCOMC__ >= 1250)) || (defined(__GNUC__) && (defined(_STDINT_H) || defined(_STDINT_H_) || defined(__UINT_FAST64_TYPE__)) )) && !defined(FIXEDINT_H_INCLUDED)
+    #include <stdint.h>
+    #define FIXEDINT_H_INCLUDED
+
+    #if defined(__WATCOMC__) && __WATCOMC__ >= 1250 && !defined(UINT64_C)
+        #include <limits.h>
+        #define UINT64_C(x) (x + (UINT64_MAX - UINT64_MAX))
+    #endif
+#endif
+
+
+#ifndef FIXEDINT_H_INCLUDED
+    #define FIXEDINT_H_INCLUDED
+    
+    #include <limits.h>
+
+    /* (u)int32_t */
+    #ifndef uint32_t
+        #if (ULONG_MAX == 0xffffffffUL)
+            typedef unsigned long uint32_t;
+        #elif (UINT_MAX == 0xffffffffUL)
+            typedef unsigned int uint32_t;
+        #elif (USHRT_MAX == 0xffffffffUL)
+            typedef unsigned short uint32_t;
+        #endif
+    #endif
+
+
+    #ifndef int32_t
+        #if (LONG_MAX == 0x7fffffffL)
+            typedef signed long int32_t;
+        #elif (INT_MAX == 0x7fffffffL)
+            typedef signed int int32_t;
+        #elif (SHRT_MAX == 0x7fffffffL)
+            typedef signed short int32_t;
+        #endif
+    #endif
+
+
+    /* (u)int64_t */
+    #if (defined(__STDC__) && defined(__STDC_VERSION__) && __STDC__ && __STDC_VERSION__ >= 199901L)
+        typedef long long int64_t;
+        typedef unsigned long long uint64_t;
+
+        #define UINT64_C(v) v ##ULL
+        #define INT64_C(v) v ##LL
+    #elif defined(__GNUC__)
+        __extension__ typedef long long int64_t;
+        __extension__ typedef unsigned long long uint64_t;
+
+        #define UINT64_C(v) v ##ULL
+        #define INT64_C(v) v ##LL
+    #elif defined(__MWERKS__) || defined(__SUNPRO_C) || defined(__SUNPRO_CC) || defined(__APPLE_CC__) || defined(_LONG_LONG) || defined(_CRAYC)
+        typedef long long int64_t;
+        typedef unsigned long long uint64_t;
+
+        #define UINT64_C(v) v ##ULL
+        #define INT64_C(v) v ##LL
+    #elif (defined(__WATCOMC__) && defined(__WATCOM_INT64__)) || (defined(_MSC_VER) && _INTEGRAL_MAX_BITS >= 64) || (defined(__BORLANDC__) && __BORLANDC__ > 0x460) || defined(__alpha) || defined(__DECC)
+        typedef __int64 int64_t;
+        typedef unsigned __int64 uint64_t;
+
+        #define UINT64_C(v) v ##UI64
+        #define INT64_C(v) v ##I64
+    #endif
+#endif
diff --git a/3rd_party/ed25519/ge.c b/3rd_party/ed25519/ge.c
new file mode 100644
index 0000000..87c691b
--- /dev/null
+++ b/3rd_party/ed25519/ge.c
@@ -0,0 +1,467 @@
+#include "ge.h"
+#include "precomp_data.h"
+
+
+/*
+r = p + q
+*/
+
+void ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) {
+    fe t0;
+    fe_add(r->X, p->Y, p->X);
+    fe_sub(r->Y, p->Y, p->X);
+    fe_mul(r->Z, r->X, q->YplusX);
+    fe_mul(r->Y, r->Y, q->YminusX);
+    fe_mul(r->T, q->T2d, p->T);
+    fe_mul(r->X, p->Z, q->Z);
+    fe_add(t0, r->X, r->X);
+    fe_sub(r->X, r->Z, r->Y);
+    fe_add(r->Y, r->Z, r->Y);
+    fe_add(r->Z, t0, r->T);
+    fe_sub(r->T, t0, r->T);
+}
+
+
+static void slide(signed char *r, const unsigned char *a) {
+    int i;
+    int b;
+    int k;
+
+    for (i = 0; i < 256; ++i) {
+        r[i] = 1 & (a[i >> 3] >> (i & 7));
+    }
+
+    for (i = 0; i < 256; ++i)
+        if (r[i]) {
+            for (b = 1; b <= 6 && i + b < 256; ++b) {
+                if (r[i + b]) {
+                    if (r[i] + (r[i + b] << b) <= 15) {
+                        r[i] += r[i + b] << b;
+                        r[i + b] = 0;
+                    } else if (r[i] - (r[i + b] << b) >= -15) {
+                        r[i] -= r[i + b] << b;
+
+                        for (k = i + b; k < 256; ++k) {
+                            if (!r[k]) {
+                                r[k] = 1;
+                                break;
+                            }
+
+                            r[k] = 0;
+                        }
+                    } else {
+                        break;
+                    }
+                }
+            }
+        }
+}
+
+/*
+r = a * A + b * B
+where a = a[0]+256*a[1]+...+256^31 a[31].
+and b = b[0]+256*b[1]+...+256^31 b[31].
+B is the Ed25519 base point (x,4/5) with x positive.
+*/
+
+void ge_double_scalarmult_vartime(ge_p2 *r, const unsigned char *a, const ge_p3 *A, const unsigned char *b) {
+    signed char aslide[256];
+    signed char bslide[256];
+    ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */
+    ge_p1p1 t;
+    ge_p3 u;
+    ge_p3 A2;
+    int i;
+    slide(aslide, a);
+    slide(bslide, b);
+    ge_p3_to_cached(&Ai[0], A);
+    ge_p3_dbl(&t, A);
+    ge_p1p1_to_p3(&A2, &t);
+    ge_add(&t, &A2, &Ai[0]);
+    ge_p1p1_to_p3(&u, &t);
+    ge_p3_to_cached(&Ai[1], &u);
+    ge_add(&t, &A2, &Ai[1]);
+    ge_p1p1_to_p3(&u, &t);
+    ge_p3_to_cached(&Ai[2], &u);
+    ge_add(&t, &A2, &Ai[2]);
+    ge_p1p1_to_p3(&u, &t);
+    ge_p3_to_cached(&Ai[3], &u);
+    ge_add(&t, &A2, &Ai[3]);
+    ge_p1p1_to_p3(&u, &t);
+    ge_p3_to_cached(&Ai[4], &u);
+    ge_add(&t, &A2, &Ai[4]);
+    ge_p1p1_to_p3(&u, &t);
+    ge_p3_to_cached(&Ai[5], &u);
+    ge_add(&t, &A2, &Ai[5]);
+    ge_p1p1_to_p3(&u, &t);
+    ge_p3_to_cached(&Ai[6], &u);
+    ge_add(&t, &A2, &Ai[6]);
+    ge_p1p1_to_p3(&u, &t);
+    ge_p3_to_cached(&Ai[7], &u);
+    ge_p2_0(r);
+
+    for (i = 255; i >= 0; --i) {
+        if (aslide[i] || bslide[i]) {
+            break;
+        }
+    }
+
+    for (; i >= 0; --i) {
+        ge_p2_dbl(&t, r);
+
+        if (aslide[i] > 0) {
+            ge_p1p1_to_p3(&u, &t);
+            ge_add(&t, &u, &Ai[aslide[i] / 2]);
+        } else if (aslide[i] < 0) {
+            ge_p1p1_to_p3(&u, &t);
+            ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]);
+        }
+
+        if (bslide[i] > 0) {
+            ge_p1p1_to_p3(&u, &t);
+            ge_madd(&t, &u, &Bi[bslide[i] / 2]);
+        } else if (bslide[i] < 0) {
+            ge_p1p1_to_p3(&u, &t);
+            ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]);
+        }
+
+        ge_p1p1_to_p2(r, &t);
+    }
+}
+
+
+static const fe d = {
+    -10913610, 13857413, -15372611, 6949391, 114729, -8787816, -6275908, -3247719, -18696448, -12055116
+};
+
+static const fe sqrtm1 = {
+    -32595792, -7943725, 9377950, 3500415, 12389472, -272473, -25146209, -2005654, 326686, 11406482
+};
+
+int ge_frombytes_negate_vartime(ge_p3 *h, const unsigned char *s) {
+    fe u;
+    fe v;
+    fe v3;
+    fe vxx;
+    fe check;
+    fe_frombytes(h->Y, s);
+    fe_1(h->Z);
+    fe_sq(u, h->Y);
+    fe_mul(v, u, d);
+    fe_sub(u, u, h->Z);     /* u = y^2-1 */
+    fe_add(v, v, h->Z);     /* v = dy^2+1 */
+    fe_sq(v3, v);
+    fe_mul(v3, v3, v);      /* v3 = v^3 */
+    fe_sq(h->X, v3);
+    fe_mul(h->X, h->X, v);
+    fe_mul(h->X, h->X, u);  /* x = uv^7 */
+    fe_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */
+    fe_mul(h->X, h->X, v3);
+    fe_mul(h->X, h->X, u);  /* x = uv^3(uv^7)^((q-5)/8) */
+    fe_sq(vxx, h->X);
+    fe_mul(vxx, vxx, v);
+    fe_sub(check, vxx, u);  /* vx^2-u */
+
+    if (fe_isnonzero(check)) {
+        fe_add(check, vxx, u); /* vx^2+u */
+
+        if (fe_isnonzero(check)) {
+            return -1;
+        }
+
+        fe_mul(h->X, h->X, sqrtm1);
+    }
+
+    if (fe_isnegative(h->X) == (s[31] >> 7)) {
+        fe_neg(h->X, h->X);
+    }
+
+    fe_mul(h->T, h->X, h->Y);
+    return 0;
+}
+
+
+/*
+r = p + q
+*/
+
+void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) {
+    fe t0;
+    fe_add(r->X, p->Y, p->X);
+    fe_sub(r->Y, p->Y, p->X);
+    fe_mul(r->Z, r->X, q->yplusx);
+    fe_mul(r->Y, r->Y, q->yminusx);
+    fe_mul(r->T, q->xy2d, p->T);
+    fe_add(t0, p->Z, p->Z);
+    fe_sub(r->X, r->Z, r->Y);
+    fe_add(r->Y, r->Z, r->Y);
+    fe_add(r->Z, t0, r->T);
+    fe_sub(r->T, t0, r->T);
+}
+
+
+/*
+r = p - q
+*/
+
+void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) {
+    fe t0;
+
+    fe_add(r->X, p->Y, p->X);
+    fe_sub(r->Y, p->Y, p->X);
+    fe_mul(r->Z, r->X, q->yminusx);
+    fe_mul(r->Y, r->Y, q->yplusx);
+    fe_mul(r->T, q->xy2d, p->T);
+    fe_add(t0, p->Z, p->Z);
+    fe_sub(r->X, r->Z, r->Y);
+    fe_add(r->Y, r->Z, r->Y);
+    fe_sub(r->Z, t0, r->T);
+    fe_add(r->T, t0, r->T);
+}
+
+
+/*
+r = p
+*/
+
+void ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p) {
+    fe_mul(r->X, p->X, p->T);
+    fe_mul(r->Y, p->Y, p->Z);
+    fe_mul(r->Z, p->Z, p->T);
+}
+
+
+
+/*
+r = p
+*/
+
+void ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p) {
+    fe_mul(r->X, p->X, p->T);
+    fe_mul(r->Y, p->Y, p->Z);
+    fe_mul(r->Z, p->Z, p->T);
+    fe_mul(r->T, p->X, p->Y);
+}
+
+
+void ge_p2_0(ge_p2 *h) {
+    fe_0(h->X);
+    fe_1(h->Y);
+    fe_1(h->Z);
+}
+
+
+
+/*
+r = 2 * p
+*/
+
+void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p) {
+    fe t0;
+
+    fe_sq(r->X, p->X);
+    fe_sq(r->Z, p->Y);
+    fe_sq2(r->T, p->Z);
+    fe_add(r->Y, p->X, p->Y);
+    fe_sq(t0, r->Y);
+    fe_add(r->Y, r->Z, r->X);
+    fe_sub(r->Z, r->Z, r->X);
+    fe_sub(r->X, t0, r->Y);
+    fe_sub(r->T, r->T, r->Z);
+}
+
+
+void ge_p3_0(ge_p3 *h) {
+    fe_0(h->X);
+    fe_1(h->Y);
+    fe_1(h->Z);
+    fe_0(h->T);
+}
+
+
+/*
+r = 2 * p
+*/
+
+void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p) {
+    ge_p2 q;
+    ge_p3_to_p2(&q, p);
+    ge_p2_dbl(r, &q);
+}
+
+
+
+/*
+r = p
+*/
+
+static const fe d2 = {
+    -21827239, -5839606, -30745221, 13898782, 229458, 15978800, -12551817, -6495438, 29715968, 9444199
+};
+
+void ge_p3_to_cached(ge_cached *r, const ge_p3 *p) {
+    fe_add(r->YplusX, p->Y, p->X);
+    fe_sub(r->YminusX, p->Y, p->X);
+    fe_copy(r->Z, p->Z);
+    fe_mul(r->T2d, p->T, d2);
+}
+
+
+/*
+r = p
+*/
+
+void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p) {
+    fe_copy(r->X, p->X);
+    fe_copy(r->Y, p->Y);
+    fe_copy(r->Z, p->Z);
+}
+
+
+void ge_p3_tobytes(unsigned char *s, const ge_p3 *h) {
+    fe recip;
+    fe x;
+    fe y;
+    fe_invert(recip, h->Z);
+    fe_mul(x, h->X, recip);
+    fe_mul(y, h->Y, recip);
+    fe_tobytes(s, y);
+    s[31] ^= fe_isnegative(x) << 7;
+}
+
+
+static unsigned char equal(signed char b, signed char c) {
+    unsigned char ub = b;
+    unsigned char uc = c;
+    unsigned char x = ub ^ uc; /* 0: yes; 1..255: no */
+    uint64_t y = x; /* 0: yes; 1..255: no */
+    y -= 1; /* large: yes; 0..254: no */
+    y >>= 63; /* 1: yes; 0: no */
+    return (unsigned char) y;
+}
+
+static unsigned char negative(signed char b) {
+    uint64_t x = b; /* 18446744073709551361..18446744073709551615: yes; 0..255: no */
+    x >>= 63; /* 1: yes; 0: no */
+    return (unsigned char) x;
+}
+
+static void cmov(ge_precomp *t, const ge_precomp *u, unsigned char b) {
+    fe_cmov(t->yplusx, u->yplusx, b);
+    fe_cmov(t->yminusx, u->yminusx, b);
+    fe_cmov(t->xy2d, u->xy2d, b);
+}
+
+
+static void select(ge_precomp *t, int pos, signed char b) {
+    ge_precomp minust;
+    unsigned char bnegative = negative(b);
+    unsigned char babs = b - (((-bnegative) & b) << 1);
+    fe_1(t->yplusx);
+    fe_1(t->yminusx);
+    fe_0(t->xy2d);
+    cmov(t, &base[pos][0], equal(babs, 1));
+    cmov(t, &base[pos][1], equal(babs, 2));
+    cmov(t, &base[pos][2], equal(babs, 3));
+    cmov(t, &base[pos][3], equal(babs, 4));
+    cmov(t, &base[pos][4], equal(babs, 5));
+    cmov(t, &base[pos][5], equal(babs, 6));
+    cmov(t, &base[pos][6], equal(babs, 7));
+    cmov(t, &base[pos][7], equal(babs, 8));
+    fe_copy(minust.yplusx, t->yminusx);
+    fe_copy(minust.yminusx, t->yplusx);
+    fe_neg(minust.xy2d, t->xy2d);
+    cmov(t, &minust, bnegative);
+}
+
+/*
+h = a * B
+where a = a[0]+256*a[1]+...+256^31 a[31]
+B is the Ed25519 base point (x,4/5) with x positive.
+
+Preconditions:
+  a[31] <= 127
+*/
+
+void ge_scalarmult_base(ge_p3 *h, const unsigned char *a) {
+    signed char e[64];
+    signed char carry;
+    ge_p1p1 r;
+    ge_p2 s;
+    ge_precomp t;
+    int i;
+
+    for (i = 0; i < 32; ++i) {
+        e[2 * i + 0] = (a[i] >> 0) & 15;
+        e[2 * i + 1] = (a[i] >> 4) & 15;
+    }
+
+    /* each e[i] is between 0 and 15 */
+    /* e[63] is between 0 and 7 */
+    carry = 0;
+
+    for (i = 0; i < 63; ++i) {
+        e[i] += carry;
+        carry = e[i] + 8;
+        carry >>= 4;
+        e[i] -= carry << 4;
+    }
+
+    e[63] += carry;
+    /* each e[i] is between -8 and 8 */
+    ge_p3_0(h);
+
+    for (i = 1; i < 64; i += 2) {
+        select(&t, i / 2, e[i]);
+        ge_madd(&r, h, &t);
+        ge_p1p1_to_p3(h, &r);
+    }
+
+    ge_p3_dbl(&r, h);
+    ge_p1p1_to_p2(&s, &r);
+    ge_p2_dbl(&r, &s);
+    ge_p1p1_to_p2(&s, &r);
+    ge_p2_dbl(&r, &s);
+    ge_p1p1_to_p2(&s, &r);
+    ge_p2_dbl(&r, &s);
+    ge_p1p1_to_p3(h, &r);
+
+    for (i = 0; i < 64; i += 2) {
+        select(&t, i / 2, e[i]);
+        ge_madd(&r, h, &t);
+        ge_p1p1_to_p3(h, &r);
+    }
+}
+
+
+/*
+r = p - q
+*/
+
+void ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) {
+    fe t0;
+    
+    fe_add(r->X, p->Y, p->X);
+    fe_sub(r->Y, p->Y, p->X);
+    fe_mul(r->Z, r->X, q->YminusX);
+    fe_mul(r->Y, r->Y, q->YplusX);
+    fe_mul(r->T, q->T2d, p->T);
+    fe_mul(r->X, p->Z, q->Z);
+    fe_add(t0, r->X, r->X);
+    fe_sub(r->X, r->Z, r->Y);
+    fe_add(r->Y, r->Z, r->Y);
+    fe_sub(r->Z, t0, r->T);
+    fe_add(r->T, t0, r->T);
+}
+
+
+void ge_tobytes(unsigned char *s, const ge_p2 *h) {
+    fe recip;
+    fe x;
+    fe y;
+    fe_invert(recip, h->Z);
+    fe_mul(x, h->X, recip);
+    fe_mul(y, h->Y, recip);
+    fe_tobytes(s, y);
+    s[31] ^= fe_isnegative(x) << 7;
+}
diff --git a/3rd_party/ed25519/ge.h b/3rd_party/ed25519/ge.h
new file mode 100644
index 0000000..17fde2d
--- /dev/null
+++ b/3rd_party/ed25519/ge.h
@@ -0,0 +1,74 @@
+#ifndef GE_H
+#define GE_H
+
+#include "fe.h"
+
+
+/*
+ge means group element.
+
+Here the group is the set of pairs (x,y) of field elements (see fe.h)
+satisfying -x^2 + y^2 = 1 + d x^2y^2
+where d = -121665/121666.
+
+Representations:
+  ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z
+  ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT
+  ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T
+  ge_precomp (Duif): (y+x,y-x,2dxy)
+*/
+
+typedef struct {
+  fe X;
+  fe Y;
+  fe Z;
+} ge_p2;
+
+typedef struct {
+  fe X;
+  fe Y;
+  fe Z;
+  fe T;
+} ge_p3;
+
+typedef struct {
+  fe X;
+  fe Y;
+  fe Z;
+  fe T;
+} ge_p1p1;
+
+typedef struct {
+  fe yplusx;
+  fe yminusx;
+  fe xy2d;
+} ge_precomp;
+
+typedef struct {
+  fe YplusX;
+  fe YminusX;
+  fe Z;
+  fe T2d;
+} ge_cached;
+
+void ge_p3_tobytes(unsigned char *s, const ge_p3 *h);
+void ge_tobytes(unsigned char *s, const ge_p2 *h);
+int ge_frombytes_negate_vartime(ge_p3 *h, const unsigned char *s);
+
+void ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q);
+void ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q);
+void ge_double_scalarmult_vartime(ge_p2 *r, const unsigned char *a, const ge_p3 *A, const unsigned char *b);
+void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q);
+void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q);
+void ge_scalarmult_base(ge_p3 *h, const unsigned char *a);
+
+void ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p);
+void ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p);
+void ge_p2_0(ge_p2 *h);
+void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p);
+void ge_p3_0(ge_p3 *h);
+void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p);
+void ge_p3_to_cached(ge_cached *r, const ge_p3 *p);
+void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p);
+
+#endif
diff --git a/3rd_party/ed25519/key_exchange.c b/3rd_party/ed25519/key_exchange.c
new file mode 100644
index 0000000..abd75da
--- /dev/null
+++ b/3rd_party/ed25519/key_exchange.c
@@ -0,0 +1,79 @@
+#include "ed25519.h"
+#include "fe.h"
+
+void ed25519_key_exchange(unsigned char *shared_secret, const unsigned char *public_key, const unsigned char *private_key) {
+    unsigned char e[32];
+    unsigned int i;
+    
+    fe x1;
+    fe x2;
+    fe z2;
+    fe x3;
+    fe z3;
+    fe tmp0;
+    fe tmp1;
+
+    int pos;
+    unsigned int swap;
+    unsigned int b;
+
+    /* copy the private key and make sure it's valid */
+    for (i = 0; i < 32; ++i) {
+        e[i] = private_key[i];
+    }
+
+    e[0] &= 248;
+    e[31] &= 63;
+    e[31] |= 64;
+
+    /* unpack the public key and convert edwards to montgomery */
+    /* due to CodesInChaos: montgomeryX = (edwardsY + 1)*inverse(1 - edwardsY) mod p */
+    fe_frombytes(x1, public_key);
+    fe_1(tmp1);
+    fe_add(tmp0, x1, tmp1);
+    fe_sub(tmp1, tmp1, x1);
+    fe_invert(tmp1, tmp1);
+    fe_mul(x1, tmp0, tmp1);
+
+    fe_1(x2);
+    fe_0(z2);
+    fe_copy(x3, x1);
+    fe_1(z3);
+
+    swap = 0;
+    for (pos = 254; pos >= 0; --pos) {
+        b = e[pos / 8] >> (pos & 7);
+        b &= 1;
+        swap ^= b;
+        fe_cswap(x2, x3, swap);
+        fe_cswap(z2, z3, swap);
+        swap = b;
+
+        /* from montgomery.h */
+        fe_sub(tmp0, x3, z3);
+        fe_sub(tmp1, x2, z2);
+        fe_add(x2, x2, z2);
+        fe_add(z2, x3, z3);
+        fe_mul(z3, tmp0, x2);
+        fe_mul(z2, z2, tmp1);
+        fe_sq(tmp0, tmp1);
+        fe_sq(tmp1, x2);
+        fe_add(x3, z3, z2);
+        fe_sub(z2, z3, z2);
+        fe_mul(x2, tmp1, tmp0);
+        fe_sub(tmp1, tmp1, tmp0);
+        fe_sq(z2, z2);
+        fe_mul121666(z3, tmp1);
+        fe_sq(x3, x3);
+        fe_add(tmp0, tmp0, z3);
+        fe_mul(z3, x1, z2);
+        fe_mul(z2, tmp1, tmp0);
+    }
+
+    fe_cswap(x2, x3, swap);
+    fe_cswap(z2, z3, swap);
+
+    fe_invert(z2, z2);
+    fe_mul(x2, x2, z2);
+    fe_tobytes(shared_secret, x2);
+}
diff --git a/3rd_party/ed25519/keypair.c b/3rd_party/ed25519/keypair.c
new file mode 100644
index 0000000..dc1b8ec
--- /dev/null
+++ b/3rd_party/ed25519/keypair.c
@@ -0,0 +1,16 @@
+#include "ed25519.h"
+#include "sha512.h"
+#include "ge.h"
+
+
+void ed25519_create_keypair(unsigned char *public_key, unsigned char *private_key, const unsigned char *seed) {
+    ge_p3 A;
+
+    sha512(seed, 32, private_key);
+    private_key[0] &= 248;
+    private_key[31] &= 63;
+    private_key[31] |= 64;
+
+    ge_scalarmult_base(&A, private_key);
+    ge_p3_tobytes(public_key, &A);
+}
diff --git a/3rd_party/ed25519/precomp_data.h b/3rd_party/ed25519/precomp_data.h
new file mode 100644
index 0000000..ff23986
--- /dev/null
+++ b/3rd_party/ed25519/precomp_data.h
@@ -0,0 +1,1391 @@
+static const ge_precomp Bi[8] = {
+    {
+        { 25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, -11754271, -6079156, 2047605 },
+        { -12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, 5043384, 19500929, -15469378 },
+        { -8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, 11864899, -24514362, -4438546 },
+    },
+    {
+        { 15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, -14772189, 28944400, -1550024 },
+        { 16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, -11775962, 7689662, 11199574 },
+        { 30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, 10017326, -17749093, -9920357 },
+    },
+    {
+        { 10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, 14515107, -15438304, 10819380 },
+        { 4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, 12483688, -12668491, 5581306 },
+        { 19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, 13850243, -23678021, -15815942 },
+    },
+    {
+        { 5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, 5230134, -23952439, -15175766 },
+        { -30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, 16520125, 30598449, 7715701 },
+        { 28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, 1370708, 29794553, -1409300 },
+    },
+    {
+        { -22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211, -1361450, -13062696, 13821877 },
+        { -6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028, -7212327, 18853322, -14220951 },
+        { 4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358, -10431137, 2207753, -3209784 },
+    },
+    {
+        { -25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364, -663000, -31111463, -16132436 },
+        { 25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789, 15725684, 171356, 6466918 },
+        { 23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339, -14088058, -30714912, 16193877 },
+    },
+    {
+        { -33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398, 4729455, -18074513, 9256800 },
+        { -25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405, 9761698, -19827198, 630305 },
+        { -13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551, -15960994, -2449256, -14291300 },
+    },
+    {
+        { -3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575, 15033784, 25105118, -7894876 },
+        { -24326370, 15950226, -31801215, -14592823, -11662737, -5090925, 1573892, -2625887, 2198790, -15804619 },
+        { -3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022, -16236442, -32461234, -12290683 },
+    },
+};
+
+
+/* base[i][j] = (j+1)*256^i*B */
+static const ge_precomp base[32][8] = {
+    {
+        {
+            { 25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, -11754271, -6079156, 2047605 },
+            { -12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, 5043384, 19500929, -15469378 },
+            { -8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, 11864899, -24514362, -4438546 },
+        },
+        {
+            { -12815894, -12976347, -21581243, 11784320, -25355658, -2750717, -11717903, -3814571, -358445, -10211303 },
+            { -21703237, 6903825, 27185491, 6451973, -29577724, -9554005, -15616551, 11189268, -26829678, -5319081 },
+            { 26966642, 11152617, 32442495, 15396054, 14353839, -12752335, -3128826, -9541118, -15472047, -4166697 },
+        },
+        {
+            { 15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, -14772189, 28944400, -1550024 },
+            { 16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, -11775962, 7689662, 11199574 },
+            { 30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, 10017326, -17749093, -9920357 },
+        },
+        {
+            { -17036878, 13921892, 10945806, -6033431, 27105052, -16084379, -28926210, 15006023, 3284568, -6276540 },
+            { 23599295, -8306047, -11193664, -7687416, 13236774, 10506355, 7464579, 9656445, 13059162, 10374397 },
+            { 7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664, -3839045, -641708, -101325 },
+        },
+        {
+            { 10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, 14515107, -15438304, 10819380 },
+            { 4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, 12483688, -12668491, 5581306 },
+            { 19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, 13850243, -23678021, -15815942 },
+        },
+        {
+            { -15371964, -12862754, 32573250, 4720197, -26436522, 5875511, -19188627, -15224819, -9818940, -12085777 },
+            { -8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240, -15689887, 1762328, 14866737 },
+            { -18199695, -15951423, -10473290, 1707278, -17185920, 3916101, -28236412, 3959421, 27914454, 4383652 },
+        },
+        {
+            { 5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, 5230134, -23952439, -15175766 },
+            { -30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, 16520125, 30598449, 7715701 },
+            { 28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, 1370708, 29794553, -1409300 },
+        },
+        {
+            { 14499471, -2729599, -33191113, -4254652, 28494862, 14271267, 30290735, 10876454, -33154098, 2381726 },
+            { -7195431, -2655363, -14730155, 462251, -27724326, 3941372, -6236617, 3696005, -32300832, 15351955 },
+            { 27431194, 8222322, 16448760, -3907995, -18707002, 11938355, -32961401, -2970515, 29551813, 10109425 },
+        },
+    },
+    {
+        {
+            { -13657040, -13155431, -31283750, 11777098, 21447386, 6519384, -2378284, -1627556, 10092783, -4764171 },
+            { 27939166, 14210322, 4677035, 16277044, -22964462, -12398139, -32508754, 12005538, -17810127, 12803510 },
+            { 17228999, -15661624, -1233527, 300140, -1224870, -11714777, 30364213, -9038194, 18016357, 4397660 },
+        },
+        {
+            { -10958843, -7690207, 4776341, -14954238, 27850028, -15602212, -26619106, 14544525, -17477504, 982639 },
+            { 29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899, -4120128, -21047696, 9934963 },
+            { 5793303, 16271923, -24131614, -10116404, 29188560, 1206517, -14747930, 4559895, -30123922, -10897950 },
+        },
+        {
+            { -27643952, -11493006, 16282657, -11036493, 28414021, -15012264, 24191034, 4541697, -13338309, 5500568 },
+            { 12650548, -1497113, 9052871, 11355358, -17680037, -8400164, -17430592, 12264343, 10874051, 13524335 },
+            { 25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038, 5080568, -22528059, 5376628 },
+        },
+        {
+            { -26088264, -4011052, -17013699, -3537628, -6726793, 1920897, -22321305, -9447443, 4535768, 1569007 },
+            { -2255422, 14606630, -21692440, -8039818, 28430649, 8775819, -30494562, 3044290, 31848280, 12543772 },
+            { -22028579, 2943893, -31857513, 6777306, 13784462, -4292203, -27377195, -2062731, 7718482, 14474653 },
+        },
+        {
+            { 2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965, -7236665, 24316168, -5253567 },
+            { 13741529, 10911568, -33233417, -8603737, -20177830, -1033297, 33040651, -13424532, -20729456, 8321686 },
+            { 21060490, -2212744, 15712757, -4336099, 1639040, 10656336, 23845965, -11874838, -9984458, 608372 },
+        },
+        {
+            { -13672732, -15087586, -10889693, -7557059, -6036909, 11305547, 1123968, -6780577, 27229399, 23887 },
+            { -23244140, -294205, -11744728, 14712571, -29465699, -2029617, 12797024, -6440308, -1633405, 16678954 },
+            { -29500620, 4770662, -16054387, 14001338, 7830047, 9564805, -1508144, -4795045, -17169265, 4904953 },
+        },
+        {
+            { 24059557, 14617003, 19037157, -15039908, 19766093, -14906429, 5169211, 16191880, 2128236, -4326833 },
+            { -16981152, 4124966, -8540610, -10653797, 30336522, -14105247, -29806336, 916033, -6882542, -2986532 },
+            { -22630907, 12419372, -7134229, -7473371, -16478904, 16739175, 285431, 2763829, 15736322, 4143876 },
+        },
+        {
+            { 2379352, 11839345, -4110402, -5988665, 11274298, 794957, 212801, -14594663, 23527084, -16458268 },
+            { 33431127, -11130478, -17838966, -15626900, 8909499, 8376530, -32625340, 4087881, -15188911, -14416214 },
+            { 1767683, 7197987, -13205226, -2022635, -13091350, 448826, 5799055, 4357868, -4774191, -16323038 },
+        },
+    },
+    {
+        {
+            { 6721966, 13833823, -23523388, -1551314, 26354293, -11863321, 23365147, -3949732, 7390890, 2759800 },
+            { 4409041, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353, -4264057, 1244380, -12919645 },
+            { -4421239, 7169619, 4982368, -2957590, 30256825, -2777540, 14086413, 9208236, 15886429, 16489664 },
+        },
+        {
+            { 1996075, 10375649, 14346367, 13311202, -6874135, -16438411, -13693198, 398369, -30606455, -712933 },
+            { -25307465, 9795880, -2777414, 14878809, -33531835, 14780363, 13348553, 12076947, -30836462, 5113182 },
+            { -17770784, 11797796, 31950843, 13929123, -25888302, 12288344, -30341101, -7336386, 13847711, 5387222 },
+        },
+        {
+            { -18582163, -3416217, 17824843, -2340966, 22744343, -10442611, 8763061, 3617786, -19600662, 10370991 },
+            { 20246567, -14369378, 22358229, -543712, 18507283, -10413996, 14554437, -8746092, 32232924, 16763880 },
+            { 9648505, 10094563, 26416693, 14745928, -30374318, -6472621, 11094161, 15689506, 3140038, -16510092 },
+        },
+        {
+            { -16160072, 5472695, 31895588, 4744994, 8823515, 10365685, -27224800, 9448613, -28774454, 366295 },
+            { 19153450, 11523972, -11096490, -6503142, -24647631, 5420647, 28344573, 8041113, 719605, 11671788 },
+            { 8678025, 2694440, -6808014, 2517372, 4964326, 11152271, -15432916, -15266516, 27000813, -10195553 },
+        },
+        {
+            { -15157904, 7134312, 8639287, -2814877, -7235688, 10421742, 564065, 5336097, 6750977, -14521026 },
+            { 11836410, -3979488, 26297894, 16080799, 23455045, 15735944, 1695823, -8819122, 8169720, 16220347 },
+            { -18115838, 8653647, 17578566, -6092619, -8025777, -16012763, -11144307, -2627664, -5990708, -14166033 },
+        },
+        {
+            { -23308498, -10968312, 15213228, -10081214, -30853605, -11050004, 27884329, 2847284, 2655861, 1738395 },
+            { -27537433, -14253021, -25336301, -8002780, -9370762, 8129821, 21651608, -3239336, -19087449, -11005278 },
+            { 1533110, 3437855, 23735889, 459276, 29970501, 11335377, 26030092, 5821408, 10478196, 8544890 },
+        },
+        {
+            { 32173121, -16129311, 24896207, 3921497, 22579056, -3410854, 19270449, 12217473, 17789017, -3395995 },
+            { -30552961, -2228401, -15578829, -10147201, 13243889, 517024, 15479401, -3853233, 30460520, 1052596 },
+            { -11614875, 13323618, 32618793, 8175907, -15230173, 12596687, 27491595, -4612359, 3179268, -9478891 },
+        },
+        {
+            { 31947069, -14366651, -4640583, -15339921, -15125977, -6039709, -14756777, -16411740, 19072640, -9511060 },
+            { 11685058, 11822410, 3158003, -13952594, 33402194, -4165066, 5977896, -5215017, 473099, 5040608 },
+            { -20290863, 8198642, -27410132, 11602123, 1290375, -2799760, 28326862, 1721092, -19558642, -3131606 },
+        },
+    },
+    {
+        {
+            { 7881532, 10687937, 7578723, 7738378, -18951012, -2553952, 21820786, 8076149, -27868496, 11538389 },
+            { -19935666, 3899861, 18283497, -6801568, -15728660, -11249211, 8754525, 7446702, -5676054, 5797016 },
+            { -11295600, -3793569, -15782110, -7964573, 12708869, -8456199, 2014099, -9050574, -2369172, -5877341 },
+        },
+        {
+            { -22472376, -11568741, -27682020, 1146375, 18956691, 16640559, 1192730, -3714199, 15123619, 10811505 },
+            { 14352098, -3419715, -18942044, 10822655, 32750596, 4699007, -70363, 15776356, -28886779, -11974553 },
+            { -28241164, -8072475, -4978962, -5315317, 29416931, 1847569, -20654173, -16484855, 4714547, -9600655 },
+        },
+        {
+            { 15200332, 8368572, 19679101, 15970074, -31872674, 1959451, 24611599, -4543832, -11745876, 12340220 },
+            { 12876937, -10480056, 33134381, 6590940, -6307776, 14872440, 9613953, 8241152, 15370987, 9608631 },
+            { -4143277, -12014408, 8446281, -391603, 4407738, 13629032, -7724868, 15866074, -28210621, -8814099 },
+        },
+        {
+            { 26660628, -15677655, 8393734, 358047, -7401291, 992988, -23904233, 858697, 20571223, 8420556 },
+            { 14620715, 13067227, -15447274, 8264467, 14106269, 15080814, 33531827, 12516406, -21574435, -12476749 },
+            { 236881, 10476226, 57258, -14677024, 6472998, 2466984, 17258519, 7256740, 8791136, 15069930 },
+        },
+        {
+            { 1276410, -9371918, 22949635, -16322807, -23493039, -5702186, 14711875, 4874229, -30663140, -2331391 },
+            { 5855666, 4990204, -13711848, 7294284, -7804282, 1924647, -1423175, -7912378, -33069337, 9234253 },
+            { 20590503, -9018988, 31529744, -7352666, -2706834, 10650548, 31559055, -11609587, 18979186, 13396066 },
+        },
+        {
+            { 24474287, 4968103, 22267082, 4407354, 24063882, -8325180, -18816887, 13594782, 33514650, 7021958 },
+            { -11566906, -6565505, -21365085, 15928892, -26158305, 4315421, -25948728, -3916677, -21480480, 12868082 },
+            { -28635013, 13504661, 19988037, -2132761, 21078225, 6443208, -21446107, 2244500, -12455797, -8089383 },
+        },
+        {
+            { -30595528, 13793479, -5852820, 319136, -25723172, -6263899, 33086546, 8957937, -15233648, 5540521 },
+            { -11630176, -11503902, -8119500, -7643073, 2620056, 1022908, -23710744, -1568984, -16128528, -14962807 },
+            { 23152971, 775386, 27395463, 14006635, -9701118, 4649512, 1689819, 892185, -11513277, -15205948 },
+        },
+        {
+            { 9770129, 9586738, 26496094, 4324120, 1556511, -3550024, 27453819, 4763127, -19179614, 5867134 },
+            { -32765025, 1927590, 31726409, -4753295, 23962434, -16019500, 27846559, 5931263, -29749703, -16108455 },
+            { 27461885, -2977536, 22380810, 1815854, -23033753, -3031938, 7283490, -15148073, -19526700, 7734629 },
+        },
+    },
+    {
+        {
+            { -8010264, -9590817, -11120403, 6196038, 29344158, -13430885, 7585295, -3176626, 18549497, 15302069 },
+            { -32658337, -6171222, -7672793, -11051681, 6258878, 13504381, 10458790, -6418461, -8872242, 8424746 },
+            { 24687205, 8613276, -30667046, -3233545, 1863892, -1830544, 19206234, 7134917, -11284482, -828919 },
+        },
+        {
+            { 11334899, -9218022, 8025293, 12707519, 17523892, -10476071, 10243738, -14685461, -5066034, 16498837 },
+            { 8911542, 6887158, -9584260, -6958590, 11145641, -9543680, 17303925, -14124238, 6536641, 10543906 },
+            { -28946384, 15479763, -17466835, 568876, -1497683, 11223454, -2669190, -16625574, -27235709, 8876771 },
+        },
+        {
+            { -25742899, -12566864, -15649966, -846607, -33026686, -796288, -33481822, 15824474, -604426, -9039817 },
+            { 10330056, 70051, 7957388, -9002667, 9764902, 15609756, 27698697, -4890037, 1657394, 3084098 },
+            { 10477963, -7470260, 12119566, -13250805, 29016247, -5365589, 31280319, 14396151, -30233575, 15272409 },
+        },
+        {
+            { -12288309, 3169463, 28813183, 16658753, 25116432, -5630466, -25173957, -12636138, -25014757, 1950504 },
+            { -26180358, 9489187, 11053416, -14746161, -31053720, 5825630, -8384306, -8767532, 15341279, 8373727 },
+            { 28685821, 7759505, -14378516, -12002860, -31971820, 4079242, 298136, -10232602, -2878207, 15190420 },
+        },
+        {
+            { -32932876, 13806336, -14337485, -15794431, -24004620, 10940928, 8669718, 2742393, -26033313, -6875003 },
+            { -1580388, -11729417, -25979658, -11445023, -17411874, -10912854, 9291594, -16247779, -12154742, 6048605 },
+            { -30305315, 14843444, 1539301, 11864366, 20201677, 1900163, 13934231, 5128323, 11213262, 9168384 },
+        },
+        {
+            { -26280513, 11007847, 19408960, -940758, -18592965, -4328580, -5088060, -11105150, 20470157, -16398701 },
+            { -23136053, 9282192, 14855179, -15390078, -7362815, -14408560, -22783952, 14461608, 14042978, 5230683 },
+            { 29969567, -2741594, -16711867, -8552442, 9175486, -2468974, 21556951, 3506042, -5933891, -12449708 },
+        },
+        {
+            { -3144746, 8744661, 19704003, 4581278, -20430686, 6830683, -21284170, 8971513, -28539189, 15326563 },
+            { -19464629, 10110288, -17262528, -3503892, -23500387, 1355669, -15523050, 15300988, -20514118, 9168260 },
+            { -5353335, 4488613, -23803248, 16314347, 7780487, -15638939, -28948358, 9601605, 33087103, -9011387 },
+        },
+        {
+            { -19443170, -15512900, -20797467, -12445323, -29824447, 10229461, -27444329, -15000531, -5996870, 15664672 },
+            { 23294591, -16632613, -22650781, -8470978, 27844204, 11461195, 13099750, -2460356, 18151676, 13417686 },
+            { -24722913, -4176517, -31150679, 5988919, -26858785, 6685065, 1661597, -12551441, 15271676, -15452665 },
+        },
+    },
+    {
+        {
+            { 11433042, -13228665, 8239631, -5279517, -1985436, -725718, -18698764, 2167544, -6921301, -13440182 },
+            { -31436171, 15575146, 30436815, 12192228, -22463353, 9395379, -9917708, -8638997, 12215110, 12028277 },
+            { 14098400, 6555944, 23007258, 5757252, -15427832, -12950502, 30123440, 4617780, -16900089, -655628 },
+        },
+        {
+            { -4026201, -15240835, 11893168, 13718664, -14809462, 1847385, -15819999, 10154009, 23973261, -12684474 },
+            { -26531820, -3695990, -1908898, 2534301, -31870557, -16550355, 18341390, -11419951, 32013174, -10103539 },
+            { -25479301, 10876443, -11771086, -14625140, -12369567, 1838104, 21911214, 6354752, 4425632, -837822 },
+        },
+        {
+            { -10433389, -14612966, 22229858, -3091047, -13191166, 776729, -17415375, -12020462, 4725005, 14044970 },
+            { 19268650, -7304421, 1555349, 8692754, -21474059, -9910664, 6347390, -1411784, -19522291, -16109756 },
+            { -24864089, 12986008, -10898878, -5558584, -11312371, -148526, 19541418, 8180106, 9282262, 10282508 },
+        },
+        {
+            { -26205082, 4428547, -8661196, -13194263, 4098402, -14165257, 15522535, 8372215, 5542595, -10702683 },
+            { -10562541, 14895633, 26814552, -16673850, -17480754, -2489360, -2781891, 6993761, -18093885, 10114655 },
+            { -20107055, -929418, 31422704, 10427861, -7110749, 6150669, -29091755, -11529146, 25953725, -106158 },
+        },
+        {
+            { -4234397, -8039292, -9119125, 3046000, 2101609, -12607294, 19390020, 6094296, -3315279, 12831125 },
+            { -15998678, 7578152, 5310217, 14408357, -33548620, -224739, 31575954, 6326196, 7381791, -2421839 },
+            { -20902779, 3296811, 24736065, -16328389, 18374254, 7318640, 6295303, 8082724, -15362489, 12339664 },
+        },
+        {
+            { 27724736, 2291157, 6088201, -14184798, 1792727, 5857634, 13848414, 15768922, 25091167, 14856294 },
+            { -18866652, 8331043, 24373479, 8541013, -701998, -9269457, 12927300, -12695493, -22182473, -9012899 },
+            { -11423429, -5421590, 11632845, 3405020, 30536730, -11674039, -27260765, 13866390, 30146206, 9142070 },
+        },
+        {
+            { 3924129, -15307516, -13817122, -10054960, 12291820, -668366, -27702774, 9326384, -8237858, 4171294 },
+            { -15921940, 16037937, 6713787, 16606682, -21612135, 2790944, 26396185, 3731949, 345228, -5462949 },
+            { -21327538, 13448259, 25284571, 1143661, 20614966, -8849387, 2031539, -12391231, -16253183, -13582083 },
+        },
+        {
+            { 31016211, -16722429, 26371392, -14451233, -5027349, 14854137, 17477601, 3842657, 28012650, -16405420 },
+            { -5075835, 9368966, -8562079, -4600902, -15249953, 6970560, -9189873, 16292057, -8867157, 3507940 },
+            { 29439664, 3537914, 23333589, 6997794, -17555561, -11018068, -15209202, -15051267, -9164929, 6580396 },
+        },
+    },
+    {
+        {
+            { -12185861, -7679788, 16438269, 10826160, -8696817, -6235611, 17860444, -9273846, -2095802, 9304567 },
+            { 20714564, -4336911, 29088195, 7406487, 11426967, -5095705, 14792667, -14608617, 5289421, -477127 },
+            { -16665533, -10650790, -6160345, -13305760, 9192020, -1802462, 17271490, 12349094, 26939669, -3752294 },
+        },
+        {
+            { -12889898, 9373458, 31595848, 16374215, 21471720, 13221525, -27283495, -12348559, -3698806, 117887 },
+            { 22263325, -6560050, 3984570, -11174646, -15114008, -566785, 28311253, 5358056, -23319780, 541964 },
+            { 16259219, 3261970, 2309254, -15534474, -16885711, -4581916, 24134070, -16705829, -13337066, -13552195 },
+        },
+        {
+            { 9378160, -13140186, -22845982, -12745264, 28198281, -7244098, -2399684, -717351, 690426, 14876244 },
+            { 24977353, -314384, -8223969, -13465086, 28432343, -1176353, -13068804, -12297348, -22380984, 6618999 },
+            { -1538174, 11685646, 12944378, 13682314, -24389511, -14413193, 8044829, -13817328, 32239829, -5652762 },
+        },
+        {
+            { -18603066, 4762990, -926250, 8885304, -28412480, -3187315, 9781647, -10350059, 32779359, 5095274 },
+            { -33008130, -5214506, -32264887, -3685216, 9460461, -9327423, -24601656, 14506724, 21639561, -2630236 },
+            { -16400943, -13112215, 25239338, 15531969, 3987758, -4499318, -1289502, -6863535, 17874574, 558605 },
+        },
+        {
+            { -13600129, 10240081, 9171883, 16131053, -20869254, 9599700, 33499487, 5080151, 2085892, 5119761 },
+            { -22205145, -2519528, -16381601, 414691, -25019550, 2170430, 30634760, -8363614, -31999993, -5759884 },
+            { -6845704, 15791202, 8550074, -1312654, 29928809, -12092256, 27534430, -7192145, -22351378, 12961482 },
+        },
+        {
+            { -24492060, -9570771, 10368194, 11582341, -23397293, -2245287, 16533930, 8206996, -30194652, -5159638 },
+            { -11121496, -3382234, 2307366, 6362031, -135455, 8868177, -16835630, 7031275, 7589640, 8945490 },
+            { -32152748, 8917967, 6661220, -11677616, -1192060, -15793393, 7251489, -11182180, 24099109, -14456170 },
+        },
+        {
+            { 5019558, -7907470, 4244127, -14714356, -26933272, 6453165, -19118182, -13289025, -6231896, -10280736 },
+            { 10853594, 10721687, 26480089, 5861829, -22995819, 1972175, -1866647, -10557898, -3363451, -6441124 },
+            { -17002408, 5906790, 221599, -6563147, 7828208, -13248918, 24362661, -2008168, -13866408, 7421392 },
+        },
+        {
+            { 8139927, -6546497, 32257646, -5890546, 30375719, 1886181, -21175108, 15441252, 28826358, -4123029 },
+            { 6267086, 9695052, 7709135, -16603597, -32869068, -1886135, 14795160, -7840124, 13746021, -1742048 },
+            { 28584902, 7787108, -6732942, -15050729, 22846041, -7571236, -3181936, -363524, 4771362, -8419958 },
+        },
+    },
+    {
+        {
+            { 24949256, 6376279, -27466481, -8174608, -18646154, -9930606, 33543569, -12141695, 3569627, 11342593 },
+            { 26514989, 4740088, 27912651, 3697550, 19331575, -11472339, 6809886, 4608608, 7325975, -14801071 },
+            { -11618399, -14554430, -24321212, 7655128, -1369274, 5214312, -27400540, 10258390, -17646694, -8186692 },
+        },
+        {
+            { 11431204, 15823007, 26570245, 14329124, 18029990, 4796082, -31446179, 15580664, 9280358, -3973687 },
+            { -160783, -10326257, -22855316, -4304997, -20861367, -13621002, -32810901, -11181622, -15545091, 4387441 },
+            { -20799378, 12194512, 3937617, -5805892, -27154820, 9340370, -24513992, 8548137, 20617071, -7482001 },
+        },
+        {
+            { -938825, -3930586, -8714311, 16124718, 24603125, -6225393, -13775352, -11875822, 24345683, 10325460 },
+            { -19855277, -1568885, -22202708, 8714034, 14007766, 6928528, 16318175, -1010689, 4766743, 3552007 },
+            { -21751364, -16730916, 1351763, -803421, -4009670, 3950935, 3217514, 14481909, 10988822, -3994762 },
+        },
+        {
+            { 15564307, -14311570, 3101243, 5684148, 30446780, -8051356, 12677127, -6505343, -8295852, 13296005 },
+            { -9442290, 6624296, -30298964, -11913677, -4670981, -2057379, 31521204, 9614054, -30000824, 12074674 },
+            { 4771191, -135239, 14290749, -13089852, 27992298, 14998318, -1413936, -1556716, 29832613, -16391035 },
+        },
+        {
+            { 7064884, -7541174, -19161962, -5067537, -18891269, -2912736, 25825242, 5293297, -27122660, 13101590 },
+            { -2298563, 2439670, -7466610, 1719965, -27267541, -16328445, 32512469, -5317593, -30356070, -4190957 },
+            { -30006540, 10162316, -33180176, 3981723, -16482138, -13070044, 14413974, 9515896, 19568978, 9628812 },
+        },
+        {
+            { 33053803, 199357, 15894591, 1583059, 27380243, -4580435, -17838894, -6106839, -6291786, 3437740 },
+            { -18978877, 3884493, 19469877, 12726490, 15913552, 13614290, -22961733, 70104, 7463304, 4176122 },
+            { -27124001, 10659917, 11482427, -16070381, 12771467, -6635117, -32719404, -5322751, 24216882, 5944158 },
+        },
+        {
+            { 8894125, 7450974, -2664149, -9765752, -28080517, -12389115, 19345746, 14680796, 11632993, 5847885 },
+            { 26942781, -2315317, 9129564, -4906607, 26024105, 11769399, -11518837, 6367194, -9727230, 4782140 },
+            { 19916461, -4828410, -22910704, -11414391, 25606324, -5972441, 33253853, 8220911, 6358847, -1873857 },
+        },
+        {
+            { 801428, -2081702, 16569428, 11065167, 29875704, 96627, 7908388, -4480480, -13538503, 1387155 },
+            { 19646058, 5720633, -11416706, 12814209, 11607948, 12749789, 14147075, 15156355, -21866831, 11835260 },
+            { 19299512, 1155910, 28703737, 14890794, 2925026, 7269399, 26121523, 15467869, -26560550, 5052483 },
+        },
+    },
+    {
+        {
+            { -3017432, 10058206, 1980837, 3964243, 22160966, 12322533, -6431123, -12618185, 12228557, -7003677 },
+            { 32944382, 14922211, -22844894, 5188528, 21913450, -8719943, 4001465, 13238564, -6114803, 8653815 },
+            { 22865569, -4652735, 27603668, -12545395, 14348958, 8234005, 24808405, 5719875, 28483275, 2841751 },
+        },
+        {
+            { -16420968, -1113305, -327719, -12107856, 21886282, -15552774, -1887966, -315658, 19932058, -12739203 },
+            { -11656086, 10087521, -8864888, -5536143, -19278573, -3055912, 3999228, 13239134, -4777469, -13910208 },
+            { 1382174, -11694719, 17266790, 9194690, -13324356, 9720081, 20403944, 11284705, -14013818, 3093230 },
+        },
+        {
+            { 16650921, -11037932, -1064178, 1570629, -8329746, 7352753, -302424, 16271225, -24049421, -6691850 },
+            { -21911077, -5927941, -4611316, -5560156, -31744103, -10785293, 24123614, 15193618, -21652117, -16739389 },
+            { -9935934, -4289447, -25279823, 4372842, 2087473, 10399484, 31870908, 14690798, 17361620, 11864968 },
+        },
+        {
+            { -11307610, 6210372, 13206574, 5806320, -29017692, -13967200, -12331205, -7486601, -25578460, -16240689 },
+            { 14668462, -12270235, 26039039, 15305210, 25515617, 4542480, 10453892, 6577524, 9145645, -6443880 },
+            { 5974874, 3053895, -9433049, -10385191, -31865124, 3225009, -7972642, 3936128, -5652273, -3050304 },
+        },
+        {
+            { 30625386, -4729400, -25555961, -12792866, -20484575, 7695099, 17097188, -16303496, -27999779, 1803632 },
+            { -3553091, 9865099, -5228566, 4272701, -5673832, -16689700, 14911344, 12196514, -21405489, 7047412 },
+            { 20093277, 9920966, -11138194, -5343857, 13161587, 12044805, -32856851, 4124601, -32343828, -10257566 },
+        },
+        {
+            { -20788824, 14084654, -13531713, 7842147, 19119038, -13822605, 4752377, -8714640, -21679658, 2288038 },
+            { -26819236, -3283715, 29965059, 3039786, -14473765, 2540457, 29457502, 14625692, -24819617, 12570232 },
+            { -1063558, -11551823, 16920318, 12494842, 1278292, -5869109, -21159943, -3498680, -11974704, 4724943 },
+        },
+        {
+            { 17960970, -11775534, -4140968, -9702530, -8876562, -1410617, -12907383, -8659932, -29576300, 1903856 },
+            { 23134274, -14279132, -10681997, -1611936, 20684485, 15770816, -12989750, 3190296, 26955097, 14109738 },
+            { 15308788, 5320727, -30113809, -14318877, 22902008, 7767164, 29425325, -11277562, 31960942, 11934971 },
+        },
+        {
+            { -27395711, 8435796, 4109644, 12222639, -24627868, 14818669, 20638173, 4875028, 10491392, 1379718 },
+            { -13159415, 9197841, 3875503, -8936108, -1383712, -5879801, 33518459, 16176658, 21432314, 12180697 },
+            { -11787308, 11500838, 13787581, -13832590, -22430679, 10140205, 1465425, 12689540, -10301319, -13872883 },
+        },
+    },
+    {
+        {
+            { 5414091, -15386041, -21007664, 9643570, 12834970, 1186149, -2622916, -1342231, 26128231, 6032912 },
+            { -26337395, -13766162, 32496025, -13653919, 17847801, -12669156, 3604025, 8316894, -25875034, -10437358 },
+            { 3296484, 6223048, 24680646, -12246460, -23052020, 5903205, -8862297, -4639164, 12376617, 3188849 },
+        },
+        {
+            { 29190488, -14659046, 27549113, -1183516, 3520066, -10697301, 32049515, -7309113, -16109234, -9852307 },
+            { -14744486, -9309156, 735818, -598978, -20407687, -5057904, 25246078, -15795669, 18640741, -960977 },
+            { -6928835, -16430795, 10361374, 5642961, 4910474, 12345252, -31638386, -494430, 10530747, 1053335 },
+        },
+        {
+            { -29265967, -14186805, -13538216, -12117373, -19457059, -10655384, -31462369, -2948985, 24018831, 15026644 },
+            { -22592535, -3145277, -2289276, 5953843, -13440189, 9425631, 25310643, 13003497, -2314791, -15145616 },
+            { -27419985, -603321, -8043984, -1669117, -26092265, 13987819, -27297622, 187899, -23166419, -2531735 },
+        },
+        {
+            { -21744398, -13810475, 1844840, 5021428, -10434399, -15911473, 9716667, 16266922, -5070217, 726099 },
+            { 29370922, -6053998, 7334071, -15342259, 9385287, 2247707, -13661962, -4839461, 30007388, -15823341 },
+            { -936379, 16086691, 23751945, -543318, -1167538, -5189036, 9137109, 730663, 9835848, 4555336 },
+        },
+        {
+            { -23376435, 1410446, -22253753, -12899614, 30867635, 15826977, 17693930, 544696, -11985298, 12422646 },
+            { 31117226, -12215734, -13502838, 6561947, -9876867, -12757670, -5118685, -4096706, 29120153, 13924425 },
+            { -17400879, -14233209, 19675799, -2734756, -11006962, -5858820, -9383939, -11317700, 7240931, -237388 },
+        },
+        {
+            { -31361739, -11346780, -15007447, -5856218, -22453340, -12152771, 1222336, 4389483, 3293637, -15551743 },
+            { -16684801, -14444245, 11038544, 11054958, -13801175, -3338533, -24319580, 7733547, 12796905, -6335822 },
+            { -8759414, -10817836, -25418864, 10783769, -30615557, -9746811, -28253339, 3647836, 3222231, -11160462 },
+        },
+        {
+            { 18606113, 1693100, -25448386, -15170272, 4112353, 10045021, 23603893, -2048234, -7550776, 2484985 },
+            { 9255317, -3131197, -12156162, -1004256, 13098013, -9214866, 16377220, -2102812, -19802075, -3034702 },
+            { -22729289, 7496160, -5742199, 11329249, 19991973, -3347502, -31718148, 9936966, -30097688, -10618797 },
+        },
+        {
+            { 21878590, -5001297, 4338336, 13643897, -3036865, 13160960, 19708896, 5415497, -7360503, -4109293 },
+            { 27736861, 10103576, 12500508, 8502413, -3413016, -9633558, 10436918, -1550276, -23659143, -8132100 },
+            { 19492550, -12104365, -29681976, -852630, -3208171, 12403437, 30066266, 8367329, 13243957, 8709688 },
+        },
+    },
+    {
+        {
+            { 12015105, 2801261, 28198131, 10151021, 24818120, -4743133, -11194191, -5645734, 5150968, 7274186 },
+            { 2831366, -12492146, 1478975, 6122054, 23825128, -12733586, 31097299, 6083058, 31021603, -9793610 },
+            { -2529932, -2229646, 445613, 10720828, -13849527, -11505937, -23507731, 16354465, 15067285, -14147707 },
+        },
+        {
+            { 7840942, 14037873, -33364863, 15934016, -728213, -3642706, 21403988, 1057586, -19379462, -12403220 },
+            { 915865, -16469274, 15608285, -8789130, -24357026, 6060030, -17371319, 8410997, -7220461, 16527025 },
+            { 32922597, -556987, 20336074, -16184568, 10903705, -5384487, 16957574, 52992, 23834301, 6588044 },
+        },
+        {
+            { 32752030, 11232950, 3381995, -8714866, 22652988, -10744103, 17159699, 16689107, -20314580, -1305992 },
+            { -4689649, 9166776, -25710296, -10847306, 11576752, 12733943, 7924251, -2752281, 1976123, -7249027 },
+            { 21251222, 16309901, -2983015, -6783122, 30810597, 12967303, 156041, -3371252, 12331345, -8237197 },
+        },
+        {
+            { 8651614, -4477032, -16085636, -4996994, 13002507, 2950805, 29054427, -5106970, 10008136, -4667901 },
+            { 31486080, 15114593, -14261250, 12951354, 14369431, -7387845, 16347321, -13662089, 8684155, -10532952 },
+            { 19443825, 11385320, 24468943, -9659068, -23919258, 2187569, -26263207, -6086921, 31316348, 14219878 },
+        },
+        {
+            { -28594490, 1193785, 32245219, 11392485, 31092169, 15722801, 27146014, 6992409, 29126555, 9207390 },
+            { 32382935, 1110093, 18477781, 11028262, -27411763, -7548111, -4980517, 10843782, -7957600, -14435730 },
+            { 2814918, 7836403, 27519878, -7868156, -20894015, -11553689, -21494559, 8550130, 28346258, 1994730 },
+        },
+        {
+            { -19578299, 8085545, -14000519, -3948622, 2785838, -16231307, -19516951, 7174894, 22628102, 8115180 },
+            { -30405132, 955511, -11133838, -15078069, -32447087, -13278079, -25651578, 3317160, -9943017, 930272 },
+            { -15303681, -6833769, 28856490, 1357446, 23421993, 1057177, 24091212, -1388970, -22765376, -10650715 },
+        },
+        {
+            { -22751231, -5303997, -12907607, -12768866, -15811511, -7797053, -14839018, -16554220, -1867018, 8398970 },
+            { -31969310, 2106403, -4736360, 1362501, 12813763, 16200670, 22981545, -6291273, 18009408, -15772772 },
+            { -17220923, -9545221, -27784654, 14166835, 29815394, 7444469, 29551787, -3727419, 19288549, 1325865 },
+        },
+        {
+            { 15100157, -15835752, -23923978, -1005098, -26450192, 15509408, 12376730, -3479146, 33166107, -8042750 },
+            { 20909231, 13023121, -9209752, 16251778, -5778415, -8094914, 12412151, 10018715, 2213263, -13878373 },
+            { 32529814, -11074689, 30361439, -16689753, -9135940, 1513226, 22922121, 6382134, -5766928, 8371348 },
+        },
+    },
+    {
+        {
+            { 9923462, 11271500, 12616794, 3544722, -29998368, -1721626, 12891687, -8193132, -26442943, 10486144 },
+            { -22597207, -7012665, 8587003, -8257861, 4084309, -12970062, 361726, 2610596, -23921530, -11455195 },
+            { 5408411, -1136691, -4969122, 10561668, 24145918, 14240566, 31319731, -4235541, 19985175, -3436086 },
+        },
+        {
+            { -13994457, 16616821, 14549246, 3341099, 32155958, 13648976, -17577068, 8849297, 65030, 8370684 },
+            { -8320926, -12049626, 31204563, 5839400, -20627288, -1057277, -19442942, 6922164, 12743482, -9800518 },
+            { -2361371, 12678785, 28815050, 4759974, -23893047, 4884717, 23783145, 11038569, 18800704, 255233 },
+        },
+        {
+            { -5269658, -1773886, 13957886, 7990715, 23132995, 728773, 13393847, 9066957, 19258688, -14753793 },
+            { -2936654, -10827535, -10432089, 14516793, -3640786, 4372541, -31934921, 2209390, -1524053, 2055794 },
+            { 580882, 16705327, 5468415, -2683018, -30926419, -14696000, -7203346, -8994389, -30021019, 7394435 },
+        },
+        {
+            { 23838809, 1822728, -15738443, 15242727, 8318092, -3733104, -21672180, -3492205, -4821741, 14799921 },
+            { 13345610, 9759151, 3371034, -16137791, 16353039, 8577942, 31129804, 13496856, -9056018, 7402518 },
+            { 2286874, -4435931, -20042458, -2008336, -13696227, 5038122, 11006906, -15760352, 8205061, 1607563 },
+        },
+        {
+            { 14414086, -8002132, 3331830, -3208217, 22249151, -5594188, 18364661, -2906958, 30019587, -9029278 },
+            { -27688051, 1585953, -10775053, 931069, -29120221, -11002319, -14410829, 12029093, 9944378, 8024 },
+            { 4368715, -3709630, 29874200, -15022983, -20230386, -11410704, -16114594, -999085, -8142388, 5640030 },
+        },
+        {
+            { 10299610, 13746483, 11661824, 16234854, 7630238, 5998374, 9809887, -16694564, 15219798, -14327783 },
+            { 27425505, -5719081, 3055006, 10660664, 23458024, 595578, -15398605, -1173195, -18342183, 9742717 },
+            { 6744077, 2427284, 26042789, 2720740, -847906, 1118974, 32324614, 7406442, 12420155, 1994844 },
+        },
+        {
+            { 14012521, -5024720, -18384453, -9578469, -26485342, -3936439, -13033478, -10909803, 24319929, -6446333 },
+            { 16412690, -4507367, 10772641, 15929391, -17068788, -4658621, 10555945, -10484049, -30102368, -4739048 },
+            { 22397382, -7767684, -9293161, -12792868, 17166287, -9755136, -27333065, 6199366, 21880021, -12250760 },
+        },
+        {
+            { -4283307, 5368523, -31117018, 8163389, -30323063, 3209128, 16557151, 8890729, 8840445, 4957760 },
+            { -15447727, 709327, -6919446, -10870178, -29777922, 6522332, -21720181, 12130072, -14796503, 5005757 },
+            { -2114751, -14308128, 23019042, 15765735, -25269683, 6002752, 10183197, -13239326, -16395286, -2176112 },
+        },
+    },
+    {
+        {
+            { -19025756, 1632005, 13466291, -7995100, -23640451, 16573537, -32013908, -3057104, 22208662, 2000468 },
+            { 3065073, -1412761, -25598674, -361432, -17683065, -5703415, -8164212, 11248527, -3691214, -7414184 },
+            { 10379208, -6045554, 8877319, 1473647, -29291284, -12507580, 16690915, 2553332, -3132688, 16400289 },
+        },
+        {
+            { 15716668, 1254266, -18472690, 7446274, -8448918, 6344164, -22097271, -7285580, 26894937, 9132066 },
+            { 24158887, 12938817, 11085297, -8177598, -28063478, -4457083, -30576463, 64452, -6817084, -2692882 },
+            { 13488534, 7794716, 22236231, 5989356, 25426474, -12578208, 2350710, -3418511, -4688006, 2364226 },
+        },
+        {
+            { 16335052, 9132434, 25640582, 6678888, 1725628, 8517937, -11807024, -11697457, 15445875, -7798101 },
+            { 29004207, -7867081, 28661402, -640412, -12794003, -7943086, 31863255, -4135540, -278050, -15759279 },
+            { -6122061, -14866665, -28614905, 14569919, -10857999, -3591829, 10343412, -6976290, -29828287, -10815811 },
+        },
+        {
+            { 27081650, 3463984, 14099042, -4517604, 1616303, -6205604, 29542636, 15372179, 17293797, 960709 },
+            { 20263915, 11434237, -5765435, 11236810, 13505955, -10857102, -16111345, 6493122, -19384511, 7639714 },
+            { -2830798, -14839232, 25403038, -8215196, -8317012, -16173699, 18006287, -16043750, 29994677, -15808121 },
+        },
+        {
+            { 9769828, 5202651, -24157398, -13631392, -28051003, -11561624, -24613141, -13860782, -31184575, 709464 },
+            { 12286395, 13076066, -21775189, -1176622, -25003198, 4057652, -32018128, -8890874, 16102007, 13205847 },
+            { 13733362, 5599946, 10557076, 3195751, -5557991, 8536970, -25540170, 8525972, 10151379, 10394400 },
+        },
+        {
+            { 4024660, -16137551, 22436262, 12276534, -9099015, -2686099, 19698229, 11743039, -33302334, 8934414 },
+            { -15879800, -4525240, -8580747, -2934061, 14634845, -698278, -9449077, 3137094, -11536886, 11721158 },
+            { 17555939, -5013938, 8268606, 2331751, -22738815, 9761013, 9319229, 8835153, -9205489, -1280045 },
+        },
+        {
+            { -461409, -7830014, 20614118, 16688288, -7514766, -4807119, 22300304, 505429, 6108462, -6183415 },
+            { -5070281, 12367917, -30663534, 3234473, 32617080, -8422642, 29880583, -13483331, -26898490, -7867459 },
+            { -31975283, 5726539, 26934134, 10237677, -3173717, -605053, 24199304, 3795095, 7592688, -14992079 },
+        },
+        {
+            { 21594432, -14964228, 17466408, -4077222, 32537084, 2739898, 6407723, 12018833, -28256052, 4298412 },
+            { -20650503, -11961496, -27236275, 570498, 3767144, -1717540, 13891942, -1569194, 13717174, 10805743 },
+            { -14676630, -15644296, 15287174, 11927123, 24177847, -8175568, -796431, 14860609, -26938930, -5863836 },
+        },
+    },
+    {
+        {
+            { 12962541, 5311799, -10060768, 11658280, 18855286, -7954201, 13286263, -12808704, -4381056, 9882022 },
+            { 18512079, 11319350, -20123124, 15090309, 18818594, 5271736, -22727904, 3666879, -23967430, -3299429 },
+            { -6789020, -3146043, 16192429, 13241070, 15898607, -14206114, -10084880, -6661110, -2403099, 5276065 },
+        },
+        {
+            { 30169808, -5317648, 26306206, -11750859, 27814964, 7069267, 7152851, 3684982, 1449224, 13082861 },
+            { 10342826, 3098505, 2119311, 193222, 25702612, 12233820, 23697382, 15056736, -21016438, -8202000 },
+            { -33150110, 3261608, 22745853, 7948688, 19370557, -15177665, -26171976, 6482814, -10300080, -11060101 },
+        },
+        {
+            { 32869458, -5408545, 25609743, 15678670, -10687769, -15471071, 26112421, 2521008, -22664288, 6904815 },
+            { 29506923, 4457497, 3377935, -9796444, -30510046, 12935080, 1561737, 3841096, -29003639, -6657642 },
+            { 10340844, -6630377, -18656632, -2278430, 12621151, -13339055, 30878497, -11824370, -25584551, 5181966 },
+        },
+        {
+            { 25940115, -12658025, 17324188, -10307374, -8671468, 15029094, 24396252, -16450922, -2322852, -12388574 },
+            { -21765684, 9916823, -1300409, 4079498, -1028346, 11909559, 1782390, 12641087, 20603771, -6561742 },
+            { -18882287, -11673380, 24849422, 11501709, 13161720, -4768874, 1925523, 11914390, 4662781, 7820689 },
+        },
+        {
+            { 12241050, -425982, 8132691, 9393934, 32846760, -1599620, 29749456, 12172924, 16136752, 15264020 },
+            { -10349955, -14680563, -8211979, 2330220, -17662549, -14545780, 10658213, 6671822, 19012087, 3772772 },
+            { 3753511, -3421066, 10617074, 2028709, 14841030, -6721664, 28718732, -15762884, 20527771, 12988982 },
+        },
+        {
+            { -14822485, -5797269, -3707987, 12689773, -898983, -10914866, -24183046, -10564943, 3299665, -12424953 },
+            { -16777703, -15253301, -9642417, 4978983, 3308785, 8755439, 6943197, 6461331, -25583147, 8991218 },
+            { -17226263, 1816362, -1673288, -6086439, 31783888, -8175991, -32948145, 7417950, -30242287, 1507265 },
+        },
+        {
+            { 29692663, 6829891, -10498800, 4334896, 20945975, -11906496, -28887608, 8209391, 14606362, -10647073 },
+            { -3481570, 8707081, 32188102, 5672294, 22096700, 1711240, -33020695, 9761487, 4170404, -2085325 },
+            { -11587470, 14855945, -4127778, -1531857, -26649089, 15084046, 22186522, 16002000, -14276837, -8400798 },
+        },
+        {
+            { -4811456, 13761029, -31703877, -2483919, -3312471, 7869047, -7113572, -9620092, 13240845, 10965870 },
+            { -7742563, -8256762, -14768334, -13656260, -23232383, 12387166, 4498947, 14147411, 29514390, 4302863 },
+            { -13413405, -12407859, 20757302, -13801832, 14785143, 8976368, -5061276, -2144373, 17846988, -13971927 },
+        },
+    },
+    {
+        {
+            { -2244452, -754728, -4597030, -1066309, -6247172, 1455299, -21647728, -9214789, -5222701, 12650267 },
+            { -9906797, -16070310, 21134160, 12198166, -27064575, 708126, 387813, 13770293, -19134326, 10958663 },
+            { 22470984, 12369526, 23446014, -5441109, -21520802, -9698723, -11772496, -11574455, -25083830, 4271862 },
+        },
+        {
+            { -25169565, -10053642, -19909332, 15361595, -5984358, 2159192, 75375, -4278529, -32526221, 8469673 },
+            { 15854970, 4148314, -8893890, 7259002, 11666551, 13824734, -30531198, 2697372, 24154791, -9460943 },
+            { 15446137, -15806644, 29759747, 14019369, 30811221, -9610191, -31582008, 12840104, 24913809, 9815020 },
+        },
+        {
+            { -4709286, -5614269, -31841498, -12288893, -14443537, 10799414, -9103676, 13438769, 18735128, 9466238 },
+            { 11933045, 9281483, 5081055, -5183824, -2628162, -4905629, -7727821, -10896103, -22728655, 16199064 },
+            { 14576810, 379472, -26786533, -8317236, -29426508, -10812974, -102766, 1876699, 30801119, 2164795 },
+        },
+        {
+            { 15995086, 3199873, 13672555, 13712240, -19378835, -4647646, -13081610, -15496269, -13492807, 1268052 },
+            { -10290614, -3659039, -3286592, 10948818, 23037027, 3794475, -3470338, -12600221, -17055369, 3565904 },
+            { 29210088, -9419337, -5919792, -4952785, 10834811, -13327726, -16512102, -10820713, -27162222, -14030531 },
+        },
+        {
+            { -13161890, 15508588, 16663704, -8156150, -28349942, 9019123, -29183421, -3769423, 2244111, -14001979 },
+            { -5152875, -3800936, -9306475, -6071583, 16243069, 14684434, -25673088, -16180800, 13491506, 4641841 },
+            { 10813417, 643330, -19188515, -728916, 30292062, -16600078, 27548447, -7721242, 14476989, -12767431 },
+        },
+        {
+            { 10292079, 9984945, 6481436, 8279905, -7251514, 7032743, 27282937, -1644259, -27912810, 12651324 },
+            { -31185513, -813383, 22271204, 11835308, 10201545, 15351028, 17099662, 3988035, 21721536, -3148940 },
+            { 10202177, -6545839, -31373232, -9574638, -32150642, -8119683, -12906320, 3852694, 13216206, 14842320 },
+        },
+        {
+            { -15815640, -10601066, -6538952, -7258995, -6984659, -6581778, -31500847, 13765824, -27434397, 9900184 },
+            { 14465505, -13833331, -32133984, -14738873, -27443187, 12990492, 33046193, 15796406, -7051866, -8040114 },
+            { 30924417, -8279620, 6359016, -12816335, 16508377, 9071735, -25488601, 15413635, 9524356, -7018878 },
+        },
+        {
+            { 12274201, -13175547, 32627641, -1785326, 6736625, 13267305, 5237659, -5109483, 15663516, 4035784 },
+            { -2951309, 8903985, 17349946, 601635, -16432815, -4612556, -13732739, -15889334, -22258478, 4659091 },
+            { -16916263, -4952973, -30393711, -15158821, 20774812, 15897498, 5736189, 15026997, -2178256, -13455585 },
+        },
+    },
+    {
+        {
+            { -8858980, -2219056, 28571666, -10155518, -474467, -10105698, -3801496, 278095, 23440562, -290208 },
+            { 10226241, -5928702, 15139956, 120818, -14867693, 5218603, 32937275, 11551483, -16571960, -7442864 },
+            { 17932739, -12437276, -24039557, 10749060, 11316803, 7535897, 22503767, 5561594, -3646624, 3898661 },
+        },
+        {
+            { 7749907, -969567, -16339731, -16464, -25018111, 15122143, -1573531, 7152530, 21831162, 1245233 },
+            { 26958459, -14658026, 4314586, 8346991, -5677764, 11960072, -32589295, -620035, -30402091, -16716212 },
+            { -12165896, 9166947, 33491384, 13673479, 29787085, 13096535, 6280834, 14587357, -22338025, 13987525 },
+        },
+        {
+            { -24349909, 7778775, 21116000, 15572597, -4833266, -5357778, -4300898, -5124639, -7469781, -2858068 },
+            { 9681908, -6737123, -31951644, 13591838, -6883821, 386950, 31622781, 6439245, -14581012, 4091397 },
+            { -8426427, 1470727, -28109679, -1596990, 3978627, -5123623, -19622683, 12092163, 29077877, -14741988 },
+        },
+        {
+            { 5269168, -6859726, -13230211, -8020715, 25932563, 1763552, -5606110, -5505881, -20017847, 2357889 },
+            { 32264008, -15407652, -5387735, -1160093, -2091322, -3946900, 23104804, -12869908, 5727338, 189038 },
+            { 14609123, -8954470, -6000566, -16622781, -14577387, -7743898, -26745169, 10942115, -25888931, -14884697 },
+        },
+        {
+            { 20513500, 5557931, -15604613, 7829531, 26413943, -2019404, -21378968, 7471781, 13913677, -5137875 },
+            { -25574376, 11967826, 29233242, 12948236, -6754465, 4713227, -8940970, 14059180, 12878652, 8511905 },
+            { -25656801, 3393631, -2955415, -7075526, -2250709, 9366908, -30223418, 6812974, 5568676, -3127656 },
+        },
+        {
+            { 11630004, 12144454, 2116339, 13606037, 27378885, 15676917, -17408753, -13504373, -14395196, 8070818 },
+            { 27117696, -10007378, -31282771, -5570088, 1127282, 12772488, -29845906, 10483306, -11552749, -1028714 },
+            { 10637467, -5688064, 5674781, 1072708, -26343588, -6982302, -1683975, 9177853, -27493162, 15431203 },
+        },
+        {
+            { 20525145, 10892566, -12742472, 12779443, -29493034, 16150075, -28240519, 14943142, -15056790, -7935931 },
+            { -30024462, 5626926, -551567, -9981087, 753598, 11981191, 25244767, -3239766, -3356550, 9594024 },
+            { -23752644, 2636870, -5163910, -10103818, 585134, 7877383, 11345683, -6492290, 13352335, -10977084 },
+        },
+        {
+            { -1931799, -5407458, 3304649, -12884869, 17015806, -4877091, -29783850, -7752482, -13215537, -319204 },
+            { 20239939, 6607058, 6203985, 3483793, -18386976, -779229, -20723742, 15077870, -22750759, 14523817 },
+            { 27406042, -6041657, 27423596, -4497394, 4996214, 10002360, -28842031, -4545494, -30172742, -4805667 },
+        },
+    },
+    {
+        {
+            { 11374242, 12660715, 17861383, -12540833, 10935568, 1099227, -13886076, -9091740, -27727044, 11358504 },
+            { -12730809, 10311867, 1510375, 10778093, -2119455, -9145702, 32676003, 11149336, -26123651, 4985768 },
+            { -19096303, 341147, -6197485, -239033, 15756973, -8796662, -983043, 13794114, -19414307, -15621255 },
+        },
+        {
+            { 6490081, 11940286, 25495923, -7726360, 8668373, -8751316, 3367603, 6970005, -1691065, -9004790 },
+            { 1656497, 13457317, 15370807, 6364910, 13605745, 8362338, -19174622, -5475723, -16796596, -5031438 },
+            { -22273315, -13524424, -64685, -4334223, -18605636, -10921968, -20571065, -7007978, -99853, -10237333 },
+        },
+        {
+            { 17747465, 10039260, 19368299, -4050591, -20630635, -16041286, 31992683, -15857976, -29260363, -5511971 },
+            { 31932027, -4986141, -19612382, 16366580, 22023614, 88450, 11371999, -3744247, 4882242, -10626905 },
+            { 29796507, 37186, 19818052, 10115756, -11829032, 3352736, 18551198, 3272828, -5190932, -4162409 },
+        },
+        {
+            { 12501286, 4044383, -8612957, -13392385, -32430052, 5136599, -19230378, -3529697, 330070, -3659409 },
+            { 6384877, 2899513, 17807477, 7663917, -2358888, 12363165, 25366522, -8573892, -271295, 12071499 },
+            { -8365515, -4042521, 25133448, -4517355, -6211027, 2265927, -32769618, 1936675, -5159697, 3829363 },
+        },
+        {
+            { 28425966, -5835433, -577090, -4697198, -14217555, 6870930, 7921550, -6567787, 26333140, 14267664 },
+            { -11067219, 11871231, 27385719, -10559544, -4585914, -11189312, 10004786, -8709488, -21761224, 8930324 },
+            { -21197785, -16396035, 25654216, -1725397, 12282012, 11008919, 1541940, 4757911, -26491501, -16408940 },
+        },
+        {
+            { 13537262, -7759490, -20604840, 10961927, -5922820, -13218065, -13156584, 6217254, -15943699, 13814990 },
+            { -17422573, 15157790, 18705543, 29619, 24409717, -260476, 27361681, 9257833, -1956526, -1776914 },
+            { -25045300, -10191966, 15366585, 15166509, -13105086, 8423556, -29171540, 12361135, -18685978, 4578290 },
+        },
+        {
+            { 24579768, 3711570, 1342322, -11180126, -27005135, 14124956, -22544529, 14074919, 21964432, 8235257 },
+            { -6528613, -2411497, 9442966, -5925588, 12025640, -1487420, -2981514, -1669206, 13006806, 2355433 },
+            { -16304899, -13605259, -6632427, -5142349, 16974359, -10911083, 27202044, 1719366, 1141648, -12796236 },
+        },
+        {
+            { -12863944, -13219986, -8318266, -11018091, -6810145, -4843894, 13475066, -3133972, 32674895, 13715045 },
+            { 11423335, -5468059, 32344216, 8962751, 24989809, 9241752, -13265253, 16086212, -28740881, -15642093 },
+            { -1409668, 12530728, -6368726, 10847387, 19531186, -14132160, -11709148, 7791794, -27245943, 4383347 },
+        },
+    },
+    {
+        {
+            { -28970898, 5271447, -1266009, -9736989, -12455236, 16732599, -4862407, -4906449, 27193557, 6245191 },
+            { -15193956, 5362278, -1783893, 2695834, 4960227, 12840725, 23061898, 3260492, 22510453, 8577507 },
+            { -12632451, 11257346, -32692994, 13548177, -721004, 10879011, 31168030, 13952092, -29571492, -3635906 },
+        },
+        {
+            { 3877321, -9572739, 32416692, 5405324, -11004407, -13656635, 3759769, 11935320, 5611860, 8164018 },
+            { -16275802, 14667797, 15906460, 12155291, -22111149, -9039718, 32003002, -8832289, 5773085, -8422109 },
+            { -23788118, -8254300, 1950875, 8937633, 18686727, 16459170, -905725, 12376320, 31632953, 190926 },
+        },
+        {
+            { -24593607, -16138885, -8423991, 13378746, 14162407, 6901328, -8288749, 4508564, -25341555, -3627528 },
+            { 8884438, -5884009, 6023974, 10104341, -6881569, -4941533, 18722941, -14786005, -1672488, 827625 },
+            { -32720583, -16289296, -32503547, 7101210, 13354605, 2659080, -1800575, -14108036, -24878478, 1541286 },
+        },
+        {
+            { 2901347, -1117687, 3880376, -10059388, -17620940, -3612781, -21802117, -3567481, 20456845, -1885033 },
+            { 27019610, 12299467, -13658288, -1603234, -12861660, -4861471, -19540150, -5016058, 29439641, 15138866 },
+            { 21536104, -6626420, -32447818, -10690208, -22408077, 5175814, -5420040, -16361163, 7779328, 109896 },
+        },
+        {
+            { 30279744, 14648750, -8044871, 6425558, 13639621, -743509, 28698390, 12180118, 23177719, -554075 },
+            { 26572847, 3405927, -31701700, 12890905, -19265668, 5335866, -6493768, 2378492, 4439158, -13279347 },
+            { -22716706, 3489070, -9225266, -332753, 18875722, -1140095, 14819434, -12731527, -17717757, -5461437 },
+        },
+        {
+            { -5056483, 16566551, 15953661, 3767752, -10436499, 15627060, -820954, 2177225, 8550082, -15114165 },
+            { -18473302, 16596775, -381660, 15663611, 22860960, 15585581, -27844109, -3582739, -23260460, -8428588 },
+            { -32480551, 15707275, -8205912, -5652081, 29464558, 2713815, -22725137, 15860482, -21902570, 1494193 },
+        },
+        {
+            { -19562091, -14087393, -25583872, -9299552, 13127842, 759709, 21923482, 16529112, 8742704, 12967017 },
+            { -28464899, 1553205, 32536856, -10473729, -24691605, -406174, -8914625, -2933896, -29903758, 15553883 },
+            { 21877909, 3230008, 9881174, 10539357, -4797115, 2841332, 11543572, 14513274, 19375923, -12647961 },
+        },
+        {
+            { 8832269, -14495485, 13253511, 5137575, 5037871, 4078777, 24880818, -6222716, 2862653, 9455043 },
+            { 29306751, 5123106, 20245049, -14149889, 9592566, 8447059, -2077124, -2990080, 15511449, 4789663 },
+            { -20679756, 7004547, 8824831, -9434977, -4045704, -3750736, -5754762, 108893, 23513200, 16652362 },
+        },
+    },
+    {
+        {
+            { -33256173, 4144782, -4476029, -6579123, 10770039, -7155542, -6650416, -12936300, -18319198, 10212860 },
+            { 2756081, 8598110, 7383731, -6859892, 22312759, -1105012, 21179801, 2600940, -9988298, -12506466 },
+            { -24645692, 13317462, -30449259, -15653928, 21365574, -10869657, 11344424, 864440, -2499677, -16710063 },
+        },
+        {
+            { -26432803, 6148329, -17184412, -14474154, 18782929, -275997, -22561534, 211300, 2719757, 4940997 },
+            { -1323882, 3911313, -6948744, 14759765, -30027150, 7851207, 21690126, 8518463, 26699843, 5276295 },
+            { -13149873, -6429067, 9396249, 365013, 24703301, -10488939, 1321586, 149635, -15452774, 7159369 },
+        },
+        {
+            { 9987780, -3404759, 17507962, 9505530, 9731535, -2165514, 22356009, 8312176, 22477218, -8403385 },
+            { 18155857, -16504990, 19744716, 9006923, 15154154, -10538976, 24256460, -4864995, -22548173, 9334109 },
+            { 2986088, -4911893, 10776628, -3473844, 10620590, -7083203, -21413845, 14253545, -22587149, 536906 },
+        },
+        {
+            { 4377756, 8115836, 24567078, 15495314, 11625074, 13064599, 7390551, 10589625, 10838060, -15420424 },
+            { -19342404, 867880, 9277171, -3218459, -14431572, -1986443, 19295826, -15796950, 6378260, 699185 },
+            { 7895026, 4057113, -7081772, -13077756, -17886831, -323126, -716039, 15693155, -5045064, -13373962 },
+        },
+        {
+            { -7737563, -5869402, -14566319, -7406919, 11385654, 13201616, 31730678, -10962840, -3918636, -9669325 },
+            { 10188286, -15770834, -7336361, 13427543, 22223443, 14896287, 30743455, 7116568, -21786507, 5427593 },
+            { 696102, 13206899, 27047647, -10632082, 15285305, -9853179, 10798490, -4578720, 19236243, 12477404 },
+        },
+        {
+            { -11229439, 11243796, -17054270, -8040865, -788228, -8167967, -3897669, 11180504, -23169516, 7733644 },
+            { 17800790, -14036179, -27000429, -11766671, 23887827, 3149671, 23466177, -10538171, 10322027, 15313801 },
+            { 26246234, 11968874, 32263343, -5468728, 6830755, -13323031, -15794704, -101982, -24449242, 10890804 },
+        },
+        {
+            { -31365647, 10271363, -12660625, -6267268, 16690207, -13062544, -14982212, 16484931, 25180797, -5334884 },
+            { -586574, 10376444, -32586414, -11286356, 19801893, 10997610, 2276632, 9482883, 316878, 13820577 },
+            { -9882808, -4510367, -2115506, 16457136, -11100081, 11674996, 30756178, -7515054, 30696930, -3712849 },
+        },
+        {
+            { 32988917, -9603412, 12499366, 7910787, -10617257, -11931514, -7342816, -9985397, -32349517, 7392473 },
+            { -8855661, 15927861, 9866406, -3649411, -2396914, -16655781, -30409476, -9134995, 25112947, -2926644 },
+            { -2504044, -436966, 25621774, -5678772, 15085042, -5479877, -24884878, -13526194, 5537438, -13914319 },
+        },
+    },
+    {
+        {
+            { -11225584, 2320285, -9584280, 10149187, -33444663, 5808648, -14876251, -1729667, 31234590, 6090599 },
+            { -9633316, 116426, 26083934, 2897444, -6364437, -2688086, 609721, 15878753, -6970405, -9034768 },
+            { -27757857, 247744, -15194774, -9002551, 23288161, -10011936, -23869595, 6503646, 20650474, 1804084 },
+        },
+        {
+            { -27589786, 15456424, 8972517, 8469608, 15640622, 4439847, 3121995, -10329713, 27842616, -202328 },
+            { -15306973, 2839644, 22530074, 10026331, 4602058, 5048462, 28248656, 5031932, -11375082, 12714369 },
+            { 20807691, -7270825, 29286141, 11421711, -27876523, -13868230, -21227475, 1035546, -19733229, 12796920 },
+        },
+        {
+            { 12076899, -14301286, -8785001, -11848922, -25012791, 16400684, -17591495, -12899438, 3480665, -15182815 },
+            { -32361549, 5457597, 28548107, 7833186, 7303070, -11953545, -24363064, -15921875, -33374054, 2771025 },
+            { -21389266, 421932, 26597266, 6860826, 22486084, -6737172, -17137485, -4210226, -24552282, 15673397 },
+        },
+        {
+            { -20184622, 2338216, 19788685, -9620956, -4001265, -8740893, -20271184, 4733254, 3727144, -12934448 },
+            { 6120119, 814863, -11794402, -622716, 6812205, -15747771, 2019594, 7975683, 31123697, -10958981 },
+            { 30069250, -11435332, 30434654, 2958439, 18399564, -976289, 12296869, 9204260, -16432438, 9648165 },
+        },
+        {
+            { 32705432, -1550977, 30705658, 7451065, -11805606, 9631813, 3305266, 5248604, -26008332, -11377501 },
+            { 17219865, 2375039, -31570947, -5575615, -19459679, 9219903, 294711, 15298639, 2662509, -16297073 },
+            { -1172927, -7558695, -4366770, -4287744, -21346413, -8434326, 32087529, -1222777, 32247248, -14389861 },
+        },
+        {
+            { 14312628, 1221556, 17395390, -8700143, -4945741, -8684635, -28197744, -9637817, -16027623, -13378845 },
+            { -1428825, -9678990, -9235681, 6549687, -7383069, -468664, 23046502, 9803137, 17597934, 2346211 },
+            { 18510800, 15337574, 26171504, 981392, -22241552, 7827556, -23491134, -11323352, 3059833, -11782870 },
+        },
+        {
+            { 10141598, 6082907, 17829293, -1947643, 9830092, 13613136, -25556636, -5544586, -33502212, 3592096 },
+            { 33114168, -15889352, -26525686, -13343397, 33076705, 8716171, 1151462, 1521897, -982665, -6837803 },
+            { -32939165, -4255815, 23947181, -324178, -33072974, -12305637, -16637686, 3891704, 26353178, 693168 },
+        },
+        {
+            { 30374239, 1595580, -16884039, 13186931, 4600344, 406904, 9585294, -400668, 31375464, 14369965 },
+            { -14370654, -7772529, 1510301, 6434173, -18784789, -6262728, 32732230, -13108839, 17901441, 16011505 },
+            { 18171223, -11934626, -12500402, 15197122, -11038147, -15230035, -19172240, -16046376, 8764035, 12309598 },
+        },
+    },
+    {
+        {
+            { 5975908, -5243188, -19459362, -9681747, -11541277, 14015782, -23665757, 1228319, 17544096, -10593782 },
+            { 5811932, -1715293, 3442887, -2269310, -18367348, -8359541, -18044043, -15410127, -5565381, 12348900 },
+            { -31399660, 11407555, 25755363, 6891399, -3256938, 14872274, -24849353, 8141295, -10632534, -585479 },
+        },
+        {
+            { -12675304, 694026, -5076145, 13300344, 14015258, -14451394, -9698672, -11329050, 30944593, 1130208 },
+            { 8247766, -6710942, -26562381, -7709309, -14401939, -14648910, 4652152, 2488540, 23550156, -271232 },
+            { 17294316, -3788438, 7026748, 15626851, 22990044, 113481, 2267737, -5908146, -408818, -137719 },
+        },
+        {
+            { 16091085, -16253926, 18599252, 7340678, 2137637, -1221657, -3364161, 14550936, 3260525, -7166271 },
+            { -4910104, -13332887, 18550887, 10864893, -16459325, -7291596, -23028869, -13204905, -12748722, 2701326 },
+            { -8574695, 16099415, 4629974, -16340524, -20786213, -6005432, -10018363, 9276971, 11329923, 1862132 },
+        },
+        {
+            { 14763076, -15903608, -30918270, 3689867, 3511892, 10313526, -21951088, 12219231, -9037963, -940300 },
+            { 8894987, -3446094, 6150753, 3013931, 301220, 15693451, -31981216, -2909717, -15438168, 11595570 },
+            { 15214962, 3537601, -26238722, -14058872, 4418657, -15230761, 13947276, 10730794, -13489462, -4363670 },
+        },
+        {
+            { -2538306, 7682793, 32759013, 263109, -29984731, -7955452, -22332124, -10188635, 977108, 699994 },
+            { -12466472, 4195084, -9211532, 550904, -15565337, 12917920, 19118110, -439841, -30534533, -14337913 },
+            { 31788461, -14507657, 4799989, 7372237, 8808585, -14747943, 9408237, -10051775, 12493932, -5409317 },
+        },
+        {
+            { -25680606, 5260744, -19235809, -6284470, -3695942, 16566087, 27218280, 2607121, 29375955, 6024730 },
+            { 842132, -2794693, -4763381, -8722815, 26332018, -12405641, 11831880, 6985184, -9940361, 2854096 },
+            { -4847262, -7969331, 2516242, -5847713, 9695691, -7221186, 16512645, 960770, 12121869, 16648078 },
+        },
+        {
+            { -15218652, 14667096, -13336229, 2013717, 30598287, -464137, -31504922, -7882064, 20237806, 2838411 },
+            { -19288047, 4453152, 15298546, -16178388, 22115043, -15972604, 12544294, -13470457, 1068881, -12499905 },
+            { -9558883, -16518835, 33238498, 13506958, 30505848, -1114596, -8486907, -2630053, 12521378, 4845654 },
+        },
+        {
+            { -28198521, 10744108, -2958380, 10199664, 7759311, -13088600, 3409348, -873400, -6482306, -12885870 },
+            { -23561822, 6230156, -20382013, 10655314, -24040585, -11621172, 10477734, -1240216, -3113227, 13974498 },
+            { 12966261, 15550616, -32038948, -1615346, 21025980, -629444, 5642325, 7188737, 18895762, 12629579 },
+        },
+    },
+    {
+        {
+            { 14741879, -14946887, 22177208, -11721237, 1279741, 8058600, 11758140, 789443, 32195181, 3895677 },
+            { 10758205, 15755439, -4509950, 9243698, -4879422, 6879879, -2204575, -3566119, -8982069, 4429647 },
+            { -2453894, 15725973, -20436342, -10410672, -5803908, -11040220, -7135870, -11642895, 18047436, -15281743 },
+        },
+        {
+            { -25173001, -11307165, 29759956, 11776784, -22262383, -15820455, 10993114, -12850837, -17620701, -9408468 },
+            { 21987233, 700364, -24505048, 14972008, -7774265, -5718395, 32155026, 2581431, -29958985, 8773375 },
+            { -25568350, 454463, -13211935, 16126715, 25240068, 8594567, 20656846, 12017935, -7874389, -13920155 },
+        },
+        {
+            { 6028182, 6263078, -31011806, -11301710, -818919, 2461772, -31841174, -5468042, -1721788, -2776725 },
+            { -12278994, 16624277, 987579, -5922598, 32908203, 1248608, 7719845, -4166698, 28408820, 6816612 },
+            { -10358094, -8237829, 19549651, -12169222, 22082623, 16147817, 20613181, 13982702, -10339570, 5067943 },
+        },
+        {
+            { -30505967, -3821767, 12074681, 13582412, -19877972, 2443951, -19719286, 12746132, 5331210, -10105944 },
+            { 30528811, 3601899, -1957090, 4619785, -27361822, -15436388, 24180793, -12570394, 27679908, -1648928 },
+            { 9402404, -13957065, 32834043, 10838634, -26580150, -13237195, 26653274, -8685565, 22611444, -12715406 },
+        },
+        {
+            { 22190590, 1118029, 22736441, 15130463, -30460692, -5991321, 19189625, -4648942, 4854859, 6622139 },
+            { -8310738, -2953450, -8262579, -3388049, -10401731, -271929, 13424426, -3567227, 26404409, 13001963 },
+            { -31241838, -15415700, -2994250, 8939346, 11562230, -12840670, -26064365, -11621720, -15405155, 11020693 },
+        },
+        {
+            { 1866042, -7949489, -7898649, -10301010, 12483315, 13477547, 3175636, -12424163, 28761762, 1406734 },
+            { -448555, -1777666, 13018551, 3194501, -9580420, -11161737, 24760585, -4347088, 25577411, -13378680 },
+            { -24290378, 4759345, -690653, -1852816, 2066747, 10693769, -29595790, 9884936, -9368926, 4745410 },
+        },
+        {
+            { -9141284, 6049714, -19531061, -4341411, -31260798, 9944276, -15462008, -11311852, 10931924, -11931931 },
+            { -16561513, 14112680, -8012645, 4817318, -8040464, -11414606, -22853429, 10856641, -20470770, 13434654 },
+            { 22759489, -10073434, -16766264, -1871422, 13637442, -10168091, 1765144, -12654326, 28445307, -5364710 },
+        },
+        {
+            { 29875063, 12493613, 2795536, -3786330, 1710620, 15181182, -10195717, -8788675, 9074234, 1167180 },
+            { -26205683, 11014233, -9842651, -2635485, -26908120, 7532294, -18716888, -9535498, 3843903, 9367684 },
+            { -10969595, -6403711, 9591134, 9582310, 11349256, 108879, 16235123, 8601684, -139197, 4242895 },
+        },
+    },
+    {
+        {
+            { 22092954, -13191123, -2042793, -11968512, 32186753, -11517388, -6574341, 2470660, -27417366, 16625501 },
+            { -11057722, 3042016, 13770083, -9257922, 584236, -544855, -7770857, 2602725, -27351616, 14247413 },
+            { 6314175, -10264892, -32772502, 15957557, -10157730, 168750, -8618807, 14290061, 27108877, -1180880 },
+        },
+        {
+            { -8586597, -7170966, 13241782, 10960156, -32991015, -13794596, 33547976, -11058889, -27148451, 981874 },
+            { 22833440, 9293594, -32649448, -13618667, -9136966, 14756819, -22928859, -13970780, -10479804, -16197962 },
+            { -7768587, 3326786, -28111797, 10783824, 19178761, 14905060, 22680049, 13906969, -15933690, 3797899 },
+        },
+        {
+            { 21721356, -4212746, -12206123, 9310182, -3882239, -13653110, 23740224, -2709232, 20491983, -8042152 },
+            { 9209270, -15135055, -13256557, -6167798, -731016, 15289673, 25947805, 15286587, 30997318, -6703063 },
+            { 7392032, 16618386, 23946583, -8039892, -13265164, -1533858, -14197445, -2321576, 17649998, -250080 },
+        },
+        {
+            { -9301088, -14193827, 30609526, -3049543, -25175069, -1283752, -15241566, -9525724, -2233253, 7662146 },
+            { -17558673, 1763594, -33114336, 15908610, -30040870, -12174295, 7335080, -8472199, -3174674, 3440183 },
+            { -19889700, -5977008, -24111293, -9688870, 10799743, -16571957, 40450, -4431835, 4862400, 1133 },
+        },
+        {
+            { -32856209, -7873957, -5422389, 14860950, -16319031, 7956142, 7258061, 311861, -30594991, -7379421 },
+            { -3773428, -1565936, 28985340, 7499440, 24445838, 9325937, 29727763, 16527196, 18278453, 15405622 },
+            { -4381906, 8508652, -19898366, -3674424, -5984453, 15149970, -13313598, 843523, -21875062, 13626197 },
+        },
+        {
+            { 2281448, -13487055, -10915418, -2609910, 1879358, 16164207, -10783882, 3953792, 13340839, 15928663 },
+            { 31727126, -7179855, -18437503, -8283652, 2875793, -16390330, -25269894, -7014826, -23452306, 5964753 },
+            { 4100420, -5959452, -17179337, 6017714, -18705837, 12227141, -26684835, 11344144, 2538215, -7570755 },
+        },
+        {
+            { -9433605, 6123113, 11159803, -2156608, 30016280, 14966241, -20474983, 1485421, -629256, -15958862 },
+            { -26804558, 4260919, 11851389, 9658551, -32017107, 16367492, -20205425, -13191288, 11659922, -11115118 },
+            { 26180396, 10015009, -30844224, -8581293, 5418197, 9480663, 2231568, -10170080, 33100372, -1306171 },
+        },
+        {
+            { 15121113, -5201871, -10389905, 15427821, -27509937, -15992507, 21670947, 4486675, -5931810, -14466380 },
+            { 16166486, -9483733, -11104130, 6023908, -31926798, -1364923, 2340060, -16254968, -10735770, -10039824 },
+            { 28042865, -3557089, -12126526, 12259706, -3717498, -6945899, 6766453, -8689599, 18036436, 5803270 },
+        },
+    },
+    {
+        {
+            { -817581, 6763912, 11803561, 1585585, 10958447, -2671165, 23855391, 4598332, -6159431, -14117438 },
+            { -31031306, -14256194, 17332029, -2383520, 31312682, -5967183, 696309, 50292, -20095739, 11763584 },
+            { -594563, -2514283, -32234153, 12643980, 12650761, 14811489, 665117, -12613632, -19773211, -10713562 },
+        },
+        {
+            { 30464590, -11262872, -4127476, -12734478, 19835327, -7105613, -24396175, 2075773, -17020157, 992471 },
+            { 18357185, -6994433, 7766382, 16342475, -29324918, 411174, 14578841, 8080033, -11574335, -10601610 },
+            { 19598397, 10334610, 12555054, 2555664, 18821899, -10339780, 21873263, 16014234, 26224780, 16452269 },
+        },
+        {
+            { -30223925, 5145196, 5944548, 16385966, 3976735, 2009897, -11377804, -7618186, -20533829, 3698650 },
+            { 14187449, 3448569, -10636236, -10810935, -22663880, -3433596, 7268410, -10890444, 27394301, 12015369 },
+            { 19695761, 16087646, 28032085, 12999827, 6817792, 11427614, 20244189, -1312777, -13259127, -3402461 },
+        },
+        {
+            { 30860103, 12735208, -1888245, -4699734, -16974906, 2256940, -8166013, 12298312, -8550524, -10393462 },
+            { -5719826, -11245325, -1910649, 15569035, 26642876, -7587760, -5789354, -15118654, -4976164, 12651793 },
+            { -2848395, 9953421, 11531313, -5282879, 26895123, -12697089, -13118820, -16517902, 9768698, -2533218 },
+        },
+        {
+            { -24719459, 1894651, -287698, -4704085, 15348719, -8156530, 32767513, 12765450, 4940095, 10678226 },
+            { 18860224, 15980149, -18987240, -1562570, -26233012, -11071856, -7843882, 13944024, -24372348, 16582019 },
+            { -15504260, 4970268, -29893044, 4175593, -20993212, -2199756, -11704054, 15444560, -11003761, 7989037 },
+        },
+        {
+            { 31490452, 5568061, -2412803, 2182383, -32336847, 4531686, -32078269, 6200206, -19686113, -14800171 },
+            { -17308668, -15879940, -31522777, -2831, -32887382, 16375549, 8680158, -16371713, 28550068, -6857132 },
+            { -28126887, -5688091, 16837845, -1820458, -6850681, 12700016, -30039981, 4364038, 1155602, 5988841 },
+        },
+        {
+            { 21890435, -13272907, -12624011, 12154349, -7831873, 15300496, 23148983, -4470481, 24618407, 8283181 },
+            { -33136107, -10512751, 9975416, 6841041, -31559793, 16356536, 3070187, -7025928, 1466169, 10740210 },
+            { -1509399, -15488185, -13503385, -10655916, 32799044, 909394, -13938903, -5779719, -32164649, -15327040 },
+        },
+        {
+            { 3960823, -14267803, -28026090, -15918051, -19404858, 13146868, 15567327, 951507, -3260321, -573935 },
+            { 24740841, 5052253, -30094131, 8961361, 25877428, 6165135, -24368180, 14397372, -7380369, -6144105 },
+            { -28888365, 3510803, -28103278, -1158478, -11238128, -10631454, -15441463, -14453128, -1625486, -6494814 },
+        },
+    },
+    {
+        {
+            { 793299, -9230478, 8836302, -6235707, -27360908, -2369593, 33152843, -4885251, -9906200, -621852 },
+            { 5666233, 525582, 20782575, -8038419, -24538499, 14657740, 16099374, 1468826, -6171428, -15186581 },
+            { -4859255, -3779343, -2917758, -6748019, 7778750, 11688288, -30404353, -9871238, -1558923, -9863646 },
+        },
+        {
+            { 10896332, -7719704, 824275, 472601, -19460308, 3009587, 25248958, 14783338, -30581476, -15757844 },
+            { 10566929, 12612572, -31944212, 11118703, -12633376, 12362879, 21752402, 8822496, 24003793, 14264025 },
+            { 27713862, -7355973, -11008240, 9227530, 27050101, 2504721, 23886875, -13117525, 13958495, -5732453 },
+        },
+        {
+            { -23481610, 4867226, -27247128, 3900521, 29838369, -8212291, -31889399, -10041781, 7340521, -15410068 },
+            { 4646514, -8011124, -22766023, -11532654, 23184553, 8566613, 31366726, -1381061, -15066784, -10375192 },
+            { -17270517, 12723032, -16993061, 14878794, 21619651, -6197576, 27584817, 3093888, -8843694, 3849921 },
+        },
+        {
+            { -9064912, 2103172, 25561640, -15125738, -5239824, 9582958, 32477045, -9017955, 5002294, -15550259 },
+            { -12057553, -11177906, 21115585, -13365155, 8808712, -12030708, 16489530, 13378448, -25845716, 12741426 },
+            { -5946367, 10645103, -30911586, 15390284, -3286982, -7118677, 24306472, 15852464, 28834118, -7646072 },
+        },
+        {
+            { -17335748, -9107057, -24531279, 9434953, -8472084, -583362, -13090771, 455841, 20461858, 5491305 },
+            { 13669248, -16095482, -12481974, -10203039, -14569770, -11893198, -24995986, 11293807, -28588204, -9421832 },
+            { 28497928, 6272777, -33022994, 14470570, 8906179, -1225630, 18504674, -14165166, 29867745, -8795943 },
+        },
+        {
+            { -16207023, 13517196, -27799630, -13697798, 24009064, -6373891, -6367600, -13175392, 22853429, -4012011 },
+            { 24191378, 16712145, -13931797, 15217831, 14542237, 1646131, 18603514, -11037887, 12876623, -2112447 },
+            { 17902668, 4518229, -411702, -2829247, 26878217, 5258055, -12860753, 608397, 16031844, 3723494 },
+        },
+        {
+            { -28632773, 12763728, -20446446, 7577504, 33001348, -13017745, 17558842, -7872890, 23896954, -4314245 },
+            { -20005381, -12011952, 31520464, 605201, 2543521, 5991821, -2945064, 7229064, -9919646, -8826859 },
+            { 28816045, 298879, -28165016, -15920938, 19000928, -1665890, -12680833, -2949325, -18051778, -2082915 },
+        },
+        {
+            { 16000882, -344896, 3493092, -11447198, -29504595, -13159789, 12577740, 16041268, -19715240, 7847707 },
+            { 10151868, 10572098, 27312476, 7922682, 14825339, 4723128, -32855931, -6519018, -10020567, 3852848 },
+            { -11430470, 15697596, -21121557, -4420647, 5386314, 15063598, 16514493, -15932110, 29330899, -15076224 },
+        },
+    },
+    {
+        {
+            { -25499735, -4378794, -15222908, -6901211, 16615731, 2051784, 3303702, 15490, -27548796, 12314391 },
+            { 15683520, -6003043, 18109120, -9980648, 15337968, -5997823, -16717435, 15921866, 16103996, -3731215 },
+            { -23169824, -10781249, 13588192, -1628807, -3798557, -1074929, -19273607, 5402699, -29815713, -9841101 },
+        },
+        {
+            { 23190676, 2384583, -32714340, 3462154, -29903655, -1529132, -11266856, 8911517, -25205859, 2739713 },
+            { 21374101, -3554250, -33524649, 9874411, 15377179, 11831242, -33529904, 6134907, 4931255, 11987849 },
+            { -7732, -2978858, -16223486, 7277597, 105524, -322051, -31480539, 13861388, -30076310, 10117930 },
+        },
+        {
+            { -29501170, -10744872, -26163768, 13051539, -25625564, 5089643, -6325503, 6704079, 12890019, 15728940 },
+            { -21972360, -11771379, -951059, -4418840, 14704840, 2695116, 903376, -10428139, 12885167, 8311031 },
+            { -17516482, 5352194, 10384213, -13811658, 7506451, 13453191, 26423267, 4384730, 1888765, -5435404 },
+        },
+        {
+            { -25817338, -3107312, -13494599, -3182506, 30896459, -13921729, -32251644, -12707869, -19464434, -3340243 },
+            { -23607977, -2665774, -526091, 4651136, 5765089, 4618330, 6092245, 14845197, 17151279, -9854116 },
+            { -24830458, -12733720, -15165978, 10367250, -29530908, -265356, 22825805, -7087279, -16866484, 16176525 },
+        },
+        {
+            { -23583256, 6564961, 20063689, 3798228, -4740178, 7359225, 2006182, -10363426, -28746253, -10197509 },
+            { -10626600, -4486402, -13320562, -5125317, 3432136, -6393229, 23632037, -1940610, 32808310, 1099883 },
+            { 15030977, 5768825, -27451236, -2887299, -6427378, -15361371, -15277896, -6809350, 2051441, -15225865 },
+        },
+        {
+            { -3362323, -7239372, 7517890, 9824992, 23555850, 295369, 5148398, -14154188, -22686354, 16633660 },
+            { 4577086, -16752288, 13249841, -15304328, 19958763, -14537274, 18559670, -10759549, 8402478, -9864273 },
+            { -28406330, -1051581, -26790155, -907698, -17212414, -11030789, 9453451, -14980072, 17983010, 9967138 },
+        },
+        {
+            { -25762494, 6524722, 26585488, 9969270, 24709298, 1220360, -1677990, 7806337, 17507396, 3651560 },
+            { -10420457, -4118111, 14584639, 15971087, -15768321, 8861010, 26556809, -5574557, -18553322, -11357135 },
+            { 2839101, 14284142, 4029895, 3472686, 14402957, 12689363, -26642121, 8459447, -5605463, -7621941 },
+        },
+        {
+            { -4839289, -3535444, 9744961, 2871048, 25113978, 3187018, -25110813, -849066, 17258084, -7977739 },
+            { 18164541, -10595176, -17154882, -1542417, 19237078, -9745295, 23357533, -15217008, 26908270, 12150756 },
+            { -30264870, -7647865, 5112249, -7036672, -1499807, -6974257, 43168, -5537701, -32302074, 16215819 },
+        },
+    },
+    {
+        {
+            { -6898905, 9824394, -12304779, -4401089, -31397141, -6276835, 32574489, 12532905, -7503072, -8675347 },
+            { -27343522, -16515468, -27151524, -10722951, 946346, 16291093, 254968, 7168080, 21676107, -1943028 },
+            { 21260961, -8424752, -16831886, -11920822, -23677961, 3968121, -3651949, -6215466, -3556191, -7913075 },
+        },
+        {
+            { 16544754, 13250366, -16804428, 15546242, -4583003, 12757258, -2462308, -8680336, -18907032, -9662799 },
+            { -2415239, -15577728, 18312303, 4964443, -15272530, -12653564, 26820651, 16690659, 25459437, -4564609 },
+            { -25144690, 11425020, 28423002, -11020557, -6144921, -15826224, 9142795, -2391602, -6432418, -1644817 },
+        },
+        {
+            { -23104652, 6253476, 16964147, -3768872, -25113972, -12296437, -27457225, -16344658, 6335692, 7249989 },
+            { -30333227, 13979675, 7503222, -12368314, -11956721, -4621693, -30272269, 2682242, 25993170, -12478523 },
+            { 4364628, 5930691, 32304656, -10044554, -8054781, 15091131, 22857016, -10598955, 31820368, 15075278 },
+        },
+        {
+            { 31879134, -8918693, 17258761, 90626, -8041836, -4917709, 24162788, -9650886, -17970238, 12833045 },
+            { 19073683, 14851414, -24403169, -11860168, 7625278, 11091125, -19619190, 2074449, -9413939, 14905377 },
+            { 24483667, -11935567, -2518866, -11547418, -1553130, 15355506, -25282080, 9253129, 27628530, -7555480 },
+        },
+        {
+            { 17597607, 8340603, 19355617, 552187, 26198470, -3176583, 4593324, -9157582, -14110875, 15297016 },
+            { 510886, 14337390, -31785257, 16638632, 6328095, 2713355, -20217417, -11864220, 8683221, 2921426 },
+            { 18606791, 11874196, 27155355, -5281482, -24031742, 6265446, -25178240, -1278924, 4674690, 13890525 },
+        },
+        {
+            { 13609624, 13069022, -27372361, -13055908, 24360586, 9592974, 14977157, 9835105, 4389687, 288396 },
+            { 9922506, -519394, 13613107, 5883594, -18758345, -434263, -12304062, 8317628, 23388070, 16052080 },
+            { 12720016, 11937594, -31970060, -5028689, 26900120, 8561328, -20155687, -11632979, -14754271, -10812892 },
+        },
+        {
+            { 15961858, 14150409, 26716931, -665832, -22794328, 13603569, 11829573, 7467844, -28822128, 929275 },
+            { 11038231, -11582396, -27310482, -7316562, -10498527, -16307831, -23479533, -9371869, -21393143, 2465074 },
+            { 20017163, -4323226, 27915242, 1529148, 12396362, 15675764, 13817261, -9658066, 2463391, -4622140 },
+        },
+        {
+            { -16358878, -12663911, -12065183, 4996454, -1256422, 1073572, 9583558, 12851107, 4003896, 12673717 },
+            { -1731589, -15155870, -3262930, 16143082, 19294135, 13385325, 14741514, -9103726, 7903886, 2348101 },
+            { 24536016, -16515207, 12715592, -3862155, 1511293, 10047386, -3842346, -7129159, -28377538, 10048127 },
+        },
+    },
+    {
+        {
+            { -12622226, -6204820, 30718825, 2591312, -10617028, 12192840, 18873298, -7297090, -32297756, 15221632 },
+            { -26478122, -11103864, 11546244, -1852483, 9180880, 7656409, -21343950, 2095755, 29769758, 6593415 },
+            { -31994208, -2907461, 4176912, 3264766, 12538965, -868111, 26312345, -6118678, 30958054, 8292160 },
+        },
+        {
+            { 31429822, -13959116, 29173532, 15632448, 12174511, -2760094, 32808831, 3977186, 26143136, -3148876 },
+            { 22648901, 1402143, -22799984, 13746059, 7936347, 365344, -8668633, -1674433, -3758243, -2304625 },
+            { -15491917, 8012313, -2514730, -12702462, -23965846, -10254029, -1612713, -1535569, -16664475, 8194478 },
+        },
+        {
+            { 27338066, -7507420, -7414224, 10140405, -19026427, -6589889, 27277191, 8855376, 28572286, 3005164 },
+            { 26287124, 4821776, 25476601, -4145903, -3764513, -15788984, -18008582, 1182479, -26094821, -13079595 },
+            { -7171154, 3178080, 23970071, 6201893, -17195577, -4489192, -21876275, -13982627, 32208683, -1198248 },
+        },
+        {
+            { -16657702, 2817643, -10286362, 14811298, 6024667, 13349505, -27315504, -10497842, -27672585, -11539858 },
+            { 15941029, -9405932, -21367050, 8062055, 31876073, -238629, -15278393, -1444429, 15397331, -4130193 },
+            { 8934485, -13485467, -23286397, -13423241, -32446090, 14047986, 31170398, -1441021, -27505566, 15087184 },
+        },
+        {
+            { -18357243, -2156491, 24524913, -16677868, 15520427, -6360776, -15502406, 11461896, 16788528, -5868942 },
+            { -1947386, 16013773, 21750665, 3714552, -17401782, -16055433, -3770287, -10323320, 31322514, -11615635 },
+            { 21426655, -5650218, -13648287, -5347537, -28812189, -4920970, -18275391, -14621414, 13040862, -12112948 },
+        },
+        {
+            { 11293895, 12478086, -27136401, 15083750, -29307421, 14748872, 14555558, -13417103, 1613711, 4896935 },
+            { -25894883, 15323294, -8489791, -8057900, 25967126, -13425460, 2825960, -4897045, -23971776, -11267415 },
+            { -15924766, -5229880, -17443532, 6410664, 3622847, 10243618, 20615400, 12405433, -23753030, -8436416 },
+        },
+        {
+            { -7091295, 12556208, -20191352, 9025187, -17072479, 4333801, 4378436, 2432030, 23097949, -566018 },
+            { 4565804, -16025654, 20084412, -7842817, 1724999, 189254, 24767264, 10103221, -18512313, 2424778 },
+            { 366633, -11976806, 8173090, -6890119, 30788634, 5745705, -7168678, 1344109, -3642553, 12412659 },
+        },
+        {
+            { -24001791, 7690286, 14929416, -168257, -32210835, -13412986, 24162697, -15326504, -3141501, 11179385 },
+            { 18289522, -14724954, 8056945, 16430056, -21729724, 7842514, -6001441, -1486897, -18684645, -11443503 },
+            { 476239, 6601091, -6152790, -9723375, 17503545, -4863900, 27672959, 13403813, 11052904, 5219329 },
+        },
+    },
+    {
+        {
+            { 20678546, -8375738, -32671898, 8849123, -5009758, 14574752, 31186971, -3973730, 9014762, -8579056 },
+            { -13644050, -10350239, -15962508, 5075808, -1514661, -11534600, -33102500, 9160280, 8473550, -3256838 },
+            { 24900749, 14435722, 17209120, -15292541, -22592275, 9878983, -7689309, -16335821, -24568481, 11788948 },
+        },
+        {
+            { -3118155, -11395194, -13802089, 14797441, 9652448, -6845904, -20037437, 10410733, -24568470, -1458691 },
+            { -15659161, 16736706, -22467150, 10215878, -9097177, 7563911, 11871841, -12505194, -18513325, 8464118 },
+            { -23400612, 8348507, -14585951, -861714, -3950205, -6373419, 14325289, 8628612, 33313881, -8370517 },
+        },
+        {
+            { -20186973, -4967935, 22367356, 5271547, -1097117, -4788838, -24805667, -10236854, -8940735, -5818269 },
+            { -6948785, -1795212, -32625683, -16021179, 32635414, -7374245, 15989197, -12838188, 28358192, -4253904 },
+            { -23561781, -2799059, -32351682, -1661963, -9147719, 10429267, -16637684, 4072016, -5351664, 5596589 },
+        },
+        {
+            { -28236598, -3390048, 12312896, 6213178, 3117142, 16078565, 29266239, 2557221, 1768301, 15373193 },
+            { -7243358, -3246960, -4593467, -7553353, -127927, -912245, -1090902, -4504991, -24660491, 3442910 },
+            { -30210571, 5124043, 14181784, 8197961, 18964734, -11939093, 22597931, 7176455, -18585478, 13365930 },
+        },
+        {
+            { -7877390, -1499958, 8324673, 4690079, 6261860, 890446, 24538107, -8570186, -9689599, -3031667 },
+            { 25008904, -10771599, -4305031, -9638010, 16265036, 15721635, 683793, -11823784, 15723479, -15163481 },
+            { -9660625, 12374379, -27006999, -7026148, -7724114, -12314514, 11879682, 5400171, 519526, -1235876 },
+        },
+        {
+            { 22258397, -16332233, -7869817, 14613016, -22520255, -2950923, -20353881, 7315967, 16648397, 7605640 },
+            { -8081308, -8464597, -8223311, 9719710, 19259459, -15348212, 23994942, -5281555, -9468848, 4763278 },
+            { -21699244, 9220969, -15730624, 1084137, -25476107, -2852390, 31088447, -7764523, -11356529, 728112 },
+        },
+        {
+            { 26047220, -11751471, -6900323, -16521798, 24092068, 9158119, -4273545, -12555558, -29365436, -5498272 },
+            { 17510331, -322857, 5854289, 8403524, 17133918, -3112612, -28111007, 12327945, 10750447, 10014012 },
+            { -10312768, 3936952, 9156313, -8897683, 16498692, -994647, -27481051, -666732, 3424691, 7540221 },
+        },
+        {
+            { 30322361, -6964110, 11361005, -4143317, 7433304, 4989748, -7071422, -16317219, -9244265, 15258046 },
+            { 13054562, -2779497, 19155474, 469045, -12482797, 4566042, 5631406, 2711395, 1062915, -5136345 },
+            { -19240248, -11254599, -29509029, -7499965, -5835763, 13005411, -6066489, 12194497, 32960380, 1459310 },
+        },
+    },
+    {
+        {
+            { 19852034, 7027924, 23669353, 10020366, 8586503, -6657907, 394197, -6101885, 18638003, -11174937 },
+            { 31395534, 15098109, 26581030, 8030562, -16527914, -5007134, 9012486, -7584354, -6643087, -5442636 },
+            { -9192165, -2347377, -1997099, 4529534, 25766844, 607986, -13222, 9677543, -32294889, -6456008 },
+        },
+        {
+            { -2444496, -149937, 29348902, 8186665, 1873760, 12489863, -30934579, -7839692, -7852844, -8138429 },
+            { -15236356, -15433509, 7766470, 746860, 26346930, -10221762, -27333451, 10754588, -9431476, 5203576 },
+            { 31834314, 14135496, -770007, 5159118, 20917671, -16768096, -7467973, -7337524, 31809243, 7347066 },
+        },
+        {
+            { -9606723, -11874240, 20414459, 13033986, 13716524, -11691881, 19797970, -12211255, 15192876, -2087490 },
+            { -12663563, -2181719, 1168162, -3804809, 26747877, -14138091, 10609330, 12694420, 33473243, -13382104 },
+            { 33184999, 11180355, 15832085, -11385430, -1633671, 225884, 15089336, -11023903, -6135662, 14480053 },
+        },
+        {
+            { 31308717, -5619998, 31030840, -1897099, 15674547, -6582883, 5496208, 13685227, 27595050, 8737275 },
+            { -20318852, -15150239, 10933843, -16178022, 8335352, -7546022, -31008351, -12610604, 26498114, 66511 },
+            { 22644454, -8761729, -16671776, 4884562, -3105614, -13559366, 30540766, -4286747, -13327787, -7515095 },
+        },
+        {
+            { -28017847, 9834845, 18617207, -2681312, -3401956, -13307506, 8205540, 13585437, -17127465, 15115439 },
+            { 23711543, -672915, 31206561, -8362711, 6164647, -9709987, -33535882, -1426096, 8236921, 16492939 },
+            { -23910559, -13515526, -26299483, -4503841, 25005590, -7687270, 19574902, 10071562, 6708380, -6222424 },
+        },
+        {
+            { 2101391, -4930054, 19702731, 2367575, -15427167, 1047675, 5301017, 9328700, 29955601, -11678310 },
+            { 3096359, 9271816, -21620864, -15521844, -14847996, -7592937, -25892142, -12635595, -9917575, 6216608 },
+            { -32615849, 338663, -25195611, 2510422, -29213566, -13820213, 24822830, -6146567, -26767480, 7525079 },
+        },
+        {
+            { -23066649, -13985623, 16133487, -7896178, -3389565, 778788, -910336, -2782495, -19386633, 11994101 },
+            { 21691500, -13624626, -641331, -14367021, 3285881, -3483596, -25064666, 9718258, -7477437, 13381418 },
+            { 18445390, -4202236, 14979846, 11622458, -1727110, -3582980, 23111648, -6375247, 28535282, 15779576 },
+        },
+        {
+            { 30098053, 3089662, -9234387, 16662135, -21306940, 11308411, -14068454, 12021730, 9955285, -16303356 },
+            { 9734894, -14576830, -7473633, -9138735, 2060392, 11313496, -18426029, 9924399, 20194861, 13380996 },
+            { -26378102, -7965207, -22167821, 15789297, -18055342, -6168792, -1984914, 15707771, 26342023, 10146099 },
+        },
+    },
+    {
+        {
+            { -26016874, -219943, 21339191, -41388, 19745256, -2878700, -29637280, 2227040, 21612326, -545728 },
+            { -13077387, 1184228, 23562814, -5970442, -20351244, -6348714, 25764461, 12243797, -20856566, 11649658 },
+            { -10031494, 11262626, 27384172, 2271902, 26947504, -15997771, 39944, 6114064, 33514190, 2333242 },
+        },
+        {
+            { -21433588, -12421821, 8119782, 7219913, -21830522, -9016134, -6679750, -12670638, 24350578, -13450001 },
+            { -4116307, -11271533, -23886186, 4843615, -30088339, 690623, -31536088, -10406836, 8317860, 12352766 },
+            { 18200138, -14475911, -33087759, -2696619, -23702521, -9102511, -23552096, -2287550, 20712163, 6719373 },
+        },
+        {
+            { 26656208, 6075253, -7858556, 1886072, -28344043, 4262326, 11117530, -3763210, 26224235, -3297458 },
+            { -17168938, -14854097, -3395676, -16369877, -19954045, 14050420, 21728352, 9493610, 18620611, -16428628 },
+            { -13323321, 13325349, 11432106, 5964811, 18609221, 6062965, -5269471, -9725556, -30701573, -16479657 },
+        },
+        {
+            { -23860538, -11233159, 26961357, 1640861, -32413112, -16737940, 12248509, -5240639, 13735342, 1934062 },
+            { 25089769, 6742589, 17081145, -13406266, 21909293, -16067981, -15136294, -3765346, -21277997, 5473616 },
+            { 31883677, -7961101, 1083432, -11572403, 22828471, 13290673, -7125085, 12469656, 29111212, -5451014 },
+        },
+        {
+            { 24244947, -15050407, -26262976, 2791540, -14997599, 16666678, 24367466, 6388839, -10295587, 452383 },
+            { -25640782, -3417841, 5217916, 16224624, 19987036, -4082269, -24236251, -5915248, 15766062, 8407814 },
+            { -20406999, 13990231, 15495425, 16395525, 5377168, 15166495, -8917023, -4388953, -8067909, 2276718 },
+        },
+        {
+            { 30157918, 12924066, -17712050, 9245753, 19895028, 3368142, -23827587, 5096219, 22740376, -7303417 },
+            { 2041139, -14256350, 7783687, 13876377, -25946985, -13352459, 24051124, 13742383, -15637599, 13295222 },
+            { 33338237, -8505733, 12532113, 7977527, 9106186, -1715251, -17720195, -4612972, -4451357, -14669444 },
+        },
+        {
+            { -20045281, 5454097, -14346548, 6447146, 28862071, 1883651, -2469266, -4141880, 7770569, 9620597 },
+            { 23208068, 7979712, 33071466, 8149229, 1758231, -10834995, 30945528, -1694323, -33502340, -14767970 },
+            { 1439958, -16270480, -1079989, -793782, 4625402, 10647766, -5043801, 1220118, 30494170, -11440799 },
+        },
+        {
+            { -5037580, -13028295, -2970559, -3061767, 15640974, -6701666, -26739026, 926050, -1684339, -13333647 },
+            { 13908495, -3549272, 30919928, -6273825, -21521863, 7989039, 9021034, 9078865, 3353509, 4033511 },
+            { -29663431, -15113610, 32259991, -344482, 24295849, -12912123, 23161163, 8839127, 27485041, 7356032 },
+        },
+    },
+    {
+        {
+            { 9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142, 2625015, 28431036, -16771834 },
+            { -23839233, -8311415, -25945511, 7480958, -17681669, -8354183, -22545972, 14150565, 15970762, 4099461 },
+            { 29262576, 16756590, 26350592, -8793563, 8529671, -11208050, 13617293, -9937143, 11465739, 8317062 },
+        },
+        {
+            { -25493081, -6962928, 32500200, -9419051, -23038724, -2302222, 14898637, 3848455, 20969334, -5157516 },
+            { -20384450, -14347713, -18336405, 13884722, -33039454, 2842114, -21610826, -3649888, 11177095, 14989547 },
+            { -24496721, -11716016, 16959896, 2278463, 12066309, 10137771, 13515641, 2581286, -28487508, 9930240 },
+        },
+        {
+            { -17751622, -2097826, 16544300, -13009300, -15914807, -14949081, 18345767, -13403753, 16291481, -5314038 },
+            { -33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774, 6957617, 4368891, 9788741 },
+            { 16660756, 7281060, -10830758, 12911820, 20108584, -8101676, -21722536, -8613148, 16250552, -11111103 },
+        },
+        {
+            { -19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584, 10604807, -30190403, 4782747 },
+            { -1354539, 14736941, -7367442, -13292886, 7710542, -14155590, -9981571, 4383045, 22546403, 437323 },
+            { 31665577, -12180464, -16186830, 1491339, -18368625, 3294682, 27343084, 2786261, -30633590, -14097016 },
+        },
+        {
+            { -14467279, -683715, -33374107, 7448552, 19294360, 14334329, -19690631, 2355319, -19284671, -6114373 },
+            { 15121312, -15796162, 6377020, -6031361, -10798111, -12957845, 18952177, 15496498, -29380133, 11754228 },
+            { -2637277, -13483075, 8488727, -14303896, 12728761, -1622493, 7141596, 11724556, 22761615, -10134141 },
+        },
+        {
+            { 16918416, 11729663, -18083579, 3022987, -31015732, -13339659, -28741185, -12227393, 32851222, 11717399 },
+            { 11166634, 7338049, -6722523, 4531520, -29468672, -7302055, 31474879, 3483633, -1193175, -4030831 },
+            { -185635, 9921305, 31456609, -13536438, -12013818, 13348923, 33142652, 6546660, -19985279, -3948376 },
+        },
+        {
+            { -32460596, 11266712, -11197107, -7899103, 31703694, 3855903, -8537131, -12833048, -30772034, -15486313 },
+            { -18006477, 12709068, 3991746, -6479188, -21491523, -10550425, -31135347, -16049879, 10928917, 3011958 },
+            { -6957757, -15594337, 31696059, 334240, 29576716, 14796075, -30831056, -12805180, 18008031, 10258577 },
+        },
+        {
+            { -22448644, 15655569, 7018479, -4410003, -30314266, -1201591, -1853465, 1367120, 25127874, 6671743 },
+            { 29701166, -14373934, -10878120, 9279288, -17568, 13127210, 21382910, 11042292, 25838796, 4642684 },
+            { -20430234, 14955537, -24126347, 8124619, -5369288, -5990470, 30468147, -13900640, 18423289, 4177476 },
+        },
+    },
+};
diff --git a/3rd_party/ed25519/sc.c b/3rd_party/ed25519/sc.c
new file mode 100644
index 0000000..ca5bad2
--- /dev/null
+++ b/3rd_party/ed25519/sc.c
@@ -0,0 +1,809 @@
+#include "fixedint.h"
+#include "sc.h"
+
+static uint64_t load_3(const unsigned char *in) {
+    uint64_t result;
+
+    result = (uint64_t) in[0];
+    result |= ((uint64_t) in[1]) << 8;
+    result |= ((uint64_t) in[2]) << 16;
+
+    return result;
+}
+
+static uint64_t load_4(const unsigned char *in) {
+    uint64_t result;
+
+    result = (uint64_t) in[0];
+    result |= ((uint64_t) in[1]) << 8;
+    result |= ((uint64_t) in[2]) << 16;
+    result |= ((uint64_t) in[3]) << 24;
+    
+    return result;
+}
+
+/*
+Input:
+  s[0]+256*s[1]+...+256^63*s[63] = s
+
+Output:
+  s[0]+256*s[1]+...+256^31*s[31] = s mod l
+  where l = 2^252 + 27742317777372353535851937790883648493.
+  Overwrites s in place.
+*/
+
+void sc_reduce(unsigned char *s) {
+    int64_t s0 = 2097151 & load_3(s);
+    int64_t s1 = 2097151 & (load_4(s + 2) >> 5);
+    int64_t s2 = 2097151 & (load_3(s + 5) >> 2);
+    int64_t s3 = 2097151 & (load_4(s + 7) >> 7);
+    int64_t s4 = 2097151 & (load_4(s + 10) >> 4);
+    int64_t s5 = 2097151 & (load_3(s + 13) >> 1);
+    int64_t s6 = 2097151 & (load_4(s + 15) >> 6);
+    int64_t s7 = 2097151 & (load_3(s + 18) >> 3);
+    int64_t s8 = 2097151 & load_3(s + 21);
+    int64_t s9 = 2097151 & (load_4(s + 23) >> 5);
+    int64_t s10 = 2097151 & (load_3(s + 26) >> 2);
+    int64_t s11 = 2097151 & (load_4(s + 28) >> 7);
+    int64_t s12 = 2097151 & (load_4(s + 31) >> 4);
+    int64_t s13 = 2097151 & (load_3(s + 34) >> 1);
+    int64_t s14 = 2097151 & (load_4(s + 36) >> 6);
+    int64_t s15 = 2097151 & (load_3(s + 39) >> 3);
+    int64_t s16 = 2097151 & load_3(s + 42);
+    int64_t s17 = 2097151 & (load_4(s + 44) >> 5);
+    int64_t s18 = 2097151 & (load_3(s + 47) >> 2);
+    int64_t s19 = 2097151 & (load_4(s + 49) >> 7);
+    int64_t s20 = 2097151 & (load_4(s + 52) >> 4);
+    int64_t s21 = 2097151 & (load_3(s + 55) >> 1);
+    int64_t s22 = 2097151 & (load_4(s + 57) >> 6);
+    int64_t s23 = (load_4(s + 60) >> 3);
+    int64_t carry0;
+    int64_t carry1;
+    int64_t carry2;
+    int64_t carry3;
+    int64_t carry4;
+    int64_t carry5;
+    int64_t carry6;
+    int64_t carry7;
+    int64_t carry8;
+    int64_t carry9;
+    int64_t carry10;
+    int64_t carry11;
+    int64_t carry12;
+    int64_t carry13;
+    int64_t carry14;
+    int64_t carry15;
+    int64_t carry16;
+
+    s11 += s23 * 666643;
+    s12 += s23 * 470296;
+    s13 += s23 * 654183;
+    s14 -= s23 * 997805;
+    s15 += s23 * 136657;
+    s16 -= s23 * 683901;
+    s23 = 0;
+    s10 += s22 * 666643;
+    s11 += s22 * 470296;
+    s12 += s22 * 654183;
+    s13 -= s22 * 997805;
+    s14 += s22 * 136657;
+    s15 -= s22 * 683901;
+    s22 = 0;
+    s9 += s21 * 666643;
+    s10 += s21 * 470296;
+    s11 += s21 * 654183;
+    s12 -= s21 * 997805;
+    s13 += s21 * 136657;
+    s14 -= s21 * 683901;
+    s21 = 0;
+    s8 += s20 * 666643;
+    s9 += s20 * 470296;
+    s10 += s20 * 654183;
+    s11 -= s20 * 997805;
+    s12 += s20 * 136657;
+    s13 -= s20 * 683901;
+    s20 = 0;
+    s7 += s19 * 666643;
+    s8 += s19 * 470296;
+    s9 += s19 * 654183;
+    s10 -= s19 * 997805;
+    s11 += s19 * 136657;
+    s12 -= s19 * 683901;
+    s19 = 0;
+    s6 += s18 * 666643;
+    s7 += s18 * 470296;
+    s8 += s18 * 654183;
+    s9 -= s18 * 997805;
+    s10 += s18 * 136657;
+    s11 -= s18 * 683901;
+    s18 = 0;
+    carry6 = (s6 + (1 << 20)) >> 21;
+    s7 += carry6;
+    s6 -= carry6 << 21;
+    carry8 = (s8 + (1 << 20)) >> 21;
+    s9 += carry8;
+    s8 -= carry8 << 21;
+    carry10 = (s10 + (1 << 20)) >> 21;
+    s11 += carry10;
+    s10 -= carry10 << 21;
+    carry12 = (s12 + (1 << 20)) >> 21;
+    s13 += carry12;
+    s12 -= carry12 << 21;
+    carry14 = (s14 + (1 << 20)) >> 21;
+    s15 += carry14;
+    s14 -= carry14 << 21;
+    carry16 = (s16 + (1 << 20)) >> 21;
+    s17 += carry16;
+    s16 -= carry16 << 21;
+    carry7 = (s7 + (1 << 20)) >> 21;
+    s8 += carry7;
+    s7 -= carry7 << 21;
+    carry9 = (s9 + (1 << 20)) >> 21;
+    s10 += carry9;
+    s9 -= carry9 << 21;
+    carry11 = (s11 + (1 << 20)) >> 21;
+    s12 += carry11;
+    s11 -= carry11 << 21;
+    carry13 = (s13 + (1 << 20)) >> 21;
+    s14 += carry13;
+    s13 -= carry13 << 21;
+    carry15 = (s15 + (1 << 20)) >> 21;
+    s16 += carry15;
+    s15 -= carry15 << 21;
+    s5 += s17 * 666643;
+    s6 += s17 * 470296;
+    s7 += s17 * 654183;
+    s8 -= s17 * 997805;
+    s9 += s17 * 136657;
+    s10 -= s17 * 683901;
+    s17 = 0;
+    s4 += s16 * 666643;
+    s5 += s16 * 470296;
+    s6 += s16 * 654183;
+    s7 -= s16 * 997805;
+    s8 += s16 * 136657;
+    s9 -= s16 * 683901;
+    s16 = 0;
+    s3 += s15 * 666643;
+    s4 += s15 * 470296;
+    s5 += s15 * 654183;
+    s6 -= s15 * 997805;
+    s7 += s15 * 136657;
+    s8 -= s15 * 683901;
+    s15 = 0;
+    s2 += s14 * 666643;
+    s3 += s14 * 470296;
+    s4 += s14 * 654183;
+    s5 -= s14 * 997805;
+    s6 += s14 * 136657;
+    s7 -= s14 * 683901;
+    s14 = 0;
+    s1 += s13 * 666643;
+    s2 += s13 * 470296;
+    s3 += s13 * 654183;
+    s4 -= s13 * 997805;
+    s5 += s13 * 136657;
+    s6 -= s13 * 683901;
+    s13 = 0;
+    s0 += s12 * 666643;
+    s1 += s12 * 470296;
+    s2 += s12 * 654183;
+    s3 -= s12 * 997805;
+    s4 += s12 * 136657;
+    s5 -= s12 * 683901;
+    s12 = 0;
+    carry0 = (s0 + (1 << 20)) >> 21;
+    s1 += carry0;
+    s0 -= carry0 << 21;
+    carry2 = (s2 + (1 << 20)) >> 21;
+    s3 += carry2;
+    s2 -= carry2 << 21;
+    carry4 = (s4 + (1 << 20)) >> 21;
+    s5 += carry4;
+    s4 -= carry4 << 21;
+    carry6 = (s6 + (1 << 20)) >> 21;
+    s7 += carry6;
+    s6 -= carry6 << 21;
+    carry8 = (s8 + (1 << 20)) >> 21;
+    s9 += carry8;
+    s8 -= carry8 << 21;
+    carry10 = (s10 + (1 << 20)) >> 21;
+    s11 += carry10;
+    s10 -= carry10 << 21;
+    carry1 = (s1 + (1 << 20)) >> 21;
+    s2 += carry1;
+    s1 -= carry1 << 21;
+    carry3 = (s3 + (1 << 20)) >> 21;
+    s4 += carry3;
+    s3 -= carry3 << 21;
+    carry5 = (s5 + (1 << 20)) >> 21;
+    s6 += carry5;
+    s5 -= carry5 << 21;
+    carry7 = (s7 + (1 << 20)) >> 21;
+    s8 += carry7;
+    s7 -= carry7 << 21;
+    carry9 = (s9 + (1 << 20)) >> 21;
+    s10 += carry9;
+    s9 -= carry9 << 21;
+    carry11 = (s11 + (1 << 20)) >> 21;
+    s12 += carry11;
+    s11 -= carry11 << 21;
+    s0 += s12 * 666643;
+    s1 += s12 * 470296;
+    s2 += s12 * 654183;
+    s3 -= s12 * 997805;
+    s4 += s12 * 136657;
+    s5 -= s12 * 683901;
+    s12 = 0;
+    carry0 = s0 >> 21;
+    s1 += carry0;
+    s0 -= carry0 << 21;
+    carry1 = s1 >> 21;
+    s2 += carry1;
+    s1 -= carry1 << 21;
+    carry2 = s2 >> 21;
+    s3 += carry2;
+    s2 -= carry2 << 21;
+    carry3 = s3 >> 21;
+    s4 += carry3;
+    s3 -= carry3 << 21;
+    carry4 = s4 >> 21;
+    s5 += carry4;
+    s4 -= carry4 << 21;
+    carry5 = s5 >> 21;
+    s6 += carry5;
+    s5 -= carry5 << 21;
+    carry6 = s6 >> 21;
+    s7 += carry6;
+    s6 -= carry6 << 21;
+    carry7 = s7 >> 21;
+    s8 += carry7;
+    s7 -= carry7 << 21;
+    carry8 = s8 >> 21;
+    s9 += carry8;
+    s8 -= carry8 << 21;
+    carry9 = s9 >> 21;
+    s10 += carry9;
+    s9 -= carry9 << 21;
+    carry10 = s10 >> 21;
+    s11 += carry10;
+    s10 -= carry10 << 21;
+    carry11 = s11 >> 21;
+    s12 += carry11;
+    s11 -= carry11 << 21;
+    s0 += s12 * 666643;
+    s1 += s12 * 470296;
+    s2 += s12 * 654183;
+    s3 -= s12 * 997805;
+    s4 += s12 * 136657;
+    s5 -= s12 * 683901;
+    s12 = 0;
+    carry0 = s0 >> 21;
+    s1 += carry0;
+    s0 -= carry0 << 21;
+    carry1 = s1 >> 21;
+    s2 += carry1;
+    s1 -= carry1 << 21;
+    carry2 = s2 >> 21;
+    s3 += carry2;
+    s2 -= carry2 << 21;
+    carry3 = s3 >> 21;
+    s4 += carry3;
+    s3 -= carry3 << 21;
+    carry4 = s4 >> 21;
+    s5 += carry4;
+    s4 -= carry4 << 21;
+    carry5 = s5 >> 21;
+    s6 += carry5;
+    s5 -= carry5 << 21;
+    carry6 = s6 >> 21;
+    s7 += carry6;
+    s6 -= carry6 << 21;
+    carry7 = s7 >> 21;
+    s8 += carry7;
+    s7 -= carry7 << 21;
+    carry8 = s8 >> 21;
+    s9 += carry8;
+    s8 -= carry8 << 21;
+    carry9 = s9 >> 21;
+    s10 += carry9;
+    s9 -= carry9 << 21;
+    carry10 = s10 >> 21;
+    s11 += carry10;
+    s10 -= carry10 << 21;
+
+    s[0] = (unsigned char) (s0 >> 0);
+    s[1] = (unsigned char) (s0 >> 8);
+    s[2] = (unsigned char) ((s0 >> 16) | (s1 << 5));
+    s[3] = (unsigned char) (s1 >> 3);
+    s[4] = (unsigned char) (s1 >> 11);
+    s[5] = (unsigned char) ((s1 >> 19) | (s2 << 2));
+    s[6] = (unsigned char) (s2 >> 6);
+    s[7] = (unsigned char) ((s2 >> 14) | (s3 << 7));
+    s[8] = (unsigned char) (s3 >> 1);
+    s[9] = (unsigned char) (s3 >> 9);
+    s[10] = (unsigned char) ((s3 >> 17) | (s4 << 4));
+    s[11] = (unsigned char) (s4 >> 4);
+    s[12] = (unsigned char) (s4 >> 12);
+    s[13] = (unsigned char) ((s4 >> 20) | (s5 << 1));
+    s[14] = (unsigned char) (s5 >> 7);
+    s[15] = (unsigned char) ((s5 >> 15) | (s6 << 6));
+    s[16] = (unsigned char) (s6 >> 2);
+    s[17] = (unsigned char) (s6 >> 10);
+    s[18] = (unsigned char) ((s6 >> 18) | (s7 << 3));
+    s[19] = (unsigned char) (s7 >> 5);
+    s[20] = (unsigned char) (s7 >> 13);
+    s[21] = (unsigned char) (s8 >> 0);
+    s[22] = (unsigned char) (s8 >> 8);
+    s[23] = (unsigned char) ((s8 >> 16) | (s9 << 5));
+    s[24] = (unsigned char) (s9 >> 3);
+    s[25] = (unsigned char) (s9 >> 11);
+    s[26] = (unsigned char) ((s9 >> 19) | (s10 << 2));
+    s[27] = (unsigned char) (s10 >> 6);
+    s[28] = (unsigned char) ((s10 >> 14) | (s11 << 7));
+    s[29] = (unsigned char) (s11 >> 1);
+    s[30] = (unsigned char) (s11 >> 9);
+    s[31] = (unsigned char) (s11 >> 17);
+}
+
+
+
+/*
+Input:
+  a[0]+256*a[1]+...+256^31*a[31] = a
+  b[0]+256*b[1]+...+256^31*b[31] = b
+  c[0]+256*c[1]+...+256^31*c[31] = c
+
+Output:
+  s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l
+  where l = 2^252 + 27742317777372353535851937790883648493.
+*/
+
+void sc_muladd(unsigned char *s, const unsigned char *a, const unsigned char *b, const unsigned char *c) {
+    int64_t a0 = 2097151 & load_3(a);
+    int64_t a1 = 2097151 & (load_4(a + 2) >> 5);
+    int64_t a2 = 2097151 & (load_3(a + 5) >> 2);
+    int64_t a3 = 2097151 & (load_4(a + 7) >> 7);
+    int64_t a4 = 2097151 & (load_4(a + 10) >> 4);
+    int64_t a5 = 2097151 & (load_3(a + 13) >> 1);
+    int64_t a6 = 2097151 & (load_4(a + 15) >> 6);
+    int64_t a7 = 2097151 & (load_3(a + 18) >> 3);
+    int64_t a8 = 2097151 & load_3(a + 21);
+    int64_t a9 = 2097151 & (load_4(a + 23) >> 5);
+    int64_t a10 = 2097151 & (load_3(a + 26) >> 2);
+    int64_t a11 = (load_4(a + 28) >> 7);
+    int64_t b0 = 2097151 & load_3(b);
+    int64_t b1 = 2097151 & (load_4(b + 2) >> 5);
+    int64_t b2 = 2097151 & (load_3(b + 5) >> 2);
+    int64_t b3 = 2097151 & (load_4(b + 7) >> 7);
+    int64_t b4 = 2097151 & (load_4(b + 10) >> 4);
+    int64_t b5 = 2097151 & (load_3(b + 13) >> 1);
+    int64_t b6 = 2097151 & (load_4(b + 15) >> 6);
+    int64_t b7 = 2097151 & (load_3(b + 18) >> 3);
+    int64_t b8 = 2097151 & load_3(b + 21);
+    int64_t b9 = 2097151 & (load_4(b + 23) >> 5);
+    int64_t b10 = 2097151 & (load_3(b + 26) >> 2);
+    int64_t b11 = (load_4(b + 28) >> 7);
+    int64_t c0 = 2097151 & load_3(c);
+    int64_t c1 = 2097151 & (load_4(c + 2) >> 5);
+    int64_t c2 = 2097151 & (load_3(c + 5) >> 2);
+    int64_t c3 = 2097151 & (load_4(c + 7) >> 7);
+    int64_t c4 = 2097151 & (load_4(c + 10) >> 4);
+    int64_t c5 = 2097151 & (load_3(c + 13) >> 1);
+    int64_t c6 = 2097151 & (load_4(c + 15) >> 6);
+    int64_t c7 = 2097151 & (load_3(c + 18) >> 3);
+    int64_t c8 = 2097151 & load_3(c + 21);
+    int64_t c9 = 2097151 & (load_4(c + 23) >> 5);
+    int64_t c10 = 2097151 & (load_3(c + 26) >> 2);
+    int64_t c11 = (load_4(c + 28) >> 7);
+    int64_t s0;
+    int64_t s1;
+    int64_t s2;
+    int64_t s3;
+    int64_t s4;
+    int64_t s5;
+    int64_t s6;
+    int64_t s7;
+    int64_t s8;
+    int64_t s9;
+    int64_t s10;
+    int64_t s11;
+    int64_t s12;
+    int64_t s13;
+    int64_t s14;
+    int64_t s15;
+    int64_t s16;
+    int64_t s17;
+    int64_t s18;
+    int64_t s19;
+    int64_t s20;
+    int64_t s21;
+    int64_t s22;
+    int64_t s23;
+    int64_t carry0;
+    int64_t carry1;
+    int64_t carry2;
+    int64_t carry3;
+    int64_t carry4;
+    int64_t carry5;
+    int64_t carry6;
+    int64_t carry7;
+    int64_t carry8;
+    int64_t carry9;
+    int64_t carry10;
+    int64_t carry11;
+    int64_t carry12;
+    int64_t carry13;
+    int64_t carry14;
+    int64_t carry15;
+    int64_t carry16;
+    int64_t carry17;
+    int64_t carry18;
+    int64_t carry19;
+    int64_t carry20;
+    int64_t carry21;
+    int64_t carry22;
+
+    s0 = c0 + a0 * b0;
+    s1 = c1 + a0 * b1 + a1 * b0;
+    s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0;
+    s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0;
+    s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0;
+    s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0;
+    s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0;
+    s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 + a6 * b1 + a7 * b0;
+    s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 + a6 * b2 + a7 * b1 + a8 * b0;
+    s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 + a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0;
+    s10 = c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 + a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0;
+    s11 = c11 + a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 + a6 * b5 + a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0;
+    s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 + a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1;
+    s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 + a9 * b4 + a10 * b3 + a11 * b2;
+    s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 + a10 * b4 + a11 * b3;
+    s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 + a11 * b4;
+    s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5;
+    s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6;
+    s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7;
+    s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8;
+    s20 = a9 * b11 + a10 * b10 + a11 * b9;
+    s21 = a10 * b11 + a11 * b10;
+    s22 = a11 * b11;
+    s23 = 0;
+    carry0 = (s0 + (1 << 20)) >> 21;
+    s1 += carry0;
+    s0 -= carry0 << 21;
+    carry2 = (s2 + (1 << 20)) >> 21;
+    s3 += carry2;
+    s2 -= carry2 << 21;
+    carry4 = (s4 + (1 << 20)) >> 21;
+    s5 += carry4;
+    s4 -= carry4 << 21;
+    carry6 = (s6 + (1 << 20)) >> 21;
+    s7 += carry6;
+    s6 -= carry6 << 21;
+    carry8 = (s8 + (1 << 20)) >> 21;
+    s9 += carry8;
+    s8 -= carry8 << 21;
+    carry10 = (s10 + (1 << 20)) >> 21;
+    s11 += carry10;
+    s10 -= carry10 << 21;
+    carry12 = (s12 + (1 << 20)) >> 21;
+    s13 += carry12;
+    s12 -= carry12 << 21;
+    carry14 = (s14 + (1 << 20)) >> 21;
+    s15 += carry14;
+    s14 -= carry14 << 21;
+    carry16 = (s16 + (1 << 20)) >> 21;
+    s17 += carry16;
+    s16 -= carry16 << 21;
+    carry18 = (s18 + (1 << 20)) >> 21;
+    s19 += carry18;
+    s18 -= carry18 << 21;
+    carry20 = (s20 + (1 << 20)) >> 21;
+    s21 += carry20;
+    s20 -= carry20 << 21;
+    carry22 = (s22 + (1 << 20)) >> 21;
+    s23 += carry22;
+    s22 -= carry22 << 21;
+    carry1 = (s1 + (1 << 20)) >> 21;
+    s2 += carry1;
+    s1 -= carry1 << 21;
+    carry3 = (s3 + (1 << 20)) >> 21;
+    s4 += carry3;
+    s3 -= carry3 << 21;
+    carry5 = (s5 + (1 << 20)) >> 21;
+    s6 += carry5;
+    s5 -= carry5 << 21;
+    carry7 = (s7 + (1 << 20)) >> 21;
+    s8 += carry7;
+    s7 -= carry7 << 21;
+    carry9 = (s9 + (1 << 20)) >> 21;
+    s10 += carry9;
+    s9 -= carry9 << 21;
+    carry11 = (s11 + (1 << 20)) >> 21;
+    s12 += carry11;
+    s11 -= carry11 << 21;
+    carry13 = (s13 + (1 << 20)) >> 21;
+    s14 += carry13;
+    s13 -= carry13 << 21;
+    carry15 = (s15 + (1 << 20)) >> 21;
+    s16 += carry15;
+    s15 -= carry15 << 21;
+    carry17 = (s17 + (1 << 20)) >> 21;
+    s18 += carry17;
+    s17 -= carry17 << 21;
+    carry19 = (s19 + (1 << 20)) >> 21;
+    s20 += carry19;
+    s19 -= carry19 << 21;
+    carry21 = (s21 + (1 << 20)) >> 21;
+    s22 += carry21;
+    s21 -= carry21 << 21;
+    s11 += s23 * 666643;
+    s12 += s23 * 470296;
+    s13 += s23 * 654183;
+    s14 -= s23 * 997805;
+    s15 += s23 * 136657;
+    s16 -= s23 * 683901;
+    s23 = 0;
+    s10 += s22 * 666643;
+    s11 += s22 * 470296;
+    s12 += s22 * 654183;
+    s13 -= s22 * 997805;
+    s14 += s22 * 136657;
+    s15 -= s22 * 683901;
+    s22 = 0;
+    s9 += s21 * 666643;
+    s10 += s21 * 470296;
+    s11 += s21 * 654183;
+    s12 -= s21 * 997805;
+    s13 += s21 * 136657;
+    s14 -= s21 * 683901;
+    s21 = 0;
+    s8 += s20 * 666643;
+    s9 += s20 * 470296;
+    s10 += s20 * 654183;
+    s11 -= s20 * 997805;
+    s12 += s20 * 136657;
+    s13 -= s20 * 683901;
+    s20 = 0;
+    s7 += s19 * 666643;
+    s8 += s19 * 470296;
+    s9 += s19 * 654183;
+    s10 -= s19 * 997805;
+    s11 += s19 * 136657;
+    s12 -= s19 * 683901;
+    s19 = 0;
+    s6 += s18 * 666643;
+    s7 += s18 * 470296;
+    s8 += s18 * 654183;
+    s9 -= s18 * 997805;
+    s10 += s18 * 136657;
+    s11 -= s18 * 683901;
+    s18 = 0;
+    carry6 = (s6 + (1 << 20)) >> 21;
+    s7 += carry6;
+    s6 -= carry6 << 21;
+    carry8 = (s8 + (1 << 20)) >> 21;
+    s9 += carry8;
+    s8 -= carry8 << 21;
+    carry10 = (s10 + (1 << 20)) >> 21;
+    s11 += carry10;
+    s10 -= carry10 << 21;
+    carry12 = (s12 + (1 << 20)) >> 21;
+    s13 += carry12;
+    s12 -= carry12 << 21;
+    carry14 = (s14 + (1 << 20)) >> 21;
+    s15 += carry14;
+    s14 -= carry14 << 21;
+    carry16 = (s16 + (1 << 20)) >> 21;
+    s17 += carry16;
+    s16 -= carry16 << 21;
+    carry7 = (s7 + (1 << 20)) >> 21;
+    s8 += carry7;
+    s7 -= carry7 << 21;
+    carry9 = (s9 + (1 << 20)) >> 21;
+    s10 += carry9;
+    s9 -= carry9 << 21;
+    carry11 = (s11 + (1 << 20)) >> 21;
+    s12 += carry11;
+    s11 -= carry11 << 21;
+    carry13 = (s13 + (1 << 20)) >> 21;
+    s14 += carry13;
+    s13 -= carry13 << 21;
+    carry15 = (s15 + (1 << 20)) >> 21;
+    s16 += carry15;
+    s15 -= carry15 << 21;
+    s5 += s17 * 666643;
+    s6 += s17 * 470296;
+    s7 += s17 * 654183;
+    s8 -= s17 * 997805;
+    s9 += s17 * 136657;
+    s10 -= s17 * 683901;
+    s17 = 0;
+    s4 += s16 * 666643;
+    s5 += s16 * 470296;
+    s6 += s16 * 654183;
+    s7 -= s16 * 997805;
+    s8 += s16 * 136657;
+    s9 -= s16 * 683901;
+    s16 = 0;
+    s3 += s15 * 666643;
+    s4 += s15 * 470296;
+    s5 += s15 * 654183;
+    s6 -= s15 * 997805;
+    s7 += s15 * 136657;
+    s8 -= s15 * 683901;
+    s15 = 0;
+    s2 += s14 * 666643;
+    s3 += s14 * 470296;
+    s4 += s14 * 654183;
+    s5 -= s14 * 997805;
+    s6 += s14 * 136657;
+    s7 -= s14 * 683901;
+    s14 = 0;
+    s1 += s13 * 666643;
+    s2 += s13 * 470296;
+    s3 += s13 * 654183;
+    s4 -= s13 * 997805;
+    s5 += s13 * 136657;
+    s6 -= s13 * 683901;
+    s13 = 0;
+    s0 += s12 * 666643;
+    s1 += s12 * 470296;
+    s2 += s12 * 654183;
+    s3 -= s12 * 997805;
+    s4 += s12 * 136657;
+    s5 -= s12 * 683901;
+    s12 = 0;
+    carry0 = (s0 + (1 << 20)) >> 21;
+    s1 += carry0;
+    s0 -= carry0 << 21;
+    carry2 = (s2 + (1 << 20)) >> 21;
+    s3 += carry2;
+    s2 -= carry2 << 21;
+    carry4 = (s4 + (1 << 20)) >> 21;
+    s5 += carry4;
+    s4 -= carry4 << 21;
+    carry6 = (s6 + (1 << 20)) >> 21;
+    s7 += carry6;
+    s6 -= carry6 << 21;
+    carry8 = (s8 + (1 << 20)) >> 21;
+    s9 += carry8;
+    s8 -= carry8 << 21;
+    carry10 = (s10 + (1 << 20)) >> 21;
+    s11 += carry10;
+    s10 -= carry10 << 21;
+    carry1 = (s1 + (1 << 20)) >> 21;
+    s2 += carry1;
+    s1 -= carry1 << 21;
+    carry3 = (s3 + (1 << 20)) >> 21;
+    s4 += carry3;
+    s3 -= carry3 << 21;
+    carry5 = (s5 + (1 << 20)) >> 21;
+    s6 += carry5;
+    s5 -= carry5 << 21;
+    carry7 = (s7 + (1 << 20)) >> 21;
+    s8 += carry7;
+    s7 -= carry7 << 21;
+    carry9 = (s9 + (1 << 20)) >> 21;
+    s10 += carry9;
+    s9 -= carry9 << 21;
+    carry11 = (s11 + (1 << 20)) >> 21;
+    s12 += carry11;
+    s11 -= carry11 << 21;
+    s0 += s12 * 666643;
+    s1 += s12 * 470296;
+    s2 += s12 * 654183;
+    s3 -= s12 * 997805;
+    s4 += s12 * 136657;
+    s5 -= s12 * 683901;
+    s12 = 0;
+    carry0 = s0 >> 21;
+    s1 += carry0;
+    s0 -= carry0 << 21;
+    carry1 = s1 >> 21;
+    s2 += carry1;
+    s1 -= carry1 << 21;
+    carry2 = s2 >> 21;
+    s3 += carry2;
+    s2 -= carry2 << 21;
+    carry3 = s3 >> 21;
+    s4 += carry3;
+    s3 -= carry3 << 21;
+    carry4 = s4 >> 21;
+    s5 += carry4;
+    s4 -= carry4 << 21;
+    carry5 = s5 >> 21;
+    s6 += carry5;
+    s5 -= carry5 << 21;
+    carry6 = s6 >> 21;
+    s7 += carry6;
+    s6 -= carry6 << 21;
+    carry7 = s7 >> 21;
+    s8 += carry7;
+    s7 -= carry7 << 21;
+    carry8 = s8 >> 21;
+    s9 += carry8;
+    s8 -= carry8 << 21;
+    carry9 = s9 >> 21;
+    s10 += carry9;
+    s9 -= carry9 << 21;
+    carry10 = s10 >> 21;
+    s11 += carry10;
+    s10 -= carry10 << 21;
+    carry11 = s11 >> 21;
+    s12 += carry11;
+    s11 -= carry11 << 21;
+    s0 += s12 * 666643;
+    s1 += s12 * 470296;
+    s2 += s12 * 654183;
+    s3 -= s12 * 997805;
+    s4 += s12 * 136657;
+    s5 -= s12 * 683901;
+    s12 = 0;
+    carry0 = s0 >> 21;
+    s1 += carry0;
+    s0 -= carry0 << 21;
+    carry1 = s1 >> 21;
+    s2 += carry1;
+    s1 -= carry1 << 21;
+    carry2 = s2 >> 21;
+    s3 += carry2;
+    s2 -= carry2 << 21;
+    carry3 = s3 >> 21;
+    s4 += carry3;
+    s3 -= carry3 << 21;
+    carry4 = s4 >> 21;
+    s5 += carry4;
+    s4 -= carry4 << 21;
+    carry5 = s5 >> 21;
+    s6 += carry5;
+    s5 -= carry5 << 21;
+    carry6 = s6 >> 21;
+    s7 += carry6;
+    s6 -= carry6 << 21;
+    carry7 = s7 >> 21;
+    s8 += carry7;
+    s7 -= carry7 << 21;
+    carry8 = s8 >> 21;
+    s9 += carry8;
+    s8 -= carry8 << 21;
+    carry9 = s9 >> 21;
+    s10 += carry9;
+    s9 -= carry9 << 21;
+    carry10 = s10 >> 21;
+    s11 += carry10;
+    s10 -= carry10 << 21;
+    
+    s[0] = (unsigned char) (s0 >> 0);
+    s[1] = (unsigned char) (s0 >> 8);
+    s[2] = (unsigned char) ((s0 >> 16) | (s1 << 5));
+    s[3] = (unsigned char) (s1 >> 3);
+    s[4] = (unsigned char) (s1 >> 11);
+    s[5] = (unsigned char) ((s1 >> 19) | (s2 << 2));
+    s[6] = (unsigned char) (s2 >> 6);
+    s[7] = (unsigned char) ((s2 >> 14) | (s3 << 7));
+    s[8] = (unsigned char) (s3 >> 1);
+    s[9] = (unsigned char) (s3 >> 9);
+    s[10] = (unsigned char) ((s3 >> 17) | (s4 << 4));
+    s[11] = (unsigned char) (s4 >> 4);
+    s[12] = (unsigned char) (s4 >> 12);
+    s[13] = (unsigned char) ((s4 >> 20) | (s5 << 1));
+    s[14] = (unsigned char) (s5 >> 7);
+    s[15] = (unsigned char) ((s5 >> 15) | (s6 << 6));
+    s[16] = (unsigned char) (s6 >> 2);
+    s[17] = (unsigned char) (s6 >> 10);
+    s[18] = (unsigned char) ((s6 >> 18) | (s7 << 3));
+    s[19] = (unsigned char) (s7 >> 5);
+    s[20] = (unsigned char) (s7 >> 13);
+    s[21] = (unsigned char) (s8 >> 0);
+    s[22] = (unsigned char) (s8 >> 8);
+    s[23] = (unsigned char) ((s8 >> 16) | (s9 << 5));
+    s[24] = (unsigned char) (s9 >> 3);
+    s[25] = (unsigned char) (s9 >> 11);
+    s[26] = (unsigned char) ((s9 >> 19) | (s10 << 2));
+    s[27] = (unsigned char) (s10 >> 6);
+    s[28] = (unsigned char) ((s10 >> 14) | (s11 << 7));
+    s[29] = (unsigned char) (s11 >> 1);
+    s[30] = (unsigned char) (s11 >> 9);
+    s[31] = (unsigned char) (s11 >> 17);
+}
diff --git a/3rd_party/ed25519/sc.h b/3rd_party/ed25519/sc.h
new file mode 100644
index 0000000..e29e7fa
--- /dev/null
+++ b/3rd_party/ed25519/sc.h
@@ -0,0 +1,12 @@
+#ifndef SC_H
+#define SC_H
+
+/*
+The set of scalars is \Z/l
+where l = 2^252 + 27742317777372353535851937790883648493.
+*/
+
+void sc_reduce(unsigned char *s);
+void sc_muladd(unsigned char *s, const unsigned char *a, const unsigned char *b, const unsigned char *c);
+
+#endif
diff --git a/3rd_party/ed25519/seed.c b/3rd_party/ed25519/seed.c
new file mode 100644
index 0000000..cf252b8
--- /dev/null
+++ b/3rd_party/ed25519/seed.c
@@ -0,0 +1,40 @@
+#include "ed25519.h"
+
+#ifndef ED25519_NO_SEED
+
+#ifdef _WIN32
+#include <windows.h>
+#include <wincrypt.h>
+#else
+#include <stdio.h>
+#endif
+
+int ed25519_create_seed(unsigned char *seed) {
+#ifdef _WIN32
+    HCRYPTPROV prov;
+
+    if (!CryptAcquireContext(&prov, NULL, NULL, PROV_RSA_FULL, CRYPT_VERIFYCONTEXT))  {
+        return 1;
+    }
+
+    if (!CryptGenRandom(prov, 32, seed))  {
+        CryptReleaseContext(prov, 0);
+        return 1;
+    }
+
+    CryptReleaseContext(prov, 0);
+#else
+    FILE *f = fopen("/dev/urandom", "rb");
+
+    if (f == NULL) {
+        return 1;
+    }
+
+    if(fread(seed, 1, 32, f)){}
+    fclose(f);
+#endif
+
+    return 0;
+}
+
+#endif
diff --git a/3rd_party/ed25519/sha512.c b/3rd_party/ed25519/sha512.c
new file mode 100644
index 0000000..cb8ae71
--- /dev/null
+++ b/3rd_party/ed25519/sha512.c
@@ -0,0 +1,275 @@
+/* LibTomCrypt, modular cryptographic library -- Tom St Denis
+ *
+ * LibTomCrypt is a library that provides various cryptographic
+ * algorithms in a highly modular and flexible manner.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+#include "fixedint.h"
+#include "sha512.h"
+
+/* the K array */
+static const uint64_t K[80] = {
+    UINT64_C(0x428a2f98d728ae22), UINT64_C(0x7137449123ef65cd), 
+    UINT64_C(0xb5c0fbcfec4d3b2f), UINT64_C(0xe9b5dba58189dbbc),
+    UINT64_C(0x3956c25bf348b538), UINT64_C(0x59f111f1b605d019), 
+    UINT64_C(0x923f82a4af194f9b), UINT64_C(0xab1c5ed5da6d8118),
+    UINT64_C(0xd807aa98a3030242), UINT64_C(0x12835b0145706fbe), 
+    UINT64_C(0x243185be4ee4b28c), UINT64_C(0x550c7dc3d5ffb4e2),
+    UINT64_C(0x72be5d74f27b896f), UINT64_C(0x80deb1fe3b1696b1), 
+    UINT64_C(0x9bdc06a725c71235), UINT64_C(0xc19bf174cf692694),
+    UINT64_C(0xe49b69c19ef14ad2), UINT64_C(0xefbe4786384f25e3), 
+    UINT64_C(0x0fc19dc68b8cd5b5), UINT64_C(0x240ca1cc77ac9c65),
+    UINT64_C(0x2de92c6f592b0275), UINT64_C(0x4a7484aa6ea6e483), 
+    UINT64_C(0x5cb0a9dcbd41fbd4), UINT64_C(0x76f988da831153b5),
+    UINT64_C(0x983e5152ee66dfab), UINT64_C(0xa831c66d2db43210), 
+    UINT64_C(0xb00327c898fb213f), UINT64_C(0xbf597fc7beef0ee4),
+    UINT64_C(0xc6e00bf33da88fc2), UINT64_C(0xd5a79147930aa725), 
+    UINT64_C(0x06ca6351e003826f), UINT64_C(0x142929670a0e6e70),
+    UINT64_C(0x27b70a8546d22ffc), UINT64_C(0x2e1b21385c26c926), 
+    UINT64_C(0x4d2c6dfc5ac42aed), UINT64_C(0x53380d139d95b3df),
+    UINT64_C(0x650a73548baf63de), UINT64_C(0x766a0abb3c77b2a8), 
+    UINT64_C(0x81c2c92e47edaee6), UINT64_C(0x92722c851482353b),
+    UINT64_C(0xa2bfe8a14cf10364), UINT64_C(0xa81a664bbc423001),
+    UINT64_C(0xc24b8b70d0f89791), UINT64_C(0xc76c51a30654be30),
+    UINT64_C(0xd192e819d6ef5218), UINT64_C(0xd69906245565a910), 
+    UINT64_C(0xf40e35855771202a), UINT64_C(0x106aa07032bbd1b8),
+    UINT64_C(0x19a4c116b8d2d0c8), UINT64_C(0x1e376c085141ab53), 
+    UINT64_C(0x2748774cdf8eeb99), UINT64_C(0x34b0bcb5e19b48a8),
+    UINT64_C(0x391c0cb3c5c95a63), UINT64_C(0x4ed8aa4ae3418acb), 
+    UINT64_C(0x5b9cca4f7763e373), UINT64_C(0x682e6ff3d6b2b8a3),
+    UINT64_C(0x748f82ee5defb2fc), UINT64_C(0x78a5636f43172f60), 
+    UINT64_C(0x84c87814a1f0ab72), UINT64_C(0x8cc702081a6439ec),
+    UINT64_C(0x90befffa23631e28), UINT64_C(0xa4506cebde82bde9), 
+    UINT64_C(0xbef9a3f7b2c67915), UINT64_C(0xc67178f2e372532b),
+    UINT64_C(0xca273eceea26619c), UINT64_C(0xd186b8c721c0c207), 
+    UINT64_C(0xeada7dd6cde0eb1e), UINT64_C(0xf57d4f7fee6ed178),
+    UINT64_C(0x06f067aa72176fba), UINT64_C(0x0a637dc5a2c898a6), 
+    UINT64_C(0x113f9804bef90dae), UINT64_C(0x1b710b35131c471b),
+    UINT64_C(0x28db77f523047d84), UINT64_C(0x32caab7b40c72493), 
+    UINT64_C(0x3c9ebe0a15c9bebc), UINT64_C(0x431d67c49c100d4c),
+    UINT64_C(0x4cc5d4becb3e42b6), UINT64_C(0x597f299cfc657e2a), 
+    UINT64_C(0x5fcb6fab3ad6faec), UINT64_C(0x6c44198c4a475817)
+};
+
+/* Various logical functions */
+
+#define ROR64c(x, y) \
+    ( ((((x)&UINT64_C(0xFFFFFFFFFFFFFFFF))>>((uint64_t)(y)&UINT64_C(63))) | \
+      ((x)<<((uint64_t)(64-((y)&UINT64_C(63)))))) & UINT64_C(0xFFFFFFFFFFFFFFFF))
+
+#define STORE64H(x, y)                                                                     \
+   { (y)[0] = (unsigned char)(((x)>>56)&255); (y)[1] = (unsigned char)(((x)>>48)&255);     \
+     (y)[2] = (unsigned char)(((x)>>40)&255); (y)[3] = (unsigned char)(((x)>>32)&255);     \
+     (y)[4] = (unsigned char)(((x)>>24)&255); (y)[5] = (unsigned char)(((x)>>16)&255);     \
+     (y)[6] = (unsigned char)(((x)>>8)&255); (y)[7] = (unsigned char)((x)&255); }
+
+#define LOAD64H(x, y)                                                      \
+   { x = (((uint64_t)((y)[0] & 255))<<56)|(((uint64_t)((y)[1] & 255))<<48) | \
+         (((uint64_t)((y)[2] & 255))<<40)|(((uint64_t)((y)[3] & 255))<<32) | \
+         (((uint64_t)((y)[4] & 255))<<24)|(((uint64_t)((y)[5] & 255))<<16) | \
+         (((uint64_t)((y)[6] & 255))<<8)|(((uint64_t)((y)[7] & 255))); }
+
+
+#define Ch(x,y,z)       (z ^ (x & (y ^ z)))
+#define Maj(x,y,z)      (((x | y) & z) | (x & y)) 
+#define S(x, n)         ROR64c(x, n)
+#define R(x, n)         (((x) &UINT64_C(0xFFFFFFFFFFFFFFFF))>>((uint64_t)n))
+#define Sigma0(x)       (S(x, 28) ^ S(x, 34) ^ S(x, 39))
+#define Sigma1(x)       (S(x, 14) ^ S(x, 18) ^ S(x, 41))
+#define Gamma0(x)       (S(x, 1) ^ S(x, 8) ^ R(x, 7))
+#define Gamma1(x)       (S(x, 19) ^ S(x, 61) ^ R(x, 6))
+#ifndef MIN
+   #define MIN(x, y) ( ((x)<(y))?(x):(y) )
+#endif
+
+/* compress 1024-bits */
+static int sha512_compress(sha512_context *md, unsigned char *buf)
+{
+    uint64_t S[8], W[80], t0, t1;
+    int i;
+
+    /* copy state into S */
+    for (i = 0; i < 8; i++) {
+        S[i] = md->state[i];
+    }
+
+    /* copy the state into 1024-bits into W[0..15] */
+    for (i = 0; i < 16; i++) {
+        LOAD64H(W[i], buf + (8*i));
+    }
+
+    /* fill W[16..79] */
+    for (i = 16; i < 80; i++) {
+        W[i] = Gamma1(W[i - 2]) + W[i - 7] + Gamma0(W[i - 15]) + W[i - 16];
+    }        
+
+/* Compress */
+    #define RND(a,b,c,d,e,f,g,h,i) \
+    t0 = h + Sigma1(e) + Ch(e, f, g) + K[i] + W[i]; \
+    t1 = Sigma0(a) + Maj(a, b, c);\
+    d += t0; \
+    h  = t0 + t1;
+
+    for (i = 0; i < 80; i += 8) {
+       RND(S[0],S[1],S[2],S[3],S[4],S[5],S[6],S[7],i+0);
+       RND(S[7],S[0],S[1],S[2],S[3],S[4],S[5],S[6],i+1);
+       RND(S[6],S[7],S[0],S[1],S[2],S[3],S[4],S[5],i+2);
+       RND(S[5],S[6],S[7],S[0],S[1],S[2],S[3],S[4],i+3);
+       RND(S[4],S[5],S[6],S[7],S[0],S[1],S[2],S[3],i+4);
+       RND(S[3],S[4],S[5],S[6],S[7],S[0],S[1],S[2],i+5);
+       RND(S[2],S[3],S[4],S[5],S[6],S[7],S[0],S[1],i+6);
+       RND(S[1],S[2],S[3],S[4],S[5],S[6],S[7],S[0],i+7);
+   }
+
+   #undef RND
+
+
+
+    /* feedback */
+   for (i = 0; i < 8; i++) {
+        md->state[i] = md->state[i] + S[i];
+    }
+
+    return 0;
+}
+
+
+/**
+   Initialize the hash state
+   @param md   The hash state you wish to initialize
+   @return 0 if successful
+*/
+int sha512_init(sha512_context * md) {
+    if (md == NULL) return 1;
+
+    md->curlen = 0;
+    md->length = 0;
+    md->state[0] = UINT64_C(0x6a09e667f3bcc908);
+    md->state[1] = UINT64_C(0xbb67ae8584caa73b);
+    md->state[2] = UINT64_C(0x3c6ef372fe94f82b);
+    md->state[3] = UINT64_C(0xa54ff53a5f1d36f1);
+    md->state[4] = UINT64_C(0x510e527fade682d1);
+    md->state[5] = UINT64_C(0x9b05688c2b3e6c1f);
+    md->state[6] = UINT64_C(0x1f83d9abfb41bd6b);
+    md->state[7] = UINT64_C(0x5be0cd19137e2179);
+
+    return 0;
+}
+
+/**
+   Process a block of memory though the hash
+   @param md     The hash state
+   @param in     The data to hash
+   @param inlen  The length of the data (octets)
+   @return 0 if successful
+*/
+int sha512_update (sha512_context * md, const unsigned char *in, size_t inlen)               
+{                                                                                           
+    size_t n;
+    size_t i;                                                                        
+    int           err;     
+    if (md == NULL) return 1;  
+    if (in == NULL) return 1;                                                              
+    if (md->curlen > sizeof(md->buf)) {                             
+       return 1;                                                            
+    }                                                                                       
+    while (inlen > 0) {                                                                     
+        if (md->curlen == 0 && inlen >= 128) {                           
+           if ((err = sha512_compress (md, (unsigned char *)in)) != 0) {               
+              return err;                                                                   
+           }                                                                                
+           md->length += 128 * 8;                                        
+           in             += 128;                                                    
+           inlen          -= 128;                                                    
+        } else {                                                                            
+           n = MIN(inlen, (128 - md->curlen));
+
+           for (i = 0; i < n; i++) {
+            md->buf[i + md->curlen] = in[i];
+           }
+
+
+           md->curlen += n;                                                     
+           in             += n;                                                             
+           inlen          -= n;                                                             
+           if (md->curlen == 128) {                                      
+              if ((err = sha512_compress (md, md->buf)) != 0) {            
+                 return err;                                                                
+              }                                                                             
+              md->length += 8*128;                                       
+              md->curlen = 0;                                                   
+           }                                                                                
+       }                                                                                    
+    }                                                                                       
+    return 0;                                                                        
+}
+
+/**
+   Terminate the hash to get the digest
+   @param md  The hash state
+   @param out [out] The destination of the hash (64 bytes)
+   @return 0 if successful
+*/
+   int sha512_final(sha512_context * md, unsigned char *out)
+   {
+    int i;
+
+    if (md == NULL) return 1;
+    if (out == NULL) return 1;
+
+    if (md->curlen >= sizeof(md->buf)) {
+     return 1;
+ }
+
+    /* increase the length of the message */
+ md->length += md->curlen * UINT64_C(8);
+
+    /* append the '1' bit */
+ md->buf[md->curlen++] = (unsigned char)0x80;
+
+    /* if the length is currently above 112 bytes we append zeros
+     * then compress.  Then we can fall back to padding zeros and length
+     * encoding like normal.
+     */
+     if (md->curlen > 112) {
+        while (md->curlen < 128) {
+            md->buf[md->curlen++] = (unsigned char)0;
+        }
+        sha512_compress(md, md->buf);
+        md->curlen = 0;
+    }
+
+    /* pad upto 120 bytes of zeroes 
+     * note: that from 112 to 120 is the 64 MSB of the length.  We assume that you won't hash
+     * > 2^64 bits of data... :-)
+     */
+while (md->curlen < 120) {
+    md->buf[md->curlen++] = (unsigned char)0;
+}
+
+    /* store length */
+STORE64H(md->length, md->buf+120);
+sha512_compress(md, md->buf);
+
+    /* copy output */
+for (i = 0; i < 8; i++) {
+    STORE64H(md->state[i], out+(8*i));
+}
+
+return 0;
+}
+
+int sha512(const unsigned char *message, size_t message_len, unsigned char *out)
+{
+    sha512_context ctx;
+    int ret;
+    if ((ret = sha512_init(&ctx))) return ret;
+    if ((ret = sha512_update(&ctx, message, message_len))) return ret;
+    if ((ret = sha512_final(&ctx, out))) return ret;
+    return 0;
+}
diff --git a/3rd_party/ed25519/sha512.h b/3rd_party/ed25519/sha512.h
new file mode 100644
index 0000000..a34dd5e
--- /dev/null
+++ b/3rd_party/ed25519/sha512.h
@@ -0,0 +1,21 @@
+#ifndef SHA512_H
+#define SHA512_H
+
+#include <stddef.h>
+
+#include "fixedint.h"
+
+/* state */
+typedef struct sha512_context_ {
+    uint64_t  length, state[8];
+    size_t curlen;
+    unsigned char buf[128];
+} sha512_context;
+
+
+int sha512_init(sha512_context * md);
+int sha512_final(sha512_context * md, unsigned char *out);
+int sha512_update(sha512_context * md, const unsigned char *in, size_t inlen);
+int sha512(const unsigned char *message, size_t message_len, unsigned char *out);
+
+#endif
diff --git a/3rd_party/ed25519/sign.c b/3rd_party/ed25519/sign.c
new file mode 100644
index 0000000..199a839
--- /dev/null
+++ b/3rd_party/ed25519/sign.c
@@ -0,0 +1,31 @@
+#include "ed25519.h"
+#include "sha512.h"
+#include "ge.h"
+#include "sc.h"
+
+
+void ed25519_sign(unsigned char *signature, const unsigned char *message, size_t message_len, const unsigned char *public_key, const unsigned char *private_key) {
+    sha512_context hash;
+    unsigned char hram[64];
+    unsigned char r[64];
+    ge_p3 R;
+
+
+    sha512_init(&hash);
+    sha512_update(&hash, private_key + 32, 32);
+    sha512_update(&hash, message, message_len);
+    sha512_final(&hash, r);
+
+    sc_reduce(r);
+    ge_scalarmult_base(&R, r);
+    ge_p3_tobytes(signature, &R);
+
+    sha512_init(&hash);
+    sha512_update(&hash, signature, 32);
+    sha512_update(&hash, public_key, 32);
+    sha512_update(&hash, message, message_len);
+    sha512_final(&hash, hram);
+
+    sc_reduce(hram);
+    sc_muladd(signature + 32, hram, private_key, r);
+}
diff --git a/3rd_party/ed25519/verify.c b/3rd_party/ed25519/verify.c
new file mode 100644
index 0000000..32f988e
--- /dev/null
+++ b/3rd_party/ed25519/verify.c
@@ -0,0 +1,77 @@
+#include "ed25519.h"
+#include "sha512.h"
+#include "ge.h"
+#include "sc.h"
+
+static int consttime_equal(const unsigned char *x, const unsigned char *y) {
+    unsigned char r = 0;
+
+    r = x[0] ^ y[0];
+    #define F(i) r |= x[i] ^ y[i]
+    F(1);
+    F(2);
+    F(3);
+    F(4);
+    F(5);
+    F(6);
+    F(7);
+    F(8);
+    F(9);
+    F(10);
+    F(11);
+    F(12);
+    F(13);
+    F(14);
+    F(15);
+    F(16);
+    F(17);
+    F(18);
+    F(19);
+    F(20);
+    F(21);
+    F(22);
+    F(23);
+    F(24);
+    F(25);
+    F(26);
+    F(27);
+    F(28);
+    F(29);
+    F(30);
+    F(31);
+    #undef F
+
+    return !r;
+}
+
+int ed25519_verify(const unsigned char *signature, const unsigned char *message, size_t message_len, const unsigned char *public_key) {
+    unsigned char h[64];
+    unsigned char checker[32];
+    sha512_context hash;
+    ge_p3 A;
+    ge_p2 R;
+
+    if (signature[63] & 224) {
+        return 0;
+    }
+
+    if (ge_frombytes_negate_vartime(&A, public_key) != 0) {
+        return 0;
+    }
+
+    sha512_init(&hash);
+    sha512_update(&hash, signature, 32);
+    sha512_update(&hash, public_key, 32);
+    sha512_update(&hash, message, message_len);
+    sha512_final(&hash, h);
+    
+    sc_reduce(h);
+    ge_double_scalarmult_vartime(&R, h, &A, signature + 32);
+    ge_tobytes(checker, &R);
+
+    if (!consttime_equal(checker, signature)) {
+        return 0;
+    }
+
+    return 1;
+}
diff --git a/3rd_party/libsrp6a-sha512/LICENSE b/3rd_party/libsrp6a-sha512/LICENSE
new file mode 100644
index 0000000..7f70640
--- /dev/null
+++ b/3rd_party/libsrp6a-sha512/LICENSE
@@ -0,0 +1,62 @@
+Licensing
+---------
+
+SRP is royalty-free worldwide for commercial and non-commercial use.
+The SRP library has been carefully written not to depend on any
+encumbered algorithms, and it is distributed under a standard
+BSD-style Open Source license which is shown below.  This license
+covers implementations based on the SRP library as well as
+independent implementations based on RFC 2945.
+
+The SRP distribution itself contains algorithms and code from
+various freeware packages; these parts fall under both the SRP
+Open Source license and the packages' own licenses.  Care has
+been taken to ensure that these licenses are compatible with
+Open Source distribution, but it is the responsibility of the
+licensee to comply with the terms of these licenses.  This
+disclaimer also applies to third-party libraries that may be
+linked into the distribution, since they may contain patented
+intellectual property.  The file "Copyrights" contains a list
+of the copyrights incorporated by portions of the software.
+
+Broader use of the SRP authentication technology, such as variants
+incorporating the use of an explicit server secret (SRP-Z), may
+require a license; please contact the Stanford Office of Technology
+Licensing (http://otl.stanford.edu/) for more information about
+terms and conditions.
+
+This software is covered under the following copyright:
+
+/*
+ * Copyright (c) 1997-2007  The Stanford SRP Authentication Project
+ * All Rights Reserved.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining
+ * a copy of this software and associated documentation files (the
+ * "Software"), to deal in the Software without restriction, including
+ * without limitation the rights to use, copy, modify, merge, publish,
+ * distribute, sublicense, and/or sell copies of the Software, and to
+ * permit persons to whom the Software is furnished to do so, subject to
+ * the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be
+ * included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS-IS" AND WITHOUT WARRANTY OF ANY KIND, 
+ * EXPRESS, IMPLIED OR OTHERWISE, INCLUDING WITHOUT LIMITATION, ANY 
+ * WARRANTY OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.  
+ *
+ * IN NO EVENT SHALL STANFORD BE LIABLE FOR ANY SPECIAL, INCIDENTAL,
+ * INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY KIND, OR ANY DAMAGES WHATSOEVER
+ * RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER OR NOT ADVISED OF
+ * THE POSSIBILITY OF DAMAGE, AND ON ANY THEORY OF LIABILITY, ARISING OUT
+ * OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
+ *
+ * Redistributions in source or binary form must retain an intact copy
+ * of this copyright notice.
+ */
+
+Address all questions regarding this license to:
+
+  Tom Wu
+  tjw@cs.Stanford.EDU
diff --git a/3rd_party/libsrp6a-sha512/Makefile.am b/3rd_party/libsrp6a-sha512/Makefile.am
new file mode 100644
index 0000000..2acd582
--- /dev/null
+++ b/3rd_party/libsrp6a-sha512/Makefile.am
@@ -0,0 +1,31 @@
+AUTOMAKE_OPTIONS = foreign no-dependencies
+
+AM_CPPFLAGS = \
+        -I$(top_srcdir)/include \
+        -I$(top_srcdir) \
+        -Wno-incompatible-pointer-types
+
+AM_CFLAGS = -DHAVE_CONFIG_H
+if HAVE_OPENSSL
+AM_CFLAGS += -DOPENSSL=1 $(openssl_CFLAGS)
+else
+if HAVE_GCRYPT
+AM_CFLAGS += -DGCRYPT=1 $(libgcrypt_CFLAGS)
+else
+if HAVE_MBEDTLS
+AM_CFLAGS += -DMBEDTLS=1 $(mbedtls_CFLAGS)
+endif
+endif
+endif
+
+noinst_LTLIBRARIES = libsrp6a-sha512.la
+
+libsrp6a_sha512_la_SOURCES = \
+  t_conv.c t_math.c t_misc.c \
+  t_truerand.c cstr.c \
+  srp.c srp6a_sha512_client.c \
+  srp.h srp_aux.h cstr.h \
+  t_sha.c
+#if !HAVE_OPENSSL
+#libsrp6a_sha512_la_SOURCES += t_sha.c
+#endif
diff --git a/3rd_party/libsrp6a-sha512/README.md b/3rd_party/libsrp6a-sha512/README.md
new file mode 100644
index 0000000..4affe4a
--- /dev/null
+++ b/3rd_party/libsrp6a-sha512/README.md
@@ -0,0 +1,35 @@
+# SRP6a-sha512 library
+
+## About
+
+This library is based on Stanford's Secure Remote Password (SRP) protocol
+implementation, or more precise on the `libsrp` part thereof.
+The entire source code for the SRP project can be obtained from [here](https://github.com/secure-remote-password/stanford-srp).
+
+It has been adapted to the needs of the libimobiledevice project, and
+contains just a part of the original code; it only supports the SRP6a
+client method which has been modified to use SHA512 instead of SHA1.
+The only supported SRP method is `SRP6a_sha512_client_method()`.
+Besides that, support for MbedTLS has been added.
+
+Also, all server-side code has been removed, and the client-side code
+has been reduced to a minimum, so that basically only the following
+functions remain operational:
+
+- `SRP_initialize_library`
+- `SRP_new`
+- `SRP_free`
+- `SRP_set_user_raw`
+- `SRP_set_params`
+- `SRP_set_auth_password`
+- `SRP_gen_pub`
+- `SRP_compute_key`
+- `SRP_respond`
+- `SRP_verify`
+
+Anything else has not been tested and must be considered non-functional.
+
+## License
+
+The license of the original work does still apply and can be found in the
+LICENSE file that comes with the code.
diff --git a/3rd_party/libsrp6a-sha512/cstr.c b/3rd_party/libsrp6a-sha512/cstr.c
new file mode 100644
index 0000000..9856f46
--- /dev/null
+++ b/3rd_party/libsrp6a-sha512/cstr.c
@@ -0,0 +1,226 @@
+#include <stdlib.h>
+#include <string.h>
+
+#include "config.h"
+#include "cstr.h"
+
+#define EXPFACTOR       2               /* Minimum expansion factor */
+#define MINSIZE         4               /* Absolute minimum - one word */
+
+static char cstr_empty_string[] = { '\0' };
+static cstr_allocator * default_alloc = NULL;
+
+/*
+ * It is assumed, for efficiency, that it is okay to pass more arguments
+ * to a function than are called for, as long as the required arguments
+ * are in proper form.  If extra arguments to malloc() and free() cause
+ * problems, define PEDANTIC_ARGS below.
+ */
+#ifdef PEDANTIC_ARGS
+static void * Cmalloc(int n, void * heap) { return malloc(n); }
+static void Cfree(void * p, void * heap) { free(p); }
+static cstr_allocator malloc_allocator = { Cmalloc, Cfree, NULL };
+#else
+static cstr_allocator malloc_allocator = { malloc, free, NULL };
+#endif
+
+_TYPE( void )
+cstr_set_allocator(cstr_allocator * alloc)
+{
+  default_alloc = alloc;
+}
+
+_TYPE( cstr * )
+cstr_new_alloc(cstr_allocator * alloc)
+{
+  cstr * str;
+
+  if(alloc == NULL) {
+    if(default_alloc == NULL) {
+      default_alloc = &malloc_allocator;
+    }
+    alloc = default_alloc;
+  }
+
+  str = (cstr *) (*alloc->alloc)(sizeof(cstr), alloc->heap);
+  if(str) {
+    str->data = cstr_empty_string;
+    str->length = str->cap = 0;
+    str->ref = 1;
+    str->allocator = alloc;
+  }
+  return str;
+}
+
+_TYPE( cstr * )
+cstr_new()
+{
+  return cstr_new_alloc(NULL);
+}
+
+_TYPE( cstr * )
+cstr_dup_alloc(const cstr * str, cstr_allocator * alloc)
+{
+  cstr * nstr = cstr_new_alloc(alloc);
+  if(nstr)
+    cstr_setn(nstr, str->data, str->length);
+  return nstr;
+}
+
+_TYPE( cstr * )
+cstr_dup(const cstr * str)
+{
+  return cstr_dup_alloc(str, NULL);
+}
+
+_TYPE( cstr * )
+cstr_create(const char * s)
+{
+  return cstr_createn(s, strlen(s));
+}
+
+_TYPE( cstr * )
+cstr_createn(const char * s, int len)
+{
+  cstr * str = cstr_new();
+  if(str) {
+    cstr_setn(str, s, len);
+  }
+  return str;
+}
+
+_TYPE( void )
+cstr_use(cstr * str)
+{
+  ++str->ref;
+}
+
+_TYPE( void )
+cstr_clear_free(cstr * str)
+{
+  if(--str->ref == 0) {
+    if(str->cap > 0) {
+      memset(str->data, 0, str->cap);
+      (*str->allocator->free)(str->data, str->allocator->heap);
+    }
+    (*str->allocator->free)(str, str->allocator->heap);
+  }
+}
+
+_TYPE( void )
+cstr_free(cstr * str)
+{
+  if(--str->ref == 0) {
+    if(str->cap > 0)
+      (*str->allocator->free)(str->data, str->allocator->heap);
+    (*str->allocator->free)(str, str->allocator->heap);
+  }
+}
+
+_TYPE( void )
+cstr_empty(cstr * str)
+{
+  if(str->cap > 0)
+    (*str->allocator->free)(str->data, str->allocator->heap);
+  str->data = cstr_empty_string;
+  str->length = str->cap = 0;
+}
+
+static int
+cstr_alloc(cstr * str, int len)
+{
+  char * t;
+
+  if(len > str->cap) {
+    if(len < EXPFACTOR * str->cap)
+      len = EXPFACTOR * str->cap;
+    if(len < MINSIZE)
+      len = MINSIZE;
+
+    t = (char *) (*str->allocator->alloc)(len * sizeof(char),
+                                          str->allocator->heap);
+    if(t) {
+      if(str->data) {
+        t[str->length] = 0;
+        if(str->cap > 0) {
+          if(str->length > 0)
+            memcpy(t, str->data, str->length);
+          free(str->data);
+        }
+      }
+      str->data = t;
+      str->cap = len;
+      return 1;
+    }
+    else
+      return -1;
+  }
+  else
+    return 0;
+}
+
+_TYPE( int )
+cstr_copy(cstr * dst, const cstr * src)
+{
+  return cstr_setn(dst, src->data, src->length);
+}
+
+_TYPE( int )
+cstr_set(cstr * str, const char * s)
+{
+  return cstr_setn(str, s, strlen(s));
+}
+
+_TYPE( int )
+cstr_setn(cstr * str, const char * s, int len)
+{
+  if(cstr_alloc(str, len + 1) < 0)
+    return -1;
+  str->data[len] = 0;
+  if(s != NULL && len > 0)
+    memmove(str->data, s, len);
+  str->length = len;
+  return 1;
+}
+
+_TYPE( int )
+cstr_set_length(cstr * str, int len)
+{
+  if(len < str->length) {
+    str->data[len] = 0;
+    str->length = len;
+    return 1;
+  }
+  else if(len > str->length) {
+    if(cstr_alloc(str, len + 1) < 0)
+      return -1;
+    memset(str->data + str->length, 0, len - str->length + 1);
+    str->length = len;
+    return 1;
+  }
+  else
+    return 0;
+}
+
+_TYPE( int )
+cstr_append(cstr * str, const char * s)
+{
+  return cstr_appendn(str, s, strlen(s));
+}
+
+_TYPE( int )
+cstr_appendn(cstr * str, const char * s, int len)
+{
+  if(cstr_alloc(str, str->length + len + 1) < 0)
+    return -1;
+  memcpy(str->data + str->length, s, len);
+  str->length += len;
+  str->data[str->length] = 0;
+  return 1;
+}
+
+_TYPE( int )
+cstr_append_str(cstr * dst, const cstr * src)
+{
+  return cstr_appendn(dst, src->data, src->length);
+}
diff --git a/3rd_party/libsrp6a-sha512/cstr.h b/3rd_party/libsrp6a-sha512/cstr.h
new file mode 100644
index 0000000..7cc019a
--- /dev/null
+++ b/3rd_party/libsrp6a-sha512/cstr.h
@@ -0,0 +1,94 @@
+#ifndef _CSTR_H_
+#define _CSTR_H_
+
+/* A general-purpose string "class" for C */
+
+#if     !defined(P)
+#ifdef  __STDC__
+#define P(x)    x
+#else
+#define P(x)    ()
+#endif
+#endif
+
+/*      For building dynamic link libraries under windows, windows NT 
+ *      using MSVC1.5 or MSVC2.0
+ */
+
+#ifndef _DLLDECL
+#define _DLLDECL
+
+#ifdef MSVC15   /* MSVC1.5 support for 16 bit apps */
+#define _MSVC15EXPORT _export
+#define _MSVC20EXPORT
+#define _DLLAPI _export _pascal
+#define _CDECL
+#define _TYPE(a) a _MSVC15EXPORT
+#define DLLEXPORT 1
+
+#elif defined(MSVC20) || (defined(_USRDLL) && defined(SRP_EXPORTS))
+#define _MSVC15EXPORT
+#define _MSVC20EXPORT _declspec(dllexport)
+#define _DLLAPI
+#define _CDECL
+#define _TYPE(a) _MSVC20EXPORT a
+#define DLLEXPORT 1
+
+#else                   /* Default, non-dll.  Use this for Unix or DOS */
+#define _MSVC15DEXPORT
+#define _MSVC20EXPORT
+#define _DLLAPI
+#if defined(WINDOWS) || defined(WIN32)
+#define _CDECL _cdecl
+#else
+#define _CDECL
+#endif
+#define _TYPE(a) a _CDECL
+#endif
+#endif /* _DLLDECL */
+
+#ifdef __cplusplus
+extern "C" {
+#endif /* __cplusplus */
+
+/* Arguments to allocator methods ordered this way for compatibility */
+typedef struct cstr_alloc_st {
+  void * (_CDECL * alloc)(size_t n, void * heap);
+  void (_CDECL * free)(void * p, void * heap);
+  void * heap;
+} cstr_allocator;
+
+typedef struct cstr_st {
+  char * data;  /* Okay to access data and length fields directly */
+  int length;
+  int cap;
+  int ref;      /* Simple reference counter */
+  cstr_allocator * allocator;
+} cstr;
+
+_TYPE( void ) cstr_set_allocator P((cstr_allocator * alloc));
+
+_TYPE( cstr * ) cstr_new P((void));
+_TYPE( cstr * ) cstr_new_alloc P((cstr_allocator * alloc));
+_TYPE( cstr * ) cstr_dup P((const cstr * str));
+_TYPE( cstr * ) cstr_dup_alloc P((const cstr * str, cstr_allocator * alloc));
+_TYPE( cstr * ) cstr_create P((const char * s));
+_TYPE( cstr * ) cstr_createn P((const char * s, int len));
+
+_TYPE( void ) cstr_free P((cstr * str));
+_TYPE( void ) cstr_clear_free P((cstr * str));
+_TYPE( void ) cstr_use P((cstr * str));
+_TYPE( void ) cstr_empty P((cstr * str));
+_TYPE( int ) cstr_copy P((cstr * dst, const cstr * src));
+_TYPE( int ) cstr_set P((cstr * str, const char * s));
+_TYPE( int ) cstr_setn P((cstr * str, const char * s, int len));
+_TYPE( int ) cstr_set_length P((cstr * str, int len));
+_TYPE( int ) cstr_append P((cstr * str, const char * s));
+_TYPE( int ) cstr_appendn P((cstr * str, const char * s, int len));
+_TYPE( int ) cstr_append_str P((cstr * dst, const cstr * src));
+
+#ifdef __cplusplus
+}
+#endif /* __cplusplus */
+
+#endif /* _CSTR_H_ */
diff --git a/3rd_party/libsrp6a-sha512/srp.c b/3rd_party/libsrp6a-sha512/srp.c
new file mode 100644
index 0000000..74e1f98
--- /dev/null
+++ b/3rd_party/libsrp6a-sha512/srp.c
@@ -0,0 +1,274 @@
+/*
+ * Copyright (c) 1997-2007  The Stanford SRP Authentication Project
+ * All Rights Reserved.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining
+ * a copy of this software and associated documentation files (the
+ * "Software"), to deal in the Software without restriction, including
+ * without limitation the rights to use, copy, modify, merge, publish,
+ * distribute, sublicense, and/or sell copies of the Software, and to
+ * permit persons to whom the Software is furnished to do so, subject to
+ * the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be
+ * included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS-IS" AND WITHOUT WARRANTY OF ANY KIND, 
+ * EXPRESS, IMPLIED OR OTHERWISE, INCLUDING WITHOUT LIMITATION, ANY 
+ * WARRANTY OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.  
+ *
+ * IN NO EVENT SHALL STANFORD BE LIABLE FOR ANY SPECIAL, INCIDENTAL,
+ * INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY KIND, OR ANY DAMAGES WHATSOEVER
+ * RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER OR NOT ADVISED OF
+ * THE POSSIBILITY OF DAMAGE, AND ON ANY THEORY OF LIABILITY, ARISING OUT
+ * OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
+ *
+ * Redistributions in source or binary form must retain an intact copy
+ * of this copyright notice.
+ */
+
+#include "t_defines.h"
+#include "srp.h"
+
+static int library_initialized = 0;
+
+_TYPE( SRP_RESULT )
+SRP_initialize_library()
+{
+  if(library_initialized == 0) {
+    BigIntegerInitialize();
+    t_stronginitrand();
+    library_initialized = 1;
+  }
+  return SRP_SUCCESS;
+}
+
+_TYPE( SRP_RESULT )
+SRP_finalize_library()
+{
+  if(library_initialized > 0) {
+    library_initialized = 0;
+    BigIntegerFinalize();
+  }
+  return SRP_SUCCESS;
+}
+
+static int srp_modulus_min_bits = SRP_DEFAULT_MIN_BITS;
+
+_TYPE( SRP_RESULT )
+SRP_set_modulus_min_bits(int minbits)
+{
+  srp_modulus_min_bits = minbits;
+  return SRP_SUCCESS;
+}
+
+_TYPE( int )
+SRP_get_modulus_min_bits()
+{
+  return srp_modulus_min_bits;
+}
+
+static int
+default_secret_bits_cb(int modsize)
+{
+  return 256;
+  /*return modsize;*/   /* Warning: Very Slow */
+}
+
+static SRP_SECRET_BITS_CB srp_sb_cb = default_secret_bits_cb;
+
+_TYPE( SRP_RESULT )
+SRP_set_secret_bits_cb(SRP_SECRET_BITS_CB cb)
+{
+  srp_sb_cb = cb;
+  return SRP_SUCCESS;
+}
+
+_TYPE( int )
+SRP_get_secret_bits(int modsize)
+{
+  return (*srp_sb_cb)(modsize);
+}
+
+_TYPE( SRP * )
+SRP_new(SRP_METHOD * meth)
+{
+  SRP * srp = (SRP *) malloc(sizeof(SRP));
+
+  if(srp == NULL)
+    return NULL;
+
+  srp->flags = 0;
+  srp->username = cstr_new();
+  srp->bctx = BigIntegerCtxNew();
+  srp->modulus = NULL;
+  srp->accel = NULL;
+  srp->generator = NULL;
+  srp->salt = NULL;
+  srp->verifier = NULL;
+  srp->password = NULL;
+  srp->pubkey = NULL;
+  srp->secret = NULL;
+  srp->u = NULL;
+  srp->key = NULL;
+  srp->ex_data = cstr_new();
+  srp->param_cb = NULL;
+  srp->meth = meth;
+  srp->meth_data = NULL;
+  //srp->slu = NULL;
+  if(srp->meth->init == NULL || (*srp->meth->init)(srp) == SRP_SUCCESS)
+    return srp;
+  free(srp);
+  return NULL;
+}
+
+_TYPE( SRP_RESULT )
+SRP_free(SRP * srp)
+{
+  if(srp->meth->finish)
+    (*srp->meth->finish)(srp);
+
+  if(srp->username)
+    cstr_clear_free(srp->username);
+  if(srp->modulus)
+    BigIntegerFree(srp->modulus);
+  if(srp->accel)
+    BigIntegerModAccelFree(srp->accel);
+  if(srp->generator)
+    BigIntegerFree(srp->generator);
+  if(srp->salt)
+    cstr_clear_free(srp->salt);
+  if(srp->verifier)
+    BigIntegerClearFree(srp->verifier);
+  if(srp->password)
+    BigIntegerClearFree(srp->password);
+  if(srp->pubkey)
+    BigIntegerFree(srp->pubkey);
+  if(srp->secret)
+    BigIntegerClearFree(srp->secret);
+  if(srp->u)
+    BigIntegerFree(srp->u);
+  if(srp->key)
+    BigIntegerClearFree(srp->key);
+  if(srp->bctx)
+    BigIntegerCtxFree(srp->bctx);
+  if(srp->ex_data)
+    cstr_clear_free(srp->ex_data);
+  free(srp);
+  return SRP_SUCCESS;
+}
+
+_TYPE( SRP_RESULT )
+SRP_set_client_param_verify_cb(SRP * srp, SRP_CLIENT_PARAM_VERIFY_CB cb)
+{
+  srp->param_cb = cb;
+  return SRP_SUCCESS;
+}
+
+_TYPE( SRP_RESULT )
+SRP_set_username(SRP * srp, const char * username)
+{
+  cstr_set(srp->username, username);
+  return SRP_SUCCESS;
+}
+
+_TYPE( SRP_RESULT )
+SRP_set_user_raw(SRP * srp, const unsigned char * user, int userlen)
+{
+  cstr_setn(srp->username, (const char*)user, userlen);
+  return SRP_SUCCESS;
+}
+
+_TYPE( SRP_RESULT )
+SRP_set_params(SRP * srp, const unsigned char * modulus, int modlen,
+               const unsigned char * generator, int genlen,
+               const unsigned char * salt, int saltlen)
+{
+  SRP_RESULT rc;
+
+  if(modulus == NULL || generator == NULL || salt == NULL)
+    return SRP_ERROR;
+
+  /* Set fields in SRP context */
+  srp->modulus = BigIntegerFromBytes(modulus, modlen);
+  if(srp->flags & SRP_FLAG_MOD_ACCEL)
+    srp->accel = BigIntegerModAccelNew(srp->modulus, srp->bctx);
+  srp->generator = BigIntegerFromBytes(generator, genlen);
+  if(srp->salt == NULL)
+    srp->salt = cstr_new();
+  cstr_setn(srp->salt, (const char*)salt, saltlen);
+
+  /* Now attempt to validate parameters */
+  if(BigIntegerBitLen(srp->modulus) < SRP_get_modulus_min_bits())
+    return SRP_ERROR;
+
+  if(srp->param_cb) {
+    rc = (*srp->param_cb)(srp, modulus, modlen, generator, genlen);
+    if(!SRP_OK(rc))
+      return rc;
+  }
+
+  return (*srp->meth->params)(srp, modulus, modlen, generator, genlen,
+                              salt, saltlen);
+}
+
+_TYPE( SRP_RESULT )
+SRP_set_authenticator(SRP * srp, const unsigned char * a, int alen)
+{
+  return (*srp->meth->auth)(srp, a, alen);
+}
+
+_TYPE( SRP_RESULT )
+SRP_set_auth_password(SRP * srp, const char * password)
+{
+  return (*srp->meth->passwd)(srp, (const unsigned char *)password,
+                              strlen(password));
+}
+
+_TYPE( SRP_RESULT )
+SRP_set_auth_password_raw(SRP * srp,
+                          const unsigned char * password, int passlen)
+{
+  return (*srp->meth->passwd)(srp, password, passlen);
+}
+
+_TYPE( SRP_RESULT )
+SRP_gen_pub(SRP * srp, cstr ** result)
+{
+  return (*srp->meth->genpub)(srp, result);
+}
+
+_TYPE( SRP_RESULT )
+SRP_add_ex_data(SRP * srp, const unsigned char * data, int datalen)
+{
+  cstr_appendn(srp->ex_data, (const char*)data, datalen);
+  return SRP_SUCCESS;
+}
+
+_TYPE( SRP_RESULT )
+SRP_compute_key(SRP * srp, cstr ** result,
+                const unsigned char * pubkey, int pubkeylen)
+{
+  return (*srp->meth->key)(srp, result, pubkey, pubkeylen);
+}
+
+_TYPE( SRP_RESULT )
+SRP_verify(SRP * srp, const unsigned char * proof, int prooflen)
+{
+  return (*srp->meth->verify)(srp, proof, prooflen);
+}
+
+_TYPE( SRP_RESULT )
+SRP_respond(SRP * srp, cstr ** proof)
+{
+  return (*srp->meth->respond)(srp, proof);
+}
+
+_TYPE( SRP_RESULT )
+SRP_use_engine(const char * engine)
+{
+  if(BigIntegerOK(BigIntegerUseEngine(engine)))
+    return SRP_SUCCESS;
+  else
+    return SRP_ERROR;
+}
diff --git a/3rd_party/libsrp6a-sha512/srp.h b/3rd_party/libsrp6a-sha512/srp.h
new file mode 100644
index 0000000..b1d46af
--- /dev/null
+++ b/3rd_party/libsrp6a-sha512/srp.h
@@ -0,0 +1,372 @@
+/*
+ * Copyright (c) 1997-2007  The Stanford SRP Authentication Project
+ * All Rights Reserved.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining
+ * a copy of this software and associated documentation files (the
+ * "Software"), to deal in the Software without restriction, including
+ * without limitation the rights to use, copy, modify, merge, publish,
+ * distribute, sublicense, and/or sell copies of the Software, and to
+ * permit persons to whom the Software is furnished to do so, subject to
+ * the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be
+ * included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS-IS" AND WITHOUT WARRANTY OF ANY KIND, 
+ * EXPRESS, IMPLIED OR OTHERWISE, INCLUDING WITHOUT LIMITATION, ANY 
+ * WARRANTY OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.  
+ *
+ * IN NO EVENT SHALL STANFORD BE LIABLE FOR ANY SPECIAL, INCIDENTAL,
+ * INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY KIND, OR ANY DAMAGES WHATSOEVER
+ * RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER OR NOT ADVISED OF
+ * THE POSSIBILITY OF DAMAGE, AND ON ANY THEORY OF LIABILITY, ARISING OUT
+ * OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
+ *
+ * Redistributions in source or binary form must retain an intact copy
+ * of this copyright notice.
+ */
+#ifndef _SRP_H_
+#define _SRP_H_
+
+#include "cstr.h"
+#include "srp_aux.h"
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/* SRP library version identification */
+#define SRP_VERSION_MAJOR 2
+#define SRP_VERSION_MINOR 0
+#define SRP_VERSION_PATCHLEVEL 1
+
+typedef int SRP_RESULT;
+/* Returned codes for SRP API functions */
+#define SRP_OK(v) ((v) == SRP_SUCCESS)
+#define SRP_SUCCESS 0
+#define SRP_ERROR -1
+
+/* Set the minimum number of bits acceptable in an SRP modulus */
+#define SRP_DEFAULT_MIN_BITS 512
+_TYPE( SRP_RESULT ) SRP_set_modulus_min_bits P((int minbits));
+_TYPE( int ) SRP_get_modulus_min_bits P((void));
+
+/*
+ * Sets the "secret size callback" function.
+ * This function is called with the modulus size in bits,
+ * and returns the size of the secret exponent in bits.
+ * The default function always returns 256 bits.
+ */
+typedef int (_CDECL * SRP_SECRET_BITS_CB)(int modsize);
+_TYPE( SRP_RESULT ) SRP_set_secret_bits_cb P((SRP_SECRET_BITS_CB cb));
+_TYPE( int ) SRP_get_secret_bits P((int modsize));
+
+typedef struct srp_st SRP;
+
+#if 0
+/* Server Lookup API */
+typedef struct srp_server_lu_st SRP_SERVER_LOOKUP;
+
+typedef struct srp_s_lu_meth_st {
+  const char * name;
+
+  SRP_RESULT (_CDECL * init)(SRP_SERVER_LOOKUP * slu);
+  SRP_RESULT (_CDECL * finish)(SRP_SERVER_LOOKUP * slu);
+
+  SRP_RESULT (_CDECL * lookup)(SRP_SERVER_LOOKUP * slu, SRP * srp, cstr * username);
+
+  void * meth_data;
+} SRP_SERVER_LOOKUP_METHOD;
+
+struct srp_server_lu_st {
+  SRP_SERVER_LOOKUP_METHOD * meth;
+  void * data;
+};
+
+/*
+ * The Server Lookup API deals with the server-side issue of
+ * mapping usernames to verifiers.  Given a username, a lookup
+ * mechanism needs to provide parameters (N, g), salt (s), and
+ * password verifier (v) for that user.
+ *
+ * A SRP_SERVER_LOOKUP_METHOD describes the general mechanism
+ * for performing lookups (e.g. files, LDAP, database, etc.)
+ * A SRP_SERVER_LOOKUP is an active "object" that is actually
+ * called to do lookups.
+ */
+_TYPE( SRP_SERVER_LOOKUP * )
+     SRP_SERVER_LOOKUP_new P((SRP_SERVER_LOOKUP_METHOD * meth));
+_TYPE( SRP_RESULT ) SRP_SERVER_LOOKUP_free P((SRP_SERVER_LOOKUP * slu));
+_TYPE( SRP_RESULT ) SRP_SERVER_do_lookup P((SRP_SERVER_LOOKUP * slu,
+                                            SRP * srp, cstr * username));
+
+/*
+ * SRP_SERVER_system_lookup supercedes SRP_server_init_user.
+ */
+_TYPE( SRP_SERVER_LOOKUP * ) SRP_SERVER_system_lookup P((void));
+#endif
+
+/*
+ * Client Parameter Verification API
+ *
+ * This callback is called from the SRP client when the
+ * parameters (modulus and generator) are set.  The callback
+ * should return SRP_SUCCESS if the parameters are okay,
+ * otherwise some error code to indicate that the parameters
+ * should be rejected.
+ */
+typedef SRP_RESULT (_CDECL * SRP_CLIENT_PARAM_VERIFY_CB)(SRP * srp, const unsigned char * mod, int modlen, const unsigned char * gen, int genlen);
+
+#if 0
+/* The default parameter verifier function */
+_TYPE( SRP_RESULT ) SRP_CLIENT_default_param_verify_cb(SRP * srp, const unsigned char * mod, int modlen, const unsigned char * gen, int genlen);
+/* A parameter verifier that only accepts builtin params (no prime test) */
+_TYPE( SRP_RESULT ) SRP_CLIENT_builtin_param_verify_cb(SRP * srp, const unsigned char * mod, int modlen, const unsigned char * gen, int genlen);
+/* The "classic" parameter verifier that accepts either builtin params
+ * immediately, and performs safe-prime tests on N and primitive-root
+ * tests on g otherwise.  SECURITY WARNING: This may allow for certain
+ * attacks based on "trapdoor" moduli, so this is not recommended. */
+_TYPE( SRP_RESULT ) SRP_CLIENT_compat_param_verify_cb(SRP * srp, const unsigned char * mod, int modlen, const unsigned char * gen, int genlen);
+
+#endif
+
+/*
+ * Main SRP API - SRP and SRP_METHOD
+ */
+
+/* SRP method definitions */
+typedef struct srp_meth_st {
+  const char * name;
+
+  SRP_RESULT (_CDECL * init)(SRP * srp);
+  SRP_RESULT (_CDECL * finish)(SRP * srp);
+
+  SRP_RESULT (_CDECL * params)(SRP * srp,
+                               const unsigned char * modulus, int modlen,
+                               const unsigned char * generator, int genlen,
+                               const unsigned char * salt, int saltlen);
+  SRP_RESULT (_CDECL * auth)(SRP * srp, const unsigned char * a, int alen);
+  SRP_RESULT (_CDECL * passwd)(SRP * srp,
+                               const unsigned char * pass, int passlen);
+  SRP_RESULT (_CDECL * genpub)(SRP * srp, cstr ** result);
+  SRP_RESULT (_CDECL * key)(SRP * srp, cstr ** result,
+                            const unsigned char * pubkey, int pubkeylen);
+  SRP_RESULT (_CDECL * verify)(SRP * srp,
+                               const unsigned char * proof, int prooflen);
+  SRP_RESULT (_CDECL * respond)(SRP * srp, cstr ** proof);
+
+  void * data;
+} SRP_METHOD;
+
+/* Magic numbers for the SRP context header */
+#define SRP_MAGIC_CLIENT 12
+#define SRP_MAGIC_SERVER 28
+
+/* Flag bits for SRP struct */
+#define SRP_FLAG_MOD_ACCEL 0x1  /* accelerate modexp operations */
+#define SRP_FLAG_LEFT_PAD 0x2   /* left-pad to length-of-N inside hashes */
+
+/*
+ * A hybrid structure that represents either client or server state.
+ */
+struct srp_st {
+  int magic;    /* To distinguish client from server (and for sanity) */
+
+  int flags;
+
+  cstr * username;
+
+  BigInteger modulus;
+  BigInteger generator;
+  cstr * salt;
+
+  BigInteger verifier;
+  BigInteger password;
+
+  BigInteger pubkey;
+  BigInteger secret;
+  BigInteger u;
+
+  BigInteger key;
+
+  cstr * ex_data;
+
+  SRP_METHOD * meth;
+  void * meth_data;
+
+  BigIntegerCtx bctx;        /* to cache temporaries if available */
+  BigIntegerModAccel accel;  /* to accelerate modexp if available */
+
+  SRP_CLIENT_PARAM_VERIFY_CB param_cb;  /* to verify params */
+  //SRP_SERVER_LOOKUP * slu;   /* to look up users */
+};
+
+/*
+ * Global initialization/de-initialization functions.
+ * Call SRP_initialize_library before using the library,
+ * and SRP_finalize_library when done.
+ */
+_TYPE( SRP_RESULT ) SRP_initialize_library();
+_TYPE( SRP_RESULT ) SRP_finalize_library();
+
+/*
+ * SRP_new() creates a new SRP context object -
+ * the method determines which "sense" (client or server)
+ * the object operates in.  SRP_free() frees it.
+ * (See RFC2945 method definitions below.)
+ */
+_TYPE( SRP * )      SRP_new P((SRP_METHOD * meth));
+_TYPE( SRP_RESULT ) SRP_free P((SRP * srp));
+
+#if 0
+/*
+ * Use the supplied lookup object to look up user parameters and
+ * password verifier.  The lookup function gets called during
+ * SRP_set_username/SRP_set_user_raw below.  Using this function
+ * means that the server can avoid calling SRP_set_params and
+ * SRP_set_authenticator, since the lookup function handles that
+ * internally.
+ */
+_TYPE( SRP_RESULT ) SRP_set_server_lookup P((SRP * srp,
+                                             SRP_SERVER_LOOKUP * lookup));
+#endif
+
+/*
+ * Use the supplied callback function to verify parameters
+ * (modulus, generator) given to the client.
+ */
+_TYPE( SRP_RESULT )
+     SRP_set_client_param_verify_cb P((SRP * srp,
+                                       SRP_CLIENT_PARAM_VERIFY_CB cb));
+
+/*
+ * Both client and server must call both SRP_set_username and
+ * SRP_set_params, in that order, before calling anything else.
+ * SRP_set_user_raw is an alternative to SRP_set_username that
+ * accepts an arbitrary length-bounded octet string as input.
+ */
+_TYPE( SRP_RESULT ) SRP_set_username P((SRP * srp, const char * username));
+_TYPE( SRP_RESULT ) SRP_set_user_raw P((SRP * srp, const unsigned char * user,
+                                        int userlen));
+_TYPE( SRP_RESULT )
+     SRP_set_params P((SRP * srp,
+                       const unsigned char * modulus, int modlen,
+                       const unsigned char * generator, int genlen,
+                       const unsigned char * salt, int saltlen));
+
+/*
+ * On the client, SRP_set_authenticator, SRP_gen_exp, and
+ * SRP_add_ex_data can be called in any order.
+ * On the server, SRP_set_authenticator must come first,
+ * followed by SRP_gen_exp and SRP_add_ex_data in either order.
+ */
+/*
+ * The authenticator is the secret possessed by either side.
+ * For the server, this is the bigendian verifier, as an octet string.
+ * For the client, this is the bigendian raw secret, as an octet string.
+ * The server's authenticator must be the generator raised to the power
+ * of the client's raw secret modulo the common modulus for authentication
+ * to succeed.
+ *
+ * SRP_set_auth_password computes the authenticator from a plaintext
+ * password and then calls SRP_set_authenticator automatically.  This is
+ * usually used on the client side, while the server usually uses
+ * SRP_set_authenticator (since it doesn't know the plaintext password).
+ */
+_TYPE( SRP_RESULT )
+     SRP_set_authenticator P((SRP * srp, const unsigned char * a, int alen));
+_TYPE( SRP_RESULT )
+     SRP_set_auth_password P((SRP * srp, const char * password));
+_TYPE( SRP_RESULT )
+     SRP_set_auth_password_raw P((SRP * srp,
+                                  const unsigned char * password,
+                                  int passlen));
+
+/*
+ * SRP_gen_pub generates the random exponential residue to send
+ * to the other side.  If using SRP-3/RFC2945, the server must
+ * withhold its result until it receives the client's number.
+ * If using SRP-6, the server can send its value immediately
+ * without waiting for the client.
+ * 
+ * If "result" points to a NULL pointer, a new cstr object will be
+ * created to hold the result, and "result" will point to it.
+ * If "result" points to a non-NULL cstr pointer, the result will be
+ * placed there.
+ * If "result" itself is NULL, no result will be returned,
+ * although the big integer value will still be available
+ * through srp->pubkey in the SRP struct.
+ */
+_TYPE( SRP_RESULT ) SRP_gen_pub P((SRP * srp, cstr ** result));
+/*
+ * Append the data to the extra data segment.  Authentication will
+ * not succeed unless both sides add precisely the same data in
+ * the same order.
+ */
+_TYPE( SRP_RESULT ) SRP_add_ex_data P((SRP * srp, const unsigned char * data,
+                                       int datalen));
+
+/*
+ * SRP_compute_key must be called after the previous three methods.
+ */
+_TYPE( SRP_RESULT ) SRP_compute_key P((SRP * srp, cstr ** result,
+                                       const unsigned char * pubkey,
+                                       int pubkeylen));
+
+/*
+ * On the client, call SRP_respond first to get the response to send
+ * to the server, and call SRP_verify to verify the server's response.
+ * On the server, call SRP_verify first to verify the client's response,
+ * and call SRP_respond ONLY if verification succeeds.
+ *
+ * It is an error to call SRP_respond with a NULL pointer.
+ */
+_TYPE( SRP_RESULT ) SRP_verify P((SRP * srp,
+                                  const unsigned char * proof, int prooflen));
+_TYPE( SRP_RESULT ) SRP_respond P((SRP * srp, cstr ** response));
+
+/* RFC2945-style SRP authentication */
+
+#define RFC2945_KEY_LEN 40      /* length of session key (bytes) */
+#define RFC2945_RESP_LEN 20     /* length of proof hashes (bytes) */
+
+/*
+ * RFC2945-style SRP authentication methods.  Use these like:
+ * SRP * srp = SRP_new(SRP_RFC2945_client_method());
+ */
+_TYPE( SRP_METHOD * ) SRP_RFC2945_client_method P((void));
+_TYPE( SRP_METHOD * ) SRP_RFC2945_server_method P((void));
+
+/*
+ * SRP-6 and SRP-6a authentication methods.
+ * SRP-6a is recommended for better resistance to 2-for-1 attacks.
+ */
+_TYPE( SRP_METHOD * ) SRP6_client_method P((void));
+_TYPE( SRP_METHOD * ) SRP6_server_method P((void));
+_TYPE( SRP_METHOD * ) SRP6a_client_method P((void));
+_TYPE( SRP_METHOD * ) SRP6a_server_method P((void));
+
+_TYPE( SRP_METHOD * ) SRP6a_sha512_client_method P((void));
+
+/*
+ * Convenience function - SRP_server_init_user
+ * Looks up the username from the system EPS configuration and calls
+ * SRP_set_username, SRP_set_params, and SRP_set_authenticator to
+ * initialize server state for that user.
+ *
+ * This is deprecated in favor of SRP_SERVER_system_lookup() and
+ * the Server Lookup API.
+ */
+_TYPE( SRP_RESULT ) SRP_server_init_user P((SRP * srp, const char * username));
+
+/*
+ * Use the named engine for acceleration.
+ */
+_TYPE( SRP_RESULT ) SRP_use_engine P((const char * engine));
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif /* _SRP_H_ */
diff --git a/3rd_party/libsrp6a-sha512/srp6a_sha512_client.c b/3rd_party/libsrp6a-sha512/srp6a_sha512_client.c
new file mode 100644
index 0000000..db59fe8
--- /dev/null
+++ b/3rd_party/libsrp6a-sha512/srp6a_sha512_client.c
@@ -0,0 +1,363 @@
+/*
+ * Copyright (c) 1997-2007  The Stanford SRP Authentication Project
+ * All Rights Reserved.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining
+ * a copy of this software and associated documentation files (the
+ * "Software"), to deal in the Software without restriction, including
+ * without limitation the rights to use, copy, modify, merge, publish,
+ * distribute, sublicense, and/or sell copies of the Software, and to
+ * permit persons to whom the Software is furnished to do so, subject to
+ * the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be
+ * included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS-IS" AND WITHOUT WARRANTY OF ANY KIND, 
+ * EXPRESS, IMPLIED OR OTHERWISE, INCLUDING WITHOUT LIMITATION, ANY 
+ * WARRANTY OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.  
+ *
+ * IN NO EVENT SHALL STANFORD BE LIABLE FOR ANY SPECIAL, INCIDENTAL,
+ * INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY KIND, OR ANY DAMAGES WHATSOEVER
+ * RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER OR NOT ADVISED OF
+ * THE POSSIBILITY OF DAMAGE, AND ON ANY THEORY OF LIABILITY, ARISING OUT
+ * OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
+ *
+ * Redistributions in source or binary form must retain an intact copy
+ * of this copyright notice.
+ */
+#include "t_defines.h"
+#include "srp.h"
+#include "t_sha.h"
+
+/*
+ * SRP-6/6a has two minor refinements relative to SRP-3/RFC2945:
+ * 1. The "g^x" value is multipled by three in the client's
+ *    calculation of its session key.
+ *    SRP-6a: The "g^x" value is multiplied by the hash of
+ *            N and g in the client's session key calculation.
+ * 2. The value of u is taken as the hash of A and B,
+ *    instead of the top 32 bits of the hash of B.
+ *    This eliminates the old restriction where the
+ *    server had to receive A before it could send B.
+ */
+
+/****************************/
+#define SHA512_DIGESTSIZE 64
+#define SRP6_SHA512_KEY_LEN 64
+
+/*
+ * The client keeps track of the running hash
+ * state via SHA512_CTX structures pointed to by the
+ * meth_data pointer.  The "hash" member is the hash value that
+ * will be sent to the other side; the "ckhash" member is the
+ * hash value expected from the other side.
+ */
+struct sha512_client_meth_st {
+  SHA512_CTX hash;
+  SHA512_CTX ckhash;
+  unsigned char k[SRP6_SHA512_KEY_LEN];
+};
+
+#define SHA512_CLIENT_CTXP(srp)    ((struct sha512_client_meth_st *)(srp)->meth_data)
+
+static SRP_RESULT
+srp6a_sha512_client_init(SRP * srp)
+{
+  srp->magic = SRP_MAGIC_CLIENT;
+  srp->flags = SRP_FLAG_MOD_ACCEL | SRP_FLAG_LEFT_PAD;
+  srp->meth_data = malloc(sizeof(struct sha512_client_meth_st));
+  SHA512Init(&SHA512_CLIENT_CTXP(srp)->hash);
+  SHA512Init(&SHA512_CLIENT_CTXP(srp)->ckhash);
+  return SRP_SUCCESS;
+}
+
+static SRP_RESULT
+srp6_sha512_client_finish(SRP * srp)
+{
+  if(srp->meth_data) {
+    memset(srp->meth_data, 0, sizeof(struct sha512_client_meth_st));
+    free(srp->meth_data);
+  }
+  return SRP_SUCCESS;
+}
+
+static SRP_RESULT
+srp6_sha512_client_params(SRP * srp, const unsigned char * modulus, int modlen,
+                   const unsigned char * generator, int genlen,
+                   const unsigned char * salt, int saltlen)
+{
+  int i;
+  unsigned char buf1[SHA512_DIGESTSIZE], buf2[SHA512_DIGESTSIZE];
+  SHA512_CTX ctxt;
+
+  /* Fields set by SRP_set_params */
+
+  /* Update hash state */
+  SHA512Init(&ctxt);
+  SHA512Update(&ctxt, modulus, modlen);
+  SHA512Final(buf1, &ctxt);     /* buf1 = H(modulus) */
+
+  SHA512Init(&ctxt);
+  SHA512Update(&ctxt, generator, genlen);
+  SHA512Final(buf2, &ctxt);     /* buf2 = H(generator) */
+
+  for(i = 0; i < sizeof(buf1); ++i)
+    buf1[i] ^= buf2[i];         /* buf1 = H(modulus) xor H(generator) */
+
+  /* hash: H(N) xor H(g) */
+  SHA512Update(&SHA512_CLIENT_CTXP(srp)->hash, buf1, sizeof(buf1));
+
+  SHA512Init(&ctxt);
+  SHA512Update(&ctxt, srp->username->data, srp->username->length);
+  SHA512Final(buf1, &ctxt);     /* buf1 = H(user) */
+
+  /* hash: (H(N) xor H(g)) | H(U) */
+  SHA512Update(&SHA512_CLIENT_CTXP(srp)->hash, buf1, sizeof(buf1));
+
+  /* hash: (H(N) xor H(g)) | H(U) | s */
+  SHA512Update(&SHA512_CLIENT_CTXP(srp)->hash, salt, saltlen);
+
+  return SRP_SUCCESS;
+}
+
+static SRP_RESULT
+srp6_sha512_client_auth(SRP * srp, const unsigned char * a, int alen)
+{
+  /* On the client, the authenticator is the raw password-derived hash */
+  srp->password = BigIntegerFromBytes(a, alen);
+
+  /* verifier = g^x mod N */
+  srp->verifier = BigIntegerFromInt(0);
+  BigIntegerModExp(srp->verifier, srp->generator, srp->password, srp->modulus, srp->bctx, srp->accel);
+
+  return SRP_SUCCESS;
+}
+
+static SRP_RESULT
+srp6_sha512_client_passwd(SRP * srp, const unsigned char * p, int plen)
+{
+  SHA512_CTX ctxt;
+  unsigned char dig[SHA512_DIGESTSIZE];
+  int r;
+
+  SHA512Init(&ctxt);
+  SHA512Update(&ctxt, srp->username->data, srp->username->length);
+  SHA512Update(&ctxt, ":", 1);
+  SHA512Update(&ctxt, p, plen);
+  SHA512Final(dig, &ctxt);      /* dig = H(U | ":" | P) */
+
+  SHA512Init(&ctxt);
+  SHA512Update(&ctxt, srp->salt->data, srp->salt->length);
+  SHA512Update(&ctxt, dig, sizeof(dig));
+  SHA512Final(dig, &ctxt);      /* dig = H(s | H(U | ":" | P)) */
+  memset(&ctxt, 0, sizeof(ctxt));
+
+  r = SRP_set_authenticator(srp, dig, sizeof(dig));
+  memset(dig, 0, sizeof(dig));
+
+  return r;
+}
+
+static SRP_RESULT
+srp6_sha512_client_genpub(SRP * srp, cstr ** result)
+{
+  cstr * astr;
+  int slen = (SRP_get_secret_bits(BigIntegerBitLen(srp->modulus)) + 7) / 8;
+
+  if(result == NULL)
+    astr = cstr_new();
+  else {
+    if(*result == NULL)
+      *result = cstr_new();
+    astr = *result;
+  }
+
+  cstr_set_length(astr, BigIntegerByteLen(srp->modulus));
+  t_random((unsigned char*)astr->data, slen);
+  srp->secret = BigIntegerFromBytes((const unsigned char*)astr->data, slen);
+  /* Force g^a mod n to "wrap around" by adding log[2](n) to "a". */
+  BigIntegerAddInt(srp->secret, srp->secret, BigIntegerBitLen(srp->modulus));
+  /* A = g^a mod n */
+  srp->pubkey = BigIntegerFromInt(0);
+  BigIntegerModExp(srp->pubkey, srp->generator, srp->secret, srp->modulus, srp->bctx, srp->accel);
+  BigIntegerToCstr(srp->pubkey, astr);
+
+  /* hash: (H(N) xor H(g)) | H(U) | s | A */
+  SHA512Update(&SHA512_CLIENT_CTXP(srp)->hash, astr->data, astr->length);
+  /* ckhash: A */
+  SHA512Update(&SHA512_CLIENT_CTXP(srp)->ckhash, astr->data, astr->length);
+
+  if(result == NULL)    /* astr was a temporary */
+    cstr_clear_free(astr);
+
+  return SRP_SUCCESS;
+}
+
+static SRP_RESULT
+srp6_sha512_client_key_ex(SRP * srp, cstr ** result,
+                   const unsigned char * pubkey, int pubkeylen, BigInteger k)
+{
+  SHA512_CTX ctxt;
+  unsigned char dig[SHA512_DIGESTSIZE];
+  BigInteger gb, e;
+  cstr * s;
+  int modlen;
+
+  modlen = BigIntegerByteLen(srp->modulus);
+  if(pubkeylen > modlen)
+    return SRP_ERROR;
+
+  /* Compute u from client's and server's values */
+  SHA512Init(&ctxt);
+  /* Use s as a temporary to store client's value */
+  s = cstr_new();
+  if(srp->flags & SRP_FLAG_LEFT_PAD) {
+    BigIntegerToCstrEx(srp->pubkey, s, modlen);
+    SHA512Update(&ctxt, s->data, s->length);
+    if(pubkeylen < modlen) {
+      memcpy(s->data + (modlen - pubkeylen), pubkey, pubkeylen);
+      memset(s->data, 0, modlen - pubkeylen);
+      SHA512Update(&ctxt, s->data, modlen);
+    }
+    else
+      SHA512Update(&ctxt, pubkey, pubkeylen);
+  }
+  else {
+    BigIntegerToCstr(srp->pubkey, s);
+    SHA512Update(&ctxt, s->data, s->length);
+    SHA512Update(&ctxt, pubkey, pubkeylen);
+  }
+  SHA512Final(dig, &ctxt);
+  srp->u = BigIntegerFromBytes(dig, SHA512_DIGESTSIZE);
+
+  /* hash: (H(N) xor H(g)) | H(U) | s | A | B */
+  SHA512Update(&SHA512_CLIENT_CTXP(srp)->hash, pubkey, pubkeylen);
+
+  gb = BigIntegerFromBytes(pubkey, pubkeylen);
+  /* reject B == 0, B >= modulus */
+  if(BigIntegerCmp(gb, srp->modulus) >= 0 || BigIntegerCmpInt(gb, 0) == 0) {
+    BigIntegerFree(gb);
+    cstr_clear_free(s);
+    return SRP_ERROR;
+  }
+  e = BigIntegerFromInt(0);
+  srp->key = BigIntegerFromInt(0);
+  /* unblind g^b (mod N) */
+  BigIntegerSub(srp->key, srp->modulus, srp->verifier);
+  /* use e as temporary, e == -k*v (mod N) */
+  BigIntegerMul(e, k, srp->key, srp->bctx);
+  BigIntegerAdd(e, e, gb);
+  BigIntegerMod(gb, e, srp->modulus, srp->bctx);
+
+  /* compute gb^(a + ux) (mod N) */
+  BigIntegerMul(e, srp->password, srp->u, srp->bctx);
+  BigIntegerAdd(e, e, srp->secret);     /* e = a + ux */
+
+  BigIntegerModExp(srp->key, gb, e, srp->modulus, srp->bctx, srp->accel);
+  BigIntegerClearFree(e);
+  BigIntegerClearFree(gb);
+
+  /* convert srp->key into a session key, update hash states */
+  BigIntegerToCstr(srp->key, s);
+  SHA512Init(&ctxt);
+  SHA512Update(&ctxt, s->data, s->length);
+  SHA512Final((unsigned char*)&SHA512_CLIENT_CTXP(srp)->k, &ctxt);
+  cstr_clear_free(s);
+
+  /* hash: (H(N) xor H(g)) | H(U) | s | A | B | K */
+  SHA512Update(&SHA512_CLIENT_CTXP(srp)->hash, SHA512_CLIENT_CTXP(srp)->k, SRP6_SHA512_KEY_LEN);
+  /* hash: (H(N) xor H(g)) | H(U) | s | A | B | K | ex_data */
+  if(srp->ex_data->length > 0)
+    SHA512Update(&SHA512_CLIENT_CTXP(srp)->hash,
+               srp->ex_data->data, srp->ex_data->length);
+  if(result) {
+    if(*result == NULL)
+      *result = cstr_new();
+    cstr_setn(*result, (const char*)SHA512_CLIENT_CTXP(srp)->k, SRP6_SHA512_KEY_LEN);
+  }
+
+  return SRP_SUCCESS;
+}
+
+static SRP_RESULT
+srp6a_sha512_client_key(SRP * srp, cstr ** result,
+                 const unsigned char * pubkey, int pubkeylen)
+{
+  SRP_RESULT ret;
+  BigInteger k;
+  cstr * s;
+  SHA512_CTX ctxt;
+  unsigned char dig[SHA512_DIGESTSIZE];
+
+  SHA512Init(&ctxt);
+  s = cstr_new();
+  BigIntegerToCstr(srp->modulus, s);
+  SHA512Update(&ctxt, s->data, s->length);
+  if(srp->flags & SRP_FLAG_LEFT_PAD)
+    BigIntegerToCstrEx(srp->generator, s, s->length);
+  else
+    BigIntegerToCstr(srp->generator, s);
+  SHA512Update(&ctxt, s->data, s->length);
+  SHA512Final(dig, &ctxt);
+  cstr_free(s);
+
+  k = BigIntegerFromBytes(dig, SHA512_DIGESTSIZE);
+  if(BigIntegerCmpInt(k, 0) == 0)
+    ret = SRP_ERROR;
+  else
+    ret = srp6_sha512_client_key_ex(srp, result, pubkey, pubkeylen, k);
+  BigIntegerClearFree(k);
+  return ret;
+}
+
+static SRP_RESULT
+srp6_sha512_client_verify(SRP * srp, const unsigned char * proof, int prooflen)
+{
+  unsigned char expected[SHA512_DIGESTSIZE];
+
+  SHA512Final(expected, &SHA512_CLIENT_CTXP(srp)->ckhash);
+  if(prooflen == SHA512_DIGESTSIZE && memcmp(expected, proof, prooflen) == 0)
+    return SRP_SUCCESS;
+  else
+    return SRP_ERROR;
+}
+
+static SRP_RESULT
+srp6_sha512_client_respond(SRP * srp, cstr ** proof)
+{
+  if(proof == NULL)
+    return SRP_ERROR;
+
+  if(*proof == NULL)
+    *proof = cstr_new();
+
+  /* proof contains client's response */
+  cstr_set_length(*proof, SHA512_DIGESTSIZE);
+  SHA512Final((unsigned char*)(*proof)->data, &SHA512_CLIENT_CTXP(srp)->hash);
+
+  /* ckhash: A | M | K */
+  SHA512Update(&SHA512_CLIENT_CTXP(srp)->ckhash, (*proof)->data, (*proof)->length);
+  SHA512Update(&SHA512_CLIENT_CTXP(srp)->ckhash, SHA512_CLIENT_CTXP(srp)->k, SRP6_SHA512_KEY_LEN);
+  return SRP_SUCCESS;
+}
+
+static SRP_METHOD srp6a_sha512_client_meth = {
+  "SRP-6a sha512 client (tjw)",
+  srp6a_sha512_client_init,
+  srp6_sha512_client_finish,
+  srp6_sha512_client_params,
+  srp6_sha512_client_auth,
+  srp6_sha512_client_passwd,
+  srp6_sha512_client_genpub,
+  srp6a_sha512_client_key,
+  srp6_sha512_client_verify,
+  srp6_sha512_client_respond,
+  NULL
+};
+
+_TYPE( SRP_METHOD * )
+SRP6a_sha512_client_method()
+{
+  return &srp6a_sha512_client_meth;
+}
diff --git a/3rd_party/libsrp6a-sha512/srp_aux.h b/3rd_party/libsrp6a-sha512/srp_aux.h
new file mode 100644
index 0000000..5088f08
--- /dev/null
+++ b/3rd_party/libsrp6a-sha512/srp_aux.h
@@ -0,0 +1,146 @@
+/*
+ * Copyright (c) 1997-2007  The Stanford SRP Authentication Project
+ * All Rights Reserved.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining
+ * a copy of this software and associated documentation files (the
+ * "Software"), to deal in the Software without restriction, including
+ * without limitation the rights to use, copy, modify, merge, publish,
+ * distribute, sublicense, and/or sell copies of the Software, and to
+ * permit persons to whom the Software is furnished to do so, subject to
+ * the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be
+ * included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS-IS" AND WITHOUT WARRANTY OF ANY KIND, 
+ * EXPRESS, IMPLIED OR OTHERWISE, INCLUDING WITHOUT LIMITATION, ANY 
+ * WARRANTY OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.  
+ *
+ * IN NO EVENT SHALL STANFORD BE LIABLE FOR ANY SPECIAL, INCIDENTAL,
+ * INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY KIND, OR ANY DAMAGES WHATSOEVER
+ * RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER OR NOT ADVISED OF
+ * THE POSSIBILITY OF DAMAGE, AND ON ANY THEORY OF LIABILITY, ARISING OUT
+ * OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
+ *
+ * Redistributions in source or binary form must retain an intact copy
+ * of this copyright notice.
+ */
+
+#ifndef SRP_AUX_H
+#define SRP_AUX_H
+
+#include "cstr.h"
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/* BigInteger abstraction API */
+
+#ifndef MATH_PRIV
+typedef void * BigInteger;
+typedef void * BigIntegerCtx;
+typedef void * BigIntegerModAccel;
+#endif
+
+/*
+ * Some functions return a BigIntegerResult.
+ * Use BigIntegerOK to test for success.
+ */
+#define BIG_INTEGER_SUCCESS 0
+#define BIG_INTEGER_ERROR -1
+#define BigIntegerOK(v) ((v) == BIG_INTEGER_SUCCESS)
+typedef int BigIntegerResult;
+
+_TYPE( BigInteger ) BigIntegerFromInt P((unsigned int number));
+_TYPE( BigInteger ) BigIntegerFromBytes P((const unsigned char * bytes,
+                                           int length));
+#define BigIntegerByteLen(X) ((BigIntegerBitLen(X)+7)/8)
+_TYPE( int ) BigIntegerToBytes P((BigInteger src,
+                                  unsigned char * dest, int destlen));
+_TYPE( BigIntegerResult ) BigIntegerToCstr P((BigInteger src, cstr * dest));
+_TYPE( BigIntegerResult ) BigIntegerToCstrEx P((BigInteger src, cstr * dest, int len));
+_TYPE( BigIntegerResult ) BigIntegerToHex P((BigInteger src,
+                                             char * dest, int destlen));
+_TYPE( BigIntegerResult ) BigIntegerToString P((BigInteger src,
+                                                char * dest, int destlen,
+                                                unsigned int radix));
+_TYPE( int ) BigIntegerBitLen P((BigInteger b));
+_TYPE( int ) BigIntegerCmp P((BigInteger c1, BigInteger c2));
+_TYPE( int ) BigIntegerCmpInt P((BigInteger c1, unsigned int c2));
+_TYPE( BigIntegerResult ) BigIntegerLShift P((BigInteger result, BigInteger x,
+                                              unsigned int bits));
+_TYPE( BigIntegerResult ) BigIntegerAdd P((BigInteger result,
+                                           BigInteger a1, BigInteger a2));
+_TYPE( BigIntegerResult ) BigIntegerAddInt P((BigInteger result,
+                                              BigInteger a1, unsigned int a2));
+_TYPE( BigIntegerResult ) BigIntegerSub P((BigInteger result,
+                                           BigInteger s1, BigInteger s2));
+_TYPE( BigIntegerResult ) BigIntegerSubInt P((BigInteger result,
+                                              BigInteger s1, unsigned int s2));
+/* For BigIntegerMul{,Int}: result != m1, m2 */
+_TYPE( BigIntegerResult ) BigIntegerMul P((BigInteger result, BigInteger m1,
+                                           BigInteger m2, BigIntegerCtx ctx));
+_TYPE( BigIntegerResult ) BigIntegerMulInt P((BigInteger result,
+                                              BigInteger m1, unsigned int m2,
+                                              BigIntegerCtx ctx));
+_TYPE( BigIntegerResult ) BigIntegerDivInt P((BigInteger result,
+                                              BigInteger d, unsigned int m,
+                                              BigIntegerCtx ctx));
+_TYPE( BigIntegerResult ) BigIntegerMod P((BigInteger result, BigInteger d,
+                                           BigInteger m, BigIntegerCtx ctx));
+_TYPE( unsigned int ) BigIntegerModInt P((BigInteger d, unsigned int m,
+                                          BigIntegerCtx ctx));
+_TYPE( BigIntegerResult ) BigIntegerModMul P((BigInteger result,
+                                              BigInteger m1, BigInteger m2,
+                                              BigInteger m, BigIntegerCtx ctx));
+_TYPE( BigIntegerResult ) BigIntegerModExp P((BigInteger result,
+                                              BigInteger base, BigInteger expt,
+                                              BigInteger modulus,
+                                              BigIntegerCtx ctx,
+                                              BigIntegerModAccel accel));
+_TYPE( int ) BigIntegerCheckPrime P((BigInteger n, BigIntegerCtx ctx));
+
+_TYPE( BigIntegerResult ) BigIntegerFree P((BigInteger b));
+_TYPE( BigIntegerResult ) BigIntegerClearFree P((BigInteger b));
+
+_TYPE( BigIntegerCtx ) BigIntegerCtxNew();
+_TYPE( BigIntegerResult ) BigIntegerCtxFree P((BigIntegerCtx ctx));
+
+_TYPE( BigIntegerModAccel ) BigIntegerModAccelNew P((BigInteger m,
+                                                     BigIntegerCtx ctx));
+_TYPE( BigIntegerResult ) BigIntegerModAccelFree P((BigIntegerModAccel accel));
+
+_TYPE( BigIntegerResult ) BigIntegerInitialize();
+_TYPE( BigIntegerResult ) BigIntegerFinalize();
+
+_TYPE( BigIntegerResult ) BigIntegerUseEngine P((const char * engine));
+_TYPE( BigIntegerResult ) BigIntegerReleaseEngine();
+
+/* Miscellaneous functions - formerly in t_pwd.h */
+
+/*
+ * "t_random" is a cryptographic random number generator, which is seeded
+ *   from various high-entropy sources and uses a one-way hash function
+ *   in a feedback configuration.
+ * "t_sessionkey" is the interleaved hash used to generate session keys
+ *   from a large integer.
+ * "t_mgf1" is an implementation of MGF1 using SHA1 to generate session
+ *   keys from large integers, and is preferred over the older
+ *   interleaved hash, and is used with SRP6.
+ * "t_getpass" reads a password from the terminal without echoing.
+ */
+_TYPE( void ) t_random P((unsigned char *, unsigned));
+_TYPE( void ) t_stronginitrand();
+_TYPE( unsigned char * )
+  t_sessionkey P((unsigned char *, unsigned char *, unsigned));
+_TYPE( void ) t_mgf1 P((unsigned char *, unsigned,
+                        const unsigned char *, unsigned));
+_TYPE( int ) t_getpass P((char *, unsigned, const char *));
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif /* SRP_AUX_H */
diff --git a/3rd_party/libsrp6a-sha512/t_conv.c b/3rd_party/libsrp6a-sha512/t_conv.c
new file mode 100644
index 0000000..76d4e58
--- /dev/null
+++ b/3rd_party/libsrp6a-sha512/t_conv.c
@@ -0,0 +1,239 @@
+/*
+ * Copyright (c) 1997-2007  The Stanford SRP Authentication Project
+ * All Rights Reserved.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining
+ * a copy of this software and associated documentation files (the
+ * "Software"), to deal in the Software without restriction, including
+ * without limitation the rights to use, copy, modify, merge, publish,
+ * distribute, sublicense, and/or sell copies of the Software, and to
+ * permit persons to whom the Software is furnished to do so, subject to
+ * the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be
+ * included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS-IS" AND WITHOUT WARRANTY OF ANY KIND, 
+ * EXPRESS, IMPLIED OR OTHERWISE, INCLUDING WITHOUT LIMITATION, ANY 
+ * WARRANTY OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.  
+ *
+ * IN NO EVENT SHALL STANFORD BE LIABLE FOR ANY SPECIAL, INCIDENTAL,
+ * INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY KIND, OR ANY DAMAGES WHATSOEVER
+ * RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER OR NOT ADVISED OF
+ * THE POSSIBILITY OF DAMAGE, AND ON ANY THEORY OF LIABILITY, ARISING OUT
+ * OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
+ *
+ * Redistributions in source or binary form must retain an intact copy
+ * of this copyright notice.
+ */
+
+/*#define _POSIX_SOURCE*/
+#include <stdio.h>
+#include "t_defines.h"
+#include "cstr.h"
+
+static int
+hexDigitToInt(char c)
+{
+  if(c >= '0' && c <= '9')
+    return c - '0';
+  else if(c >= 'a' && c <= 'f')
+    return c - 'a' + 10;
+  else if(c >= 'A' && c <= 'F')
+    return c - 'A' + 10;
+  else
+    return 0;
+}
+
+/*
+ * Convert a hex string to a string of bytes; return size of dst
+ */
+_TYPE( int )
+t_fromhex(char *dst, const char *src)
+{
+  register char *chp = dst;
+  register unsigned size = strlen(src);
+
+  /* FIXME: handle whitespace and non-hex digits by setting size and src
+     appropriately. */
+
+  if(size % 2 == 1) {
+    *chp++ = hexDigitToInt(*src++);
+    --size;
+  }
+  while(size > 0) {
+    *chp++ = (hexDigitToInt(*src) << 4) | hexDigitToInt(*(src + 1));
+    src += 2;
+    size -= 2;
+  }
+  return chp - dst;
+}
+
+/*
+ * Convert a string of bytes to their hex representation
+ */
+_TYPE( char * )
+t_tohex(char *dst, const char *src, unsigned size)
+{
+   int notleading = 0;
+
+   register char *chp = dst;
+   *dst = '\0';
+   if (size != 0) do {
+      if(notleading || *src != '\0') {
+        if(!notleading && (*src & 0xf0) == 0) {
+          sprintf(chp, "%.1X", * (unsigned char *) src);
+          chp += 1;
+        }
+        else {
+          sprintf(chp, "%.2X", * (unsigned char *) src);
+          chp += 2;
+        }
+        notleading = 1;
+      }
+      ++src;
+   } while (--size != 0);
+   return dst;
+}
+
+_TYPE( char * )
+t_tohexcstr(cstr *dst, const char *src, unsigned size)
+{
+  cstr_set_length(dst, 2 * size + 1);
+  return t_tohex(dst->data, src, size);
+}
+
+static char b64table[] =
+  "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz./";
+
+/*
+ * Convert a base64 string into raw byte array representation.
+ */
+_TYPE( int )
+t_fromb64(char *dst, const char *src)
+{
+  unsigned char *a;
+  char *loc;
+  int i, j;
+  unsigned int size;
+
+  while(*src && (*src == ' ' || *src == '\t' || *src == '\n'))
+      ++src;
+  size = strlen(src);
+
+  a = malloc((size + 1) * sizeof(unsigned char));
+  if(a == (unsigned char *) 0)
+    return -1;
+
+  i = 0;
+  while(i < size) {
+    loc = strchr(b64table, src[i]);
+    if(loc == (char *) 0)
+      break;
+    else
+      a[i] = loc - b64table;
+    ++i;
+  }
+  size = i;
+
+  i = size - 1;
+  j = size;
+  while(1) {
+    a[j] = a[i];
+    if(--i < 0)
+      break;
+    a[j] |= (a[i] & 3) << 6;
+    --j;
+    a[j] = (unsigned char) ((a[i] & 0x3c) >> 2);
+    if(--i < 0)
+      break;
+    a[j] |= (a[i] & 0xf) << 4;
+    --j;
+    a[j] = (unsigned char) ((a[i] & 0x30) >> 4);
+    if(--i < 0)
+      break;
+    a[j] |= (a[i] << 2);
+
+    a[--j] = 0;
+    if(--i < 0)
+      break;
+  }
+
+  while(a[j] == 0 && j <= size)
+    ++j;
+
+  memcpy(dst, a + j, size - j + 1);
+  free(a);
+  return size - j + 1;
+}
+
+_TYPE( int )
+t_cstrfromb64(cstr *dst, const char *src)
+{
+  int len;
+  cstr_set_length(dst, (strlen(src) * 6 + 7) / 8);
+  len = t_fromb64(dst->data, src);
+  cstr_set_length(dst, len);
+  return len;
+}
+
+/*
+ * Convert a raw byte string into a null-terminated base64 ASCII string.
+ */
+_TYPE( char * )
+t_tob64(char *dst, const char *src, unsigned size)
+{
+  int c, pos = size % 3;
+  unsigned char b0 = 0, b1 = 0, b2 = 0, notleading = 0;
+  char *olddst = dst;
+
+  switch(pos) {
+  case 1:
+    b2 = src[0];
+    break;
+  case 2:
+    b1 = src[0];
+    b2 = src[1];
+    break;
+  }
+
+  while(1) {
+    c = (b0 & 0xfc) >> 2;
+    if(notleading || c != 0) {
+      *dst++ = b64table[c];
+      notleading = 1;
+    }
+    c = ((b0 & 3) << 4) | ((b1 & 0xf0) >> 4);
+    if(notleading || c != 0) {
+      *dst++ = b64table[c];
+      notleading = 1;
+    }
+    c = ((b1 & 0xf) << 2) | ((b2 & 0xc0) >> 6);
+    if(notleading || c != 0) {
+      *dst++ = b64table[c];
+      notleading = 1;
+    }
+    c = b2 & 0x3f;
+    if(notleading || c != 0) {
+      *dst++ = b64table[c];
+      notleading = 1;
+    }
+    if(pos >= size)
+      break;
+    else {
+      b0 = src[pos++];
+      b1 = src[pos++];
+      b2 = src[pos++];
+    }
+  }
+
+  *dst++ = '\0';
+  return olddst;
+}
+
+_TYPE( char * )
+t_tob64cstr(cstr *dst, const char *src, unsigned int sz)
+{
+  cstr_set_length(dst, (sz * 8 + 5) / 6 + 1);
+  return t_tob64(dst->data, src, sz);
+}
diff --git a/3rd_party/libsrp6a-sha512/t_defines.h b/3rd_party/libsrp6a-sha512/t_defines.h
new file mode 100644
index 0000000..447263f
--- /dev/null
+++ b/3rd_party/libsrp6a-sha512/t_defines.h
@@ -0,0 +1,137 @@
+/*
+ * Copyright (c) 1997-2007  The Stanford SRP Authentication Project
+ * All Rights Reserved.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining
+ * a copy of this software and associated documentation files (the
+ * "Software"), to deal in the Software without restriction, including
+ * without limitation the rights to use, copy, modify, merge, publish,
+ * distribute, sublicense, and/or sell copies of the Software, and to
+ * permit persons to whom the Software is furnished to do so, subject to
+ * the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be
+ * included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS-IS" AND WITHOUT WARRANTY OF ANY KIND, 
+ * EXPRESS, IMPLIED OR OTHERWISE, INCLUDING WITHOUT LIMITATION, ANY 
+ * WARRANTY OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.  
+ *
+ * IN NO EVENT SHALL STANFORD BE LIABLE FOR ANY SPECIAL, INCIDENTAL,
+ * INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY KIND, OR ANY DAMAGES WHATSOEVER
+ * RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER OR NOT ADVISED OF
+ * THE POSSIBILITY OF DAMAGE, AND ON ANY THEORY OF LIABILITY, ARISING OUT
+ * OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
+ *
+ * Redistributions in source or binary form must retain an intact copy
+ * of this copyright notice.
+ */
+
+#ifndef T_DEFINES_H
+#define T_DEFINES_H
+
+#ifndef P
+#if defined(__STDC__) || defined(__cplusplus)
+#define P(x) x
+#else
+#define P(x) ()
+#endif
+#endif
+
+#ifdef HAVE_CONFIG_H
+#include "config.h"
+#endif /* HAVE_CONFIG_H */
+
+#ifndef _DLLDECL
+#define _DLLDECL
+
+#ifdef MSVC15   /* MSVC1.5 support for 16 bit apps */
+#define _MSVC15EXPORT _export
+#define _MSVC20EXPORT
+#define _DLLAPI _export _pascal
+#define _CDECL
+#define _TYPE(a) a _MSVC15EXPORT
+#define DLLEXPORT 1
+
+#elif defined(MSVC20) || (defined(_USRDLL) && defined(SRP_EXPORTS))
+#define _MSVC15EXPORT
+#define _MSVC20EXPORT _declspec(dllexport)
+#define _DLLAPI
+#define _CDECL
+#define _TYPE(a) _MSVC20EXPORT a
+#define DLLEXPORT 1
+
+#else                   /* Default, non-dll.  Use this for Unix or DOS */
+#define _MSVC15DEXPORT
+#define _MSVC20EXPORT
+#define _DLLAPI
+#if defined(WINDOWS) || defined(WIN32)
+#define _CDECL _cdecl
+#else
+#define _CDECL
+#endif
+#define _TYPE(a) a _CDECL
+#endif
+#endif
+
+#if STDC_HEADERS
+#include <stdlib.h>
+#include <string.h>
+#else /* not STDC_HEADERS */
+#ifndef HAVE_STRCHR
+#define strchr index
+#define strrchr rindex
+#endif
+char *strchr(), *strrchr(), *strtok();
+#ifndef HAVE_MEMCPY
+#define memcpy(d, s, n) bcopy((s), (d), (n))
+#endif
+#endif /* not STDC_HEADERS */
+
+#include <sys/types.h>
+
+#if TIME_WITH_SYS_TIME
+#include <sys/time.h>
+#include <time.h>
+#else  /* not TIME_WITH_SYS_TIME */
+#if HAVE_SYS_TIME_H
+#include <sys/time.h>
+#else
+#include <time.h>
+#endif
+#endif /* not TIME_WITH_SYS_TIME */
+
+#if HAVE_TERMIOS_H
+#include <termios.h>
+#define STTY(fd, termio) tcsetattr(fd, TCSANOW, termio)
+#define GTTY(fd, termio) tcgetattr(fd, termio)
+#define TERMIO struct termios
+#define USE_TERMIOS
+#elif HAVE_TERMIO_H
+#include <sys/ioctl.h>
+#include <termio.h>
+#define STTY(fd, termio) ioctl(fd, TCSETA, termio)
+#define GTTY(fd, termio) ioctl(fd, TCGETA, termio)
+#define TEMRIO struct termio
+#define USE_TERMIO
+#elif HAVE_SGTTY_H
+#include <sgtty.h>
+#define STTY(fd, termio) stty(fd, termio)
+#define GTTY(fd, termio) gtty(fd, termio)
+#define TERMIO struct sgttyb
+#define USE_SGTTY
+#endif
+
+#ifdef WIN32
+#define USE_FTIME 1
+#define USE_RENAME 1
+#define NO_FCHMOD 1
+#endif
+
+#ifdef USE_FTIME
+#include <sys/timeb.h>
+#endif
+
+/* Looking for BigInteger math functions?  They've moved to <srp_aux.h>. */
+
+#endif
diff --git a/3rd_party/libsrp6a-sha512/t_math.c b/3rd_party/libsrp6a-sha512/t_math.c
new file mode 100644
index 0000000..dac19ec
--- /dev/null
+++ b/3rd_party/libsrp6a-sha512/t_math.c
@@ -0,0 +1,968 @@
+/*
+ * Copyright (c) 1997-2007  The Stanford SRP Authentication Project
+ * All Rights Reserved.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining
+ * a copy of this software and associated documentation files (the
+ * "Software"), to deal in the Software without restriction, including
+ * without limitation the rights to use, copy, modify, merge, publish,
+ * distribute, sublicense, and/or sell copies of the Software, and to
+ * permit persons to whom the Software is furnished to do so, subject to
+ * the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be
+ * included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS-IS" AND WITHOUT WARRANTY OF ANY KIND, 
+ * EXPRESS, IMPLIED OR OTHERWISE, INCLUDING WITHOUT LIMITATION, ANY 
+ * WARRANTY OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.  
+ *
+ * IN NO EVENT SHALL STANFORD BE LIABLE FOR ANY SPECIAL, INCIDENTAL,
+ * INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY KIND, OR ANY DAMAGES WHATSOEVER
+ * RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER OR NOT ADVISED OF
+ * THE POSSIBILITY OF DAMAGE, AND ON ANY THEORY OF LIABILITY, ARISING OUT
+ * OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
+ *
+ * Redistributions in source or binary form must retain an intact copy
+ * of this copyright notice.
+ */
+
+#include <stdio.h>
+#include <sys/types.h>
+
+#include "config.h"
+
+#ifdef OPENSSL
+# include "openssl/opensslv.h"
+# include "openssl/bn.h"
+typedef BIGNUM * BigInteger;
+typedef BN_CTX * BigIntegerCtx;
+typedef BN_MONT_CTX * BigIntegerModAccel;
+#include <limits.h>
+#if OPENSSL_VERSION_NUMBER < 0x30000000L
+# ifndef OPENSSL_NO_ENGINE
+#  define OPENSSL_ENGINE
+#  include "openssl/engine.h"
+static ENGINE * default_engine = NULL;
+# endif /* OPENSSL_ENGINE */
+#endif
+typedef int (*modexp_meth)(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
+                           const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *mctx);
+static modexp_meth default_modexp = NULL;
+#elif defined(CRYPTOLIB)
+# include "libcrypt.h"
+typedef BigInt BigInteger;
+typedef void * BigIntegerCtx;
+typedef void * BigIntegerModAccel;
+#elif defined(GNU_MP)
+# include "gmp.h"
+typedef MP_INT * BigInteger;
+typedef void * BigIntegerCtx;
+typedef void * BigIntegerModAccel;
+# if __GNU_MP_VERSION >= 4 || (__GNU_MP_VERSION == 4 && __GNU_MP_VERSION_MINOR >= 1)
+/* GMP 4.1 and up has fast import/export routines for integer conversion */
+#  define GMP_IMPEXP 1
+# endif
+#elif defined(TOMMATH)
+# ifdef TOMCRYPT
+   /* as of v0.96 */
+#  include "ltc_tommath.h"
+# else
+#  include "tommath.h"
+# endif
+typedef mp_int * BigInteger;
+typedef void * BigIntegerCtx;
+typedef void * BigIntegerModAccel;
+#elif defined(GCRYPT)
+# include "gcrypt.h"
+typedef gcry_mpi_t BigInteger;
+typedef void * BigIntegerCtx;
+typedef void * BigIntegerModAccel;
+#elif defined(MPI)
+# include "mpi.h"
+typedef mp_int * BigInteger;
+typedef void * BigIntegerCtx;
+typedef void * BigIntegerModAccel;
+#elif defined(MBEDTLS)
+#include <mbedtls/bignum.h>
+#include <mbedtls/error.h>
+typedef mbedtls_mpi* BigInteger;
+typedef void * BigIntegerCtx;
+typedef void * BigIntegerModAccel;
+#else
+# error "no math library specified"
+#endif
+#define MATH_PRIV
+
+#include "t_defines.h"
+#include "t_pwd.h"
+#include "srp_aux.h"
+
+/* Math library interface stubs */
+
+BigInteger
+BigIntegerFromInt(unsigned int n)
+{
+#ifdef OPENSSL
+  BIGNUM * a = BN_new();
+  if(a)
+    BN_set_word(a, n);
+  return a;
+#elif defined(CRYPTOLIB)
+  return bigInit(n);
+#elif defined(GNU_MP)
+  BigInteger rv = (BigInteger) malloc(sizeof(MP_INT));
+  if(rv)
+    mpz_init_set_ui(rv, n);
+  return rv;
+#elif defined(GCRYPT)
+  BigInteger rv = gcry_mpi_new(32);
+  gcry_mpi_set_ui(rv, n);
+  return rv;
+#elif defined(MPI) || defined(TOMMATH)
+  BigInteger rv = (BigInteger) malloc(sizeof(mp_int));
+  if(rv) {
+    mp_init(rv);
+    mp_set_int(rv, n);
+  }
+  return rv;
+#elif defined(MBEDTLS)
+  mbedtls_mpi* a = (mbedtls_mpi*)malloc(sizeof(mbedtls_mpi));
+  if (a) {
+    mbedtls_mpi_init(a);
+    mbedtls_mpi_lset(a, n);
+  }
+  return a;
+#endif
+}
+
+BigInteger
+BigIntegerFromBytes(const unsigned char *bytes, int length)
+{
+#ifdef OPENSSL
+  BIGNUM * a = BN_new();
+  BN_bin2bn(bytes, length, a);
+  return a;
+#elif defined(CRYPTOLIB)
+  BigInteger rv, t;
+  int i, n;
+
+  rv = bigInit(0);
+  if(rv == NULL)
+    return rv;
+  if(length % 4 == 0)
+    RSA_bufToBig(bytes, length, rv);
+  else {        /* Wouldn't need this if cryptolib behaved better */
+    i = length & 0x3;
+    if(length > i)
+      RSA_bufToBig(bytes + i, length - i, rv);
+    for(n = 0; i > 0; --i)
+      n = (n << 8) | *bytes++;
+    t = bigInit(n);
+    bigLeftShift(t, (length & ~0x3) << 3, t);
+    bigAdd(rv, t, rv);
+    freeBignum(t);
+  }
+  return rv;
+#elif defined(GNU_MP)
+  BigInteger rv = (BigInteger) malloc(sizeof(MP_INT));
+
+# ifdef GMP_IMPEXP
+  if(rv) {
+    mpz_init(rv);
+    mpz_import(rv, length, 1, 1, 1, 0, bytes);
+  }
+# else
+  cstr * hexbuf = cstr_new();
+
+  if(hexbuf) {
+    if(rv)
+      mpz_init_set_str(rv, t_tohexcstr(hexbuf, bytes, length), 16);
+    cstr_clear_free(hexbuf);
+  }
+# endif /* GMP_IMPEXP */
+
+  return rv;
+#elif defined(GCRYPT)
+  BigInteger rv;
+  gcry_mpi_scan(&rv, GCRYMPI_FMT_USG, bytes, length, NULL);
+  return rv;
+#elif defined(MPI) || defined(TOMMATH)
+  BigInteger rv = (BigInteger) malloc(sizeof(mp_int));
+  if(rv) {
+    mp_init(rv);
+    mp_read_unsigned_bin(rv, (unsigned char *)bytes, length);
+  }
+  return rv;
+#elif defined(MBEDTLS)
+  mbedtls_mpi* a = (mbedtls_mpi*)malloc(sizeof(mbedtls_mpi));
+  if (a) {
+    mbedtls_mpi_init(a);
+    mbedtls_mpi_read_binary(a, bytes, length);
+  }
+  return a;
+#endif
+}
+
+int
+BigIntegerToBytes(BigInteger src, unsigned char *dest, int destlen)
+{
+#ifdef OPENSSL
+  return BN_bn2bin(src, dest);
+#elif defined(CRYPTOLIB)
+  int i, j;
+  cstr * rawbuf;
+
+  trim(src);
+  i = bigBytes(src);
+  j = (bigBits(src) + 7) / 8;
+  if(i == j)
+    RSA_bigToBuf(src, i, dest);
+  else {        /* Wouldn't need this if cryptolib behaved better */
+    rawbuf = cstr_new();
+    cstr_set_length(rawbuf, i);
+    RSA_bigToBuf(src, i, rawbuf->data);
+    memcpy(dest, rawbuf->data + (i-j), j);
+    cstr_clear_free(rawbuf);
+  }
+  return j;
+#elif defined(GNU_MP)
+  size_t r = 0;
+# ifdef GMP_IMPEXP
+  mpz_export(dest, &r, 1, 1, 1, 0, src);
+# else
+  cstr * hexbuf = cstr_new();
+
+  if(hexbuf) {
+    cstr_set_length(hexbuf, mpz_sizeinbase(src, 16) + 1);
+    mpz_get_str(hexbuf->data, 16, src);
+    r = t_fromhex(dest, hexbuf->data);
+    cstr_clear_free(hexbuf);
+  }
+# endif
+  return r;
+#elif defined(GCRYPT)
+  size_t r = 0;
+  gcry_mpi_print(GCRYMPI_FMT_USG, dest, destlen, &r, src);
+  return r;
+#elif defined(MPI) || defined(TOMMATH)
+  mp_to_unsigned_bin(src, dest);
+  return mp_unsigned_bin_size(src);
+#elif defined(MBEDTLS)
+  size_t r = mbedtls_mpi_size(src);
+  mbedtls_mpi_write_binary(src, dest, r);
+  return r;
+#endif
+}
+
+BigIntegerResult
+BigIntegerToCstr(BigInteger x, cstr * out)
+{
+  int n = BigIntegerByteLen(x);
+  if(cstr_set_length(out, n) < 0)
+    return BIG_INTEGER_ERROR;
+  if(cstr_set_length(out, BigIntegerToBytes(x, (unsigned char*)out->data, n)) < 0)
+    return BIG_INTEGER_ERROR;
+  return BIG_INTEGER_SUCCESS;
+}
+
+BigIntegerResult
+BigIntegerToCstrEx(BigInteger x, cstr * out, int len)
+{
+  int n;
+  if(cstr_set_length(out, len) < 0)
+    return BIG_INTEGER_ERROR;
+#if defined(MBEDTLS)
+  /* mbedtls will prefix the output with zeros if the buffer is larger */
+  mbedtls_mpi_write_binary(x, (unsigned char*)out->data, len);
+#else
+  n = BigIntegerToBytes(x, (unsigned char*)out->data, len);
+  if(n < len) {
+    memmove(out->data + (len - n), out->data, n);
+    memset(out->data, 0, len - n);
+  }
+#endif
+  return BIG_INTEGER_SUCCESS;
+}
+
+BigIntegerResult
+BigIntegerToHex(BigInteger src, char *dest, int destlen)
+{
+#ifdef OPENSSL
+  strncpy(dest, BN_bn2hex(src), destlen);
+#elif defined(CRYPTOLIB)
+  trim(src);
+  bigsprint(src, dest);
+#elif defined(GNU_MP)
+  mpz_get_str(dest, 16, src);
+#elif defined(GCRYPT)
+  gcry_mpi_print(GCRYMPI_FMT_HEX, dest, destlen, NULL, src);
+#elif defined(MPI) || defined(TOMMATH)
+  mp_toradix(src, dest, 16);
+#elif defined(MBEDTLS)
+  size_t olen = 0;
+  mbedtls_mpi_write_string(src, 16, dest, destlen, &olen);
+#endif
+  return BIG_INTEGER_SUCCESS;
+}
+
+static char b64table[] =
+  "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz./";
+
+BigIntegerResult
+BigIntegerToString(BigInteger src, char *dest, int destlen, unsigned int radix)
+{
+  BigInteger t = BigIntegerFromInt(0);
+  char * p = dest;
+  char c;
+
+  *p++ = b64table[BigIntegerModInt(src, radix, NULL)];
+  BigIntegerDivInt(t, src, radix, NULL);
+  while(BigIntegerCmpInt(t, 0) > 0) {
+    *p++ = b64table[BigIntegerModInt(t, radix, NULL)];
+    BigIntegerDivInt(t, t, radix, NULL);
+  }
+  BigIntegerFree(t);
+  *p-- = '\0';
+  /* reverse the string */
+  while(p > dest) {
+    c = *p;
+    *p-- =  *dest;
+    *dest++ = c;
+  }
+  return BIG_INTEGER_SUCCESS;
+}
+
+int
+BigIntegerBitLen(BigInteger b)
+{
+#ifdef OPENSSL
+  return BN_num_bits(b);
+#elif defined(CRYPTOLIB)
+  return bigBits(b);
+#elif defined(GNU_MP)
+  return mpz_sizeinbase(b, 2);
+#elif defined(GCRYPT)
+  return gcry_mpi_get_nbits(b);
+#elif defined(MPI) || defined(TOMMATH)
+  return mp_count_bits(b);
+#elif defined(MBEDTLS)
+  return (int)mbedtls_mpi_bitlen(b);
+#endif
+}
+
+int
+BigIntegerCmp(BigInteger c1, BigInteger c2)
+{
+#ifdef OPENSSL
+  return BN_cmp(c1, c2);
+#elif defined(CRYPTOLIB)
+  return bigCompare(c1, c2);
+#elif defined(GNU_MP)
+  return mpz_cmp(c1, c2);
+#elif defined(GCRYPT)
+  return gcry_mpi_cmp(c1, c2);
+#elif defined(MPI) || defined(TOMMATH)
+  return mp_cmp(c1, c2);
+#elif defined(MBEDTLS)
+  return mbedtls_mpi_cmp_mpi(c1, c2);
+#endif
+}
+
+int
+BigIntegerCmpInt(BigInteger c1, unsigned int c2)
+{
+#ifdef OPENSSL
+  BigInteger bc2 = BigIntegerFromInt(c2);
+  int rv = BigIntegerCmp(c1, bc2);
+  BigIntegerFree(bc2);
+  return rv;
+#elif defined(CRYPTOLIB)
+  BigInteger t;
+  int rv;
+
+  t = bigInit(c2);
+  rv = bigCompare(c1, t);
+  freeBignum(t);
+  return rv;
+#elif defined(GNU_MP)
+  return mpz_cmp_ui(c1, c2);
+#elif defined(TOMMATH)
+  return mp_cmp_d(c1, c2);
+#elif defined(GCRYPT)
+  return gcry_mpi_cmp_ui(c1, c2);
+#elif defined(MPI)
+  return mp_cmp_int(c1, c2);
+#elif defined(MBEDTLS)
+  return mbedtls_mpi_cmp_int(c1, c2);
+#endif
+}
+
+BigIntegerResult
+BigIntegerLShift(BigInteger result, BigInteger x, unsigned int bits)
+{
+#ifdef OPENSSL
+  BN_lshift(result, x, bits);
+#elif defined(CRYPTOLIB)
+  bigLeftShift(x, bits, result);
+#elif defined(GNU_MP)
+  mpz_mul_2exp(result, x, bits);
+#elif defined(GCRYPT)
+  gcry_mpi_mul_2exp(result, x, bits);
+#elif defined(MPI) || defined(TOMMATH)
+  mp_mul_2d(x, bits, result);
+#elif defined(MBEDTLS)
+  mbedtls_mpi_copy(result, x);
+  mbedtls_mpi_shift_l(result, bits);
+#endif
+  return BIG_INTEGER_SUCCESS;
+}
+
+BigIntegerResult
+BigIntegerAdd(BigInteger result, BigInteger a1, BigInteger a2)
+{
+#ifdef OPENSSL
+  BN_add(result, a1, a2);
+#elif defined(CRYPTOLIB)
+  bigAdd(a1, a2, result);
+#elif defined(GNU_MP)
+  mpz_add(result, a1, a2);
+#elif defined(GCRYPT)
+  gcry_mpi_add(result, a1, a2);
+#elif defined(MPI) || defined(TOMMATH)
+  mp_add(a1, a2, result);
+#elif defined(MBEDTLS)
+  mbedtls_mpi_add_mpi(result, a1, a2);
+#endif
+  return BIG_INTEGER_SUCCESS;
+}
+
+BigIntegerResult
+BigIntegerAddInt(BigInteger result, BigInteger a1, unsigned int a2)
+{
+#ifdef OPENSSL
+  if(result != a1)
+    BN_copy(result, a1);
+  BN_add_word(result, a2);
+#elif defined(CRYPTOLIB)
+  BigInteger t;
+
+  t = bigInit(a2);
+  bigAdd(a1, t, result);
+  freeBignum(t);
+#elif defined(GNU_MP)
+  mpz_add_ui(result, a1, a2);
+#elif defined(GCRYPT)
+  gcry_mpi_add_ui(result, a1, a2);
+#elif defined(MPI) || defined(TOMMATH)
+  mp_add_d(a1, a2, result);
+#elif defined(MBEDTLS)
+  mbedtls_mpi_add_int(result, a1, a2);
+#endif
+  return BIG_INTEGER_SUCCESS;
+}
+
+BigIntegerResult
+BigIntegerSub(BigInteger result, BigInteger s1, BigInteger s2)
+{
+#ifdef OPENSSL
+  BN_sub(result, s1, s2);
+#elif defined(CRYPTOLIB)
+  bigSubtract(s1, s2, result);
+#elif defined(GNU_MP)
+  mpz_sub(result, s1, s2);
+#elif defined(GCRYPT)
+  gcry_mpi_sub(result, s1, s2);
+#elif defined(MPI) || defined(TOMMATH)
+  mp_sub(s1, s2, result);
+#elif defined(MBEDTLS)
+  mbedtls_mpi_sub_mpi(result, s1, s2);
+#endif
+  return BIG_INTEGER_SUCCESS;
+}
+
+BigIntegerResult
+BigIntegerSubInt(BigInteger result, BigInteger s1, unsigned int s2)
+{
+#ifdef OPENSSL
+  if(result != s1)
+    BN_copy(result, s1);
+  BN_sub_word(result, s2);
+#elif defined(CRYPTOLIB)
+  BigInteger t;
+
+  t = bigInit(s2);
+  bigSubtract(s1, t, result);
+  freeBignum(t);
+#elif defined(GNU_MP)
+  mpz_sub_ui(result, s1, s2);
+#elif defined(GCRYPT)
+  gcry_mpi_sub_ui(result, s1, s2);
+#elif defined(MPI) || defined(TOMMATH)
+  mp_sub_d(s1, s2, result);
+#elif defined(MBEDTLS)
+  mbedtls_mpi_sub_int(result, s1, s2);
+#endif
+  return BIG_INTEGER_SUCCESS;
+}
+
+BigIntegerResult
+BigIntegerMul(BigInteger result, BigInteger m1, BigInteger m2, BigIntegerCtx c)
+{
+#ifdef OPENSSL
+  BN_CTX * ctx = NULL;
+  if(c == NULL)
+    c = ctx = BN_CTX_new();
+  BN_mul(result, m1, m2, c);
+  if(ctx)
+    BN_CTX_free(ctx);
+#elif defined(CRYPTOLIB)
+  bigMultiply(m1, m2, result);
+#elif defined(GNU_MP)
+  mpz_mul(result, m1, m2);
+#elif defined(GCRYPT)
+  gcry_mpi_mul(result, m1, m2);
+#elif defined(MPI) || defined(TOMMATH)
+  mp_mul(m1, m2, result);
+#elif defined(MBEDTLS)
+  mbedtls_mpi_mul_mpi(result, m1, m2);
+#endif
+  return BIG_INTEGER_SUCCESS;
+}
+
+BigIntegerResult
+BigIntegerMulInt(BigInteger result, BigInteger m1, unsigned int m2, BigIntegerCtx c)
+{
+#ifdef OPENSSL
+  if(result != m1)
+    BN_copy(result, m1);
+  BN_mul_word(result, m2);
+#elif defined(CRYPTOLIB)
+  BigInteger t;
+
+  t = bigInit(m2);
+  bigMultiply(m1, t, result);
+  freeBignum(t);
+#elif defined(GNU_MP)
+  mpz_mul_ui(result, m1, m2);
+#elif defined(GCRYPT)
+  gcry_mpi_mul_ui(result, m1, m2);
+#elif defined(MPI) || defined(TOMMATH)
+  mp_mul_d(m1, m2, result);
+#elif defined(MBEDTLS)
+  mbedtls_mpi_mul_int(result, m1, m2);
+#endif
+  return BIG_INTEGER_SUCCESS;
+}
+
+BigIntegerResult
+BigIntegerDivInt(BigInteger result, BigInteger d, unsigned int m, BigIntegerCtx c)
+{
+#ifdef OPENSSL
+  if(result != d)
+    BN_copy(result, d);
+  BN_div_word(result, m);
+#elif defined(CRYPTOLIB)
+  BigInteger t, u, q;
+
+  t = bigInit(m);
+  u = bigInit(0);
+  /* We use a separate variable q because cryptolib breaks if result == d */
+  q = bigInit(0);
+  bigDivide(d, t, q, u);
+  freeBignum(t);
+  freeBignum(u);
+  bigCopy(q, result);
+  freeBignum(q);
+#elif defined(GNU_MP)
+# ifdef GMP2
+  mpz_fdiv_q_ui(result, d, m);
+# else
+  mpz_div_ui(result, d, m);
+# endif
+#elif defined(GCRYPT)
+  BigInteger t = BigIntegerFromInt(m);
+  gcry_mpi_div(result, NULL, d, t, -1);
+  BigIntegerFree(t);
+#elif defined(MPI) || defined(TOMMATH)
+  mp_div_d(d, m, result, NULL);
+#elif defined(MBEDTLS)
+  mbedtls_mpi_div_int(result, NULL, d, m);
+#endif
+  return BIG_INTEGER_SUCCESS;
+}
+
+BigIntegerResult
+BigIntegerMod(BigInteger result, BigInteger d, BigInteger m, BigIntegerCtx c)
+{
+#ifdef OPENSSL
+  BN_CTX * ctx = NULL;
+  if(c == NULL)
+    c = ctx = BN_CTX_new();
+  BN_mod(result, d, m, c);
+  if(ctx)
+    BN_CTX_free(ctx);
+#elif defined(CRYPTOLIB)
+  bigMod(d, m, result);
+#elif defined(GNU_MP)
+  mpz_mod(result, d, m);
+#elif defined(GCRYPT)
+  gcry_mpi_mod(result, d, m);
+#elif defined(MPI) || defined(TOMMATH)
+  mp_mod(d, m, result);
+#elif defined(MBEDTLS)
+  mbedtls_mpi_mod_mpi(result, d, m);
+#endif
+  return BIG_INTEGER_SUCCESS;
+}
+
+unsigned int
+BigIntegerModInt(BigInteger d, unsigned int m, BigIntegerCtx c)
+{
+#ifdef OPENSSL
+  return BN_mod_word(d, m);
+#elif defined(CRYPTOLIB)
+  BigInteger t, u;
+  unsigned char r[4];
+
+  t = bigInit(m);
+  u = bigInit(0);
+  bigMod(d, t, u);
+  bigToBuf(u, sizeof(r), r);
+  freeBignum(t);
+  freeBignum(u);
+  return r[0] | (r[1] << 8) | (r[2] << 16) | (r[3] << 24);
+#elif defined(GNU_MP)
+  MP_INT result;
+  unsigned int i;
+
+  mpz_init(&result);
+
+/* Define GMP2 if you're using an old gmp.h but want to link against a
+ * newer libgmp.a (e.g. 2.0 or later). */
+
+# ifdef GMP2
+  mpz_fdiv_r_ui(&result, d, m);
+# else
+  mpz_mod_ui(&result, d, m);
+# endif
+  i = mpz_get_ui(&result);
+  mpz_clear(&result);
+  return i;
+#elif defined(GCRYPT)
+  /* TODO: any way to clean this up??? */
+  unsigned char r[4];
+  size_t len, i;
+  unsigned int ret = 0;
+  BigInteger t = BigIntegerFromInt(m);
+  BigInteger a = BigIntegerFromInt(0);
+  gcry_mpi_mod(a, d, t);
+  gcry_mpi_print(GCRYMPI_FMT_USG, r, 4, &len, a);
+  for(i = 0; i < len; ++i)
+    ret = (ret << 8) | r[i];
+  BigIntegerFree(t);
+  BigIntegerFree(a);
+  return ret;
+#elif defined(MPI) || defined(TOMMATH)
+  mp_digit r;
+  mp_mod_d(d, m, &r);
+  return r;
+#elif defined(MBEDTLS)
+  mbedtls_mpi_uint r = 0;
+  mbedtls_mpi_mod_int(&r, d, m);
+  return r;
+#endif
+}
+
+BigIntegerResult
+BigIntegerModMul(BigInteger r, BigInteger m1, BigInteger m2, BigInteger modulus, BigIntegerCtx c)
+{
+#ifdef OPENSSL
+  BN_CTX * ctx = NULL;
+  if(c == NULL)
+    c = ctx = BN_CTX_new();
+  BN_mod_mul(r, m1, m2, modulus, c);
+  if(ctx)
+    BN_CTX_free(ctx);
+#elif defined(CRYPTOLIB)
+  bigMultiply(m1, m2, r);
+  bigMod(r, modulus, r);
+#elif defined(GNU_MP)
+  mpz_mul(r, m1, m2);
+  mpz_mod(r, r, modulus);
+#elif defined(GCRYPT)
+  gcry_mpi_mulm(r, m1, m2, modulus);
+#elif defined(MPI) || defined(TOMMATH)
+  mp_mulmod(m1, m2, modulus, r);
+#elif defined(MBEDTLS)
+  mbedtls_mpi d;
+  mbedtls_mpi_init(&d);
+  mbedtls_mpi_mul_mpi(&d, m1, m2);
+  mbedtls_mpi_mod_mpi(r, &d, modulus);
+  mbedtls_mpi_free(&d);
+#endif
+  return BIG_INTEGER_SUCCESS;
+}
+
+BigIntegerResult
+BigIntegerModExp(BigInteger r, BigInteger b, BigInteger e, BigInteger m, BigIntegerCtx c, BigIntegerModAccel a)
+{
+#ifdef OPENSSL
+#if OPENSSL_VERSION_NUMBER >= 0x00906000
+  BN_ULONG B = BN_get_word(b);
+#endif
+  BN_CTX * ctx = NULL;
+  if(c == NULL)
+    c = ctx = BN_CTX_new();
+  if(default_modexp) {
+    (*default_modexp)(r, b, e, m, c, a);
+  }
+  else if(a == NULL) {
+    BN_mod_exp(r, b, e, m, c);
+  }
+/*
+ * In LibreSSL BN_mod_exp_mont_word() is not a public symbol where BN_mod_exp()
+ * and BN_mod_exp_mont() will use the word optimization when appropriate.
+ */
+#if OPENSSL_VERSION_NUMBER >= 0x00906000 && !defined(LIBRESSL_VERSION_NUMBER)
+  else if(B > 0 && B < ULONG_MAX) {  /* 0.9.6 and above has mont_word optimization */
+    BN_mod_exp_mont_word(r, B, e, m, c, a);
+  }
+#endif
+  else
+    BN_mod_exp_mont(r, b, e, m, c, a);
+  if(ctx)
+    BN_CTX_free(ctx);
+#elif defined(CRYPTOLIB)
+  bigPow(b, e, m, r);
+#elif defined(GNU_MP)
+  mpz_powm(r, b, e, m);
+#elif defined(GCRYPT)
+  gcry_mpi_powm(r, b, e, m);
+#elif defined(MPI) || defined(TOMMATH)
+  mp_exptmod(b, e, m, r);
+#elif defined(MBEDTLS)
+  mbedtls_mpi_exp_mod(r, b, e, m, NULL);
+#endif
+  return BIG_INTEGER_SUCCESS;
+}
+
+#if defined(MBEDTLS)
+int _mbedtls_f_rng(void* unused, unsigned char *buf, size_t size)
+{
+  t_random(buf, size);
+  return 0;
+}
+#endif
+
+int
+BigIntegerCheckPrime(BigInteger n, BigIntegerCtx c)
+{
+#ifdef OPENSSL
+  int rv;
+  BN_CTX * ctx = NULL;
+  if(c == NULL)
+    c = ctx = BN_CTX_new();
+#if OPENSSL_VERSION_NUMBER >= 0x00908000
+  #if OPENSSL_VERSION_NUMBER >= 0x30000000L
+    rv = BN_check_prime(n, c, NULL);
+  #else
+    rv = BN_is_prime_ex(n, 25, c, NULL);
+  #endif
+#else
+  rv = BN_is_prime(n, 25, NULL, c, NULL);
+#endif
+  if(ctx)
+    BN_CTX_free(ctx);
+  return rv;
+#elif defined(CRYPTOLIB)
+#if 0
+  /*
+   * Ugh.  Not only is cryptolib's bigDivide sensitive to inputs
+   * and outputs being the same, but now the primeTest needs random
+   * numbers, which it gets by calling cryptolib's broken truerand
+   * implementation(!)  We have to fake it out by doing our own
+   * seeding explicitly.
+   */
+  static int seeded = 0;
+  static unsigned char seedbuf[64];
+  if(!seeded) {
+    t_random(seedbuf, sizeof(seedbuf));
+    seedDesRandom(seedbuf, sizeof(seedbuf));
+    memset(seedbuf, 0, sizeof(seedbuf));
+    seeded = 1;
+  }
+#endif /* 0 */
+  t_random(NULL, 0);
+  return primeTest(n);
+#elif defined(GNU_MP)
+  return mpz_probab_prime_p(n, 25);
+#elif defined(GCRYPT)
+  return (gcry_prime_check(n, 0) == GPG_ERR_NO_ERROR);
+#elif defined(TOMMATH)
+  int rv;
+  mp_prime_is_prime(n, 25, &rv);
+  return rv;
+#elif defined(MPI)
+  return (mpp_pprime(n, 25) == MP_YES);
+#elif defined(MBEDTLS)
+  return mbedtls_mpi_is_prime_ext(n, 25, _mbedtls_f_rng, NULL);
+#endif
+}
+
+BigIntegerResult
+BigIntegerFree(BigInteger b)
+{
+#ifdef OPENSSL
+  BN_free(b);
+#elif defined(CRYPTOLIB)
+  freeBignum(b);
+#elif defined(GNU_MP)
+  mpz_clear(b);
+  free(b);
+#elif defined(GCRYPT)
+  gcry_mpi_release(b);
+#elif defined(MPI) || defined(TOMMATH)
+  mp_clear(b);
+  free(b);
+#elif defined(MBEDTLS)
+  mbedtls_mpi_free(b);
+  free(b);
+#endif
+  return BIG_INTEGER_SUCCESS;
+}
+
+BigIntegerResult
+BigIntegerClearFree(BigInteger b)
+{
+#ifdef OPENSSL
+  BN_clear_free(b);
+#elif defined(CRYPTOLIB)
+  /* TODO */
+  freeBignum(b);
+#elif defined(GNU_MP)
+  /* TODO */
+  mpz_clear(b);
+  free(b);
+#elif defined(GCRYPT)
+  /* TODO */
+  gcry_mpi_release(b);
+#elif defined(MPI) || defined(TOMMATH)
+  /* TODO */
+  mp_clear(b);
+  free(b);
+#elif defined(MBEDTLS)
+  mbedtls_mpi_free(b);
+  free(b);
+#endif
+  return BIG_INTEGER_SUCCESS;
+}
+
+BigIntegerCtx
+BigIntegerCtxNew()
+{
+#ifdef OPENSSL
+  return BN_CTX_new();
+#else
+  return NULL;
+#endif
+}
+
+BigIntegerResult
+BigIntegerCtxFree(BigIntegerCtx ctx)
+{
+#ifdef OPENSSL
+  if(ctx)
+    BN_CTX_free(ctx);
+#endif
+  return BIG_INTEGER_SUCCESS;
+}
+
+BigIntegerModAccel
+BigIntegerModAccelNew(BigInteger m, BigIntegerCtx c)
+{
+#ifdef OPENSSL
+  BN_CTX * ctx = NULL;
+  BN_MONT_CTX * mctx;
+  if(default_modexp)
+    return NULL;
+  if(c == NULL)
+    c = ctx = BN_CTX_new();
+  mctx = BN_MONT_CTX_new();
+  BN_MONT_CTX_set(mctx, m, c);
+  if(ctx)
+    BN_CTX_free(ctx);
+  return mctx;
+#else
+  return NULL;
+#endif
+}
+
+BigIntegerResult
+BigIntegerModAccelFree(BigIntegerModAccel accel)
+{
+#ifdef OPENSSL
+  if(accel)
+    BN_MONT_CTX_free(accel);
+#endif
+  return BIG_INTEGER_SUCCESS;
+}
+
+BigIntegerResult
+BigIntegerInitialize()
+{
+#if OPENSSL_VERSION_NUMBER >= 0x00907000 && defined(OPENSSL_ENGINE)
+  ENGINE_load_builtin_engines();
+#endif
+  return BIG_INTEGER_SUCCESS;
+}
+
+BigIntegerResult
+BigIntegerFinalize()
+{
+  return BigIntegerReleaseEngine();
+}
+
+BigIntegerResult
+BigIntegerUseEngine(const char * engine)
+{
+#if defined(OPENSSL) && defined(OPENSSL_ENGINE)
+  ENGINE * e = ENGINE_by_id(engine);
+  if(e) {
+    if(ENGINE_init(e) > 0) {
+#if OPENSSL_VERSION_NUMBER >= 0x00907000
+      /* 0.9.7 loses the BN_mod_exp method.  Pity. */
+      const RSA_METHOD * rsa = ENGINE_get_RSA(e);
+      if(rsa)
+#if (defined(LIBRESSL_VERSION_NUMBER) && LIBRESSL_VERSION_NUMBER >= 0x3000000fL) || (!defined(LIBRESSL_VERSION_NUMBER) && OPENSSL_VERSION_NUMBER >= 0x10100005L)
+        default_modexp = (modexp_meth)RSA_meth_get_bn_mod_exp(rsa);
+#else
+        default_modexp = (modexp_meth)rsa->bn_mod_exp;
+#endif
+#else
+      default_modexp = (modexp_meth)ENGINE_get_BN_mod_exp(e);
+#endif
+      BigIntegerReleaseEngine();
+      default_engine = e;
+      return BIG_INTEGER_SUCCESS;
+    }
+    else
+      ENGINE_free(e);
+  }
+#endif
+  return BIG_INTEGER_ERROR;
+}
+
+BigIntegerResult
+BigIntegerReleaseEngine()
+{
+#if defined(OPENSSL) && defined(OPENSSL_ENGINE)
+  if(default_engine) {
+    ENGINE_finish(default_engine);
+    ENGINE_free(default_engine);
+    default_engine = NULL;
+    default_modexp = NULL;
+  }
+#endif
+  return BIG_INTEGER_SUCCESS;
+}
diff --git a/3rd_party/libsrp6a-sha512/t_misc.c b/3rd_party/libsrp6a-sha512/t_misc.c
new file mode 100644
index 0000000..3a2cda1
--- /dev/null
+++ b/3rd_party/libsrp6a-sha512/t_misc.c
@@ -0,0 +1,439 @@
+/*
+ * Copyright (c) 1997-2007  The Stanford SRP Authentication Project
+ * All Rights Reserved.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining
+ * a copy of this software and associated documentation files (the
+ * "Software"), to deal in the Software without restriction, including
+ * without limitation the rights to use, copy, modify, merge, publish,
+ * distribute, sublicense, and/or sell copies of the Software, and to
+ * permit persons to whom the Software is furnished to do so, subject to
+ * the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be
+ * included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS-IS" AND WITHOUT WARRANTY OF ANY KIND, 
+ * EXPRESS, IMPLIED OR OTHERWISE, INCLUDING WITHOUT LIMITATION, ANY 
+ * WARRANTY OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.  
+ *
+ * IN NO EVENT SHALL STANFORD BE LIABLE FOR ANY SPECIAL, INCIDENTAL,
+ * INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY KIND, OR ANY DAMAGES WHATSOEVER
+ * RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER OR NOT ADVISED OF
+ * THE POSSIBILITY OF DAMAGE, AND ON ANY THEORY OF LIABILITY, ARISING OUT
+ * OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
+ *
+ * Redistributions in source or binary form must retain an intact copy
+ * of this copyright notice.
+ */
+
+#include "t_defines.h"
+
+#ifdef HAVE_UNISTD_H
+#include <unistd.h>
+#endif /* HAVE_UNISTD_H */
+
+#include <stdio.h>
+#include <sys/types.h>
+#include <sys/stat.h>
+#include <fcntl.h>
+
+#ifdef WIN32
+#include <process.h>
+#include <io.h>
+#endif
+
+#include "t_sha.h"
+
+#ifndef NULL
+#define NULL 0
+#endif
+
+#ifdef OPENSSL
+#include <openssl/opensslv.h>
+#include <openssl/rand.h>
+#elif defined(TOMCRYPT)
+#include "tomcrypt.h"
+static prng_state g_rng;
+static unsigned char entropy[32];
+#elif defined(CRYPTOLIB)
+# include "libcrypt.h"
+static unsigned char crpool[64];
+#else
+static unsigned char randpool[SHA_DIGESTSIZE], randout[SHA_DIGESTSIZE];
+static unsigned long randcnt = 0;
+static unsigned int outpos = 0;
+SHA1_CTX randctxt;
+#endif /* OPENSSL */
+
+/*
+ * t_envhash - Generate a 160-bit SHA hash of the environment
+ *
+ * This routine performs an SHA hash of all the "name=value" pairs
+ * in the environment concatenated together and dumps them in the
+ * output.  While it is true that anyone on the system can see
+ * your environment, someone not on the system will have a very
+ * difficult time guessing it, especially since some systems play
+ * tricks with variable ordering and sometimes define quirky
+ * environment variables like $WINDOWID or $_.
+ */
+extern char ** environ;
+
+static void
+t_envhash(unsigned char * out)
+{
+  char ** ptr;
+  char ebuf[256];
+  SHA1_CTX ctxt;
+
+  SHA1Init(&ctxt);
+  for(ptr = environ; *ptr; ++ptr) {
+    strncpy(ebuf, *ptr, 255);
+    ebuf[255] = '\0';
+    SHA1Update(&ctxt, ebuf, strlen(ebuf));
+  }
+  SHA1Final(out, &ctxt);
+}
+
+/*
+ * t_fshash - Generate a 160-bit SHA hash from the file system
+ *
+ * This routine climbs up the directory tree from the current
+ * directory, running stat() on each directory until it hits the
+ * root directory.  This information is sensitive to the last
+ * access/modification times of all the directories above you,
+ * so someone who lists one of those directories injects some
+ * entropy into the system.  Obviously, this hash is very sensitive
+ * to your current directory when the program is run.
+ *
+ * For good measure, it also performs an fstat on the standard input,
+ * usually your tty, throws that into the buffer, creates a file in
+ * /tmp (the inode is unpredictable on a busy system), and runs stat()
+ * on that before deleting it.
+ *
+ * The entire buffer is run once through SHA to obtain the final result.
+ */
+static void
+t_fshash(unsigned char * out)
+{
+  char dotpath[128];
+  struct stat st;
+  SHA1_CTX ctxt;
+  int i, pinode;
+  dev_t pdev;
+
+  SHA1Init(&ctxt);
+  if(stat(".", &st) >= 0) {
+    SHA1Update(&ctxt, (unsigned char *) &st, sizeof(st));
+    pinode = st.st_ino;
+    pdev = st.st_dev;
+    strcpy(dotpath, "..");
+    for(i = 0; i < 40; ++i) {
+      if(stat(dotpath, &st) < 0)
+        break;
+      if(st.st_ino == pinode && st.st_dev == pdev)
+        break;
+      SHA1Update(&ctxt, (unsigned char *) &st, sizeof(st));
+      pinode = st.st_ino;
+      pdev = st.st_dev;
+      strcat(dotpath, "/..");
+    }
+  }
+
+  if(fstat(0, &st) >= 0)
+    SHA1Update(&ctxt, (unsigned char *) &st, sizeof(st));
+
+  sprintf(dotpath, "/tmp/rnd.%d", getpid());
+  if(creat(dotpath, 0600) >= 0 && stat(dotpath, &st) >= 0)
+    SHA1Update(&ctxt, (unsigned char *) &st, sizeof(st));
+  unlink(dotpath);
+
+  SHA1Final(out, &ctxt);
+}
+
+/*
+ * Generate a high-entropy seed for the strong random number generator.
+ * This uses a wide variety of quickly gathered and somewhat unpredictable
+ * system information.  The 'preseed' structure is assembled from:
+ *
+ *   The system time in seconds
+ *   The system time in microseconds
+ *   The current process ID
+ *   The parent process ID
+ *   A hash of the user's environment
+ *   A hash gathered from the file system
+ *   Input from a random device, if available
+ *   Timings of system interrupts
+ *
+ * The entire structure (60 bytes on most systems) is fed to SHA to produce
+ * a 160-bit seed for the strong random number generator.  It is believed
+ * that in the worst case (on a quiet system with no random device versus
+ * an attacker who has access to the system already), the seed contains at
+ * least about 80 bits of entropy.  Versus an attacker who does not have
+ * access to the system, the entropy should be slightly over 128 bits.
+ */
+static char initialized = 0;
+
+static struct {
+  unsigned int trand1;
+  time_t sec;
+  time_t subsec;
+  short pid;
+  short ppid;
+  unsigned char envh[SHA_DIGESTSIZE];
+  unsigned char fsh[SHA_DIGESTSIZE];
+  unsigned char devrand[20];
+  unsigned int trand2;
+} preseed;
+
+unsigned long raw_truerand();
+
+static void
+t_initrand()
+{
+  SHA1_CTX ctxt;
+#ifdef USE_FTIME
+  struct timeb t;
+#else
+  struct timeval t;
+#endif
+  int i, r=0;
+
+  if(initialized)
+    return;
+
+  initialized = 1;
+
+#if defined(OPENSSL)    /* OpenSSL has nifty win32 entropy-gathering code */
+#if OPENSSL_VERSION_NUMBER >= 0x00905100
+  r = RAND_status();
+#if defined(WINDOWS) || defined(WIN32)
+  if(r)         /* Don't do the Unix-y stuff on Windows if possible */
+    return;
+#else
+#endif
+#endif
+
+#elif defined(TOMCRYPT)
+  yarrow_start(&g_rng);
+  r = rng_get_bytes(entropy, sizeof(entropy), NULL);
+  if(r > 0) {
+    yarrow_add_entropy(entropy, r, &g_rng);
+    memset(entropy, 0, sizeof(entropy));
+# if defined(WINDOWS) || defined(WIN32)
+    /* Don't do the Unix-y stuff on Windows if possible */
+    yarrow_ready(&g_rng);
+    return;
+# endif
+  }
+#endif
+
+#if !defined(WINDOWS) && !defined(WIN32)
+  i = open("/dev/urandom", O_RDONLY);
+  if(i > 0) {
+    r += read(i, preseed.devrand, sizeof(preseed.devrand));
+    close(i);
+  }
+#endif /* !WINDOWS && !WIN32 */
+
+  /* Resort to truerand only if desperate for some Real entropy */
+  if(r == 0)
+    preseed.trand1 = raw_truerand();
+
+#ifdef USE_FTIME
+  ftime(&t);
+  preseed.sec = t.time;
+  preseed.subsec = t.millitm;
+#else
+  gettimeofday(&t, NULL);
+  preseed.sec = t.tv_sec;
+  preseed.subsec = t.tv_usec;
+#endif
+  preseed.pid = getpid();
+#ifndef WIN32
+  preseed.ppid = getppid();
+#endif
+  t_envhash(preseed.envh);
+  t_fshash(preseed.fsh);
+
+  if(r == 0)
+    preseed.trand2 = raw_truerand();
+
+#ifdef OPENSSL
+  RAND_seed((unsigned char *)&preseed, sizeof(preseed));
+#elif defined(TOMCRYPT)
+  yarrow_add_entropy((unsigned char *)&preseed, sizeof(preseed), &g_rng);
+  yarrow_ready(&g_rng);
+#elif defined(CRYPTOLIB)
+  t_mgf1(crpool, sizeof(crpool), (unsigned char *) &preseed, sizeof(preseed));
+  seedDesRandom(crpool, sizeof(crpool));
+  memset(crpool, 0, sizeof(crpool));
+#elif defined(GCRYPT)
+  gcry_random_add_bytes((unsigned char *)&preseed, sizeof(preseed), -1);
+#else
+  SHA1Init(&ctxt);
+  SHA1Update(&ctxt, (unsigned char *) &preseed, sizeof(preseed));
+  SHA1Final(randpool, &ctxt);
+  memset((unsigned char *) &ctxt, 0, sizeof(ctxt));
+  outpos = 0;
+#endif /* OPENSSL */
+  memset((unsigned char *) &preseed, 0, sizeof(preseed));
+}
+
+#define NUM_RANDOMS 12
+
+_TYPE( void )
+t_stronginitrand()
+{
+#if 1   /* t_initrand() has been improved enough to make this unnecessary */
+  t_initrand();
+#else
+  SHA1_CTX ctxt;
+  unsigned int rawrand[NUM_RANDOMS];
+  int i;
+
+  if(!initialized)
+    t_initrand();
+  for(i = 0; i < NUM_RANDOMS; ++i)
+    rawrand[i] = raw_truerand();
+  SHA1Init(&ctxt);
+  SHA1Update(&ctxt, (unsigned char *) rawrand, sizeof(rawrand));
+  SHA1Final(randkey2, &ctxt);
+  memset(rawrand, 0, sizeof(rawrand));
+#endif
+}
+
+/*
+ * The strong random number generator.  This uses a 160-bit seed
+ * and uses SHA-1 in a feedback configuration to generate successive
+ * outputs.  If S[0] is set to the initial seed, then:
+ *
+ *         S[i+1] = SHA-1(i || S[i])
+ *         A[i] = SHA-1(S[i])
+ *
+ * where the A[i] are the output blocks starting with i=0.
+ * Each cycle generates 20 bytes of new output.
+ */
+_TYPE( void )
+t_random(unsigned char * data, unsigned size)
+{
+  if(!initialized)
+    t_initrand();
+
+  if(size <= 0)         /* t_random(NULL, 0) forces seed initialization */
+    return;
+
+#ifdef OPENSSL
+  RAND_bytes(data, size);
+#elif defined(TOMCRYPT)
+  yarrow_read(data, size, &g_rng);
+#elif defined(GCRYPT)
+  gcry_randomize(data, size, GCRY_STRONG_RANDOM);
+#elif defined(CRYPTOLIB)
+  randomBytes(data, size, PSEUDO);
+#else
+  while(size > outpos) {
+    if(outpos > 0) {
+      memcpy(data, randout + (sizeof(randout) - outpos), outpos);
+      data += outpos;
+      size -= outpos;
+    }
+
+    /* Recycle */
+    SHA1Init(&randctxt);
+    SHA1Update(&randctxt, randpool, sizeof(randpool));
+    SHA1Final(randout, &randctxt);
+    SHA1Init(&randctxt);
+    SHA1Update(&randctxt, (unsigned char *) &randcnt, sizeof(randcnt));
+    SHA1Update(&randctxt, randpool, sizeof(randpool));
+    SHA1Final(randpool, &randctxt);
+    ++randcnt;
+    outpos = sizeof(randout);
+  }
+
+  if(size > 0) {
+    memcpy(data, randout + (sizeof(randout) - outpos), size);
+    outpos -= size;
+  }
+#endif
+}
+
+/*
+ * The interleaved session-key hash.  This separates the even and the odd
+ * bytes of the input (ignoring the first byte if the input length is odd),
+ * hashes them separately, and re-interleaves the two outputs to form a
+ * single 320-bit value.
+ */
+_TYPE( unsigned char * )
+t_sessionkey(unsigned char * key, unsigned char * sk, unsigned sklen)
+{
+  unsigned i, klen;
+  unsigned char * hbuf;
+  unsigned char hout[SHA_DIGESTSIZE];
+  SHA1_CTX ctxt;
+
+  while(sklen > 0 && *sk == 0) {        /* Skip leading 0's */
+    --sklen;
+    ++sk;
+  }
+
+  klen = sklen / 2;
+  if((hbuf = malloc(klen * sizeof(char))) == 0)
+    return 0;
+
+  for(i = 0; i < klen; ++i)
+    hbuf[i] = sk[sklen - 2 * i - 1];
+  SHA1Init(&ctxt);
+  SHA1Update(&ctxt, hbuf, klen);
+  SHA1Final(hout, &ctxt);
+  for(i = 0; i < sizeof(hout); ++i)
+    key[2 * i] = hout[i];
+
+  for(i = 0; i < klen; ++i)
+    hbuf[i] = sk[sklen - 2 * i - 2];
+  SHA1Init(&ctxt);
+  SHA1Update(&ctxt, hbuf, klen);
+  SHA1Final(hout, &ctxt);
+  for(i = 0; i < sizeof(hout); ++i)
+    key[2 * i + 1] = hout[i];
+
+  memset(hout, 0, sizeof(hout));
+  memset(hbuf, 0, klen);
+  free(hbuf);
+  return key;
+}
+
+_TYPE( void )
+t_mgf1(unsigned char * mask, unsigned masklen, const unsigned char * seed, unsigned seedlen)
+{
+  SHA1_CTX ctxt;
+  unsigned i = 0;
+  unsigned pos = 0;
+  unsigned char cnt[4];
+  unsigned char hout[SHA_DIGESTSIZE];
+
+  while(pos < masklen) {
+    cnt[0] = (i >> 24) & 0xFF;
+    cnt[1] = (i >> 16) & 0xFF;
+    cnt[2] = (i >> 8) & 0xFF;
+    cnt[3] = i & 0xFF;
+    SHA1Init(&ctxt);
+    SHA1Update(&ctxt, seed, seedlen);
+    SHA1Update(&ctxt, cnt, 4);
+
+    if(pos + SHA_DIGESTSIZE > masklen) {
+      SHA1Final(hout, &ctxt);
+      memcpy(mask + pos, hout, masklen - pos);
+      pos = masklen;
+    }
+    else {
+      SHA1Final(mask + pos, &ctxt);
+      pos += SHA_DIGESTSIZE;
+    }
+
+    ++i;
+  }
+
+  memset(hout, 0, sizeof(hout));
+  memset((unsigned char *)&ctxt, 0, sizeof(ctxt));
+}
diff --git a/3rd_party/libsrp6a-sha512/t_pwd.h b/3rd_party/libsrp6a-sha512/t_pwd.h
new file mode 100644
index 0000000..a90a364
--- /dev/null
+++ b/3rd_party/libsrp6a-sha512/t_pwd.h
@@ -0,0 +1,246 @@
+/*
+ * Copyright (c) 1997-2007  The Stanford SRP Authentication Project
+ * All Rights Reserved.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining
+ * a copy of this software and associated documentation files (the
+ * "Software"), to deal in the Software without restriction, including
+ * without limitation the rights to use, copy, modify, merge, publish,
+ * distribute, sublicense, and/or sell copies of the Software, and to
+ * permit persons to whom the Software is furnished to do so, subject to
+ * the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be
+ * included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS-IS" AND WITHOUT WARRANTY OF ANY KIND, 
+ * EXPRESS, IMPLIED OR OTHERWISE, INCLUDING WITHOUT LIMITATION, ANY 
+ * WARRANTY OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.  
+ *
+ * IN NO EVENT SHALL STANFORD BE LIABLE FOR ANY SPECIAL, INCIDENTAL,
+ * INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY KIND, OR ANY DAMAGES WHATSOEVER
+ * RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER OR NOT ADVISED OF
+ * THE POSSIBILITY OF DAMAGE, AND ON ANY THEORY OF LIABILITY, ARISING OUT
+ * OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
+ *
+ * Redistributions in source or binary form must retain an intact copy
+ * of this copyright notice.
+ */
+
+#ifndef T_PWD_H
+#define T_PWD_H
+
+#include <stdio.h>
+#include "cstr.h"
+
+#define MAXPARAMBITS    2048
+#define MAXPARAMLEN     ((MAXPARAMBITS + 7) / 8)
+#define MAXB64PARAMLEN  ((MAXPARAMBITS + 5) / 6 + 1)
+#define MAXHEXPARAMLEN  ((MAXPARAMBITS + 3) / 4 + 1)
+#define MAXOCTPARAMLEN  ((MAXPARAMBITS + 2) / 3 + 1)
+
+#define MAXUSERLEN      32
+#define MAXSALTLEN      32
+#define MAXB64SALTLEN   44      /* 256 bits in b64 + null */
+#define SALTLEN         10      /* Normally 80 bits */
+
+#define RESPONSE_LEN    20      /* 160-bit proof hashes */
+#define SESSION_KEY_LEN (2 * RESPONSE_LEN)      /* 320-bit session key */
+
+#define DEFAULT_PASSWD  "/etc/tpasswd"
+#define DEFAULT_CONF    "/etc/tpasswd.conf"
+
+struct t_num {  /* Standard byte-oriented integer representation */
+  int len;
+  unsigned char * data;
+};
+
+struct t_preconf {      /* Structure returned by t_getpreparam() */
+  char * mod_b64;
+  char * gen_b64;
+  char * comment;
+
+  struct t_num modulus;
+  struct t_num generator;
+};
+
+/*
+ * The built-in (known good) parameters access routines
+ *
+ * "t_getprecount" returns the number of precompiled parameter sets.
+ * "t_getpreparam" returns the indicated parameter set.
+ * Memory is statically allocated - callers need not perform any memory mgmt.
+ */
+_TYPE( int ) t_getprecount();
+_TYPE( struct t_preconf * ) t_getpreparam P((int));
+
+struct t_confent {      /* One configuration file entry (index, N, g) */
+  int index;
+  struct t_num modulus;
+  struct t_num generator;
+};
+
+struct t_conf {         /* An open configuration file */
+  FILE * instream;
+  char close_on_exit;
+  cstr * modbuf;
+  cstr * genbuf;
+  struct t_confent tcbuf;
+};
+
+/*
+ * The configuration file routines are designed along the lines of the
+ * "getpw" functions in the standard C library.
+ *
+ * "t_openconf" accepts a stdio stream and interprets it as a config file.
+ * "t_openconfbyname" accepts a filename and does the same thing.
+ * "t_closeconf" closes the config file.
+ * "t_getconfent" fetches the next sequential configuration entry.
+ * "t_getconfbyindex" fetches the configuration entry whose index
+ *   matches the one supplied, or NULL if one can't be found.
+ * "t_getconflast" fetches the last configuration entry in the file.
+ * "t_makeconfent" generates a set of configuration entry parameters
+ *   randomly.
+ * "t_newconfent" returns an empty configuration entry.
+ * "t_cmpconfent" compares two configuration entries a la strcmp.
+ * "t_checkconfent" verifies that a set of configuration parameters
+ *   are suitable.  N must be prime and should be a safe prime.
+ * "t_putconfent" writes a configuration entry to a stream.
+ */
+_TYPE( struct t_conf * ) t_openconf P((FILE *));
+_TYPE( struct t_conf * ) t_openconfbyname P((const char *));
+_TYPE( void ) t_closeconf P((struct t_conf *));
+_TYPE( void ) t_rewindconf P((struct t_conf *));
+_TYPE( struct t_confent * ) t_getconfent P((struct t_conf *));
+_TYPE( struct t_confent * ) t_getconfbyindex P((struct t_conf *, int));
+_TYPE( struct t_confent * ) t_getconflast P((struct t_conf *));
+_TYPE( struct t_confent * ) t_makeconfent P((struct t_conf *, int));
+_TYPE( struct t_confent * ) t_makeconfent_c P((struct t_conf *, int));
+_TYPE( struct t_confent * ) t_newconfent P((struct t_conf *));
+_TYPE( int ) t_cmpconfent P((const struct t_confent *, const struct t_confent *));
+_TYPE( int ) t_checkconfent P((const struct t_confent *));
+_TYPE( void ) t_putconfent P((const struct t_confent *, FILE *));
+
+/* libc-style system conf file access */
+_TYPE( struct t_confent *) gettcent();
+_TYPE( struct t_confent *) gettcid P((int));
+_TYPE( void ) settcent();
+_TYPE( void ) endtcent();
+
+#ifdef ENABLE_NSW
+extern struct t_confent * _gettcent();
+extern struct t_confent * _gettcid P((int));
+extern void _settcent();
+extern void _endtcent();
+#endif
+
+/* A hack to support '+'-style entries in the passwd file */
+
+typedef enum fstate {
+  FILE_ONLY,    /* Ordinary file, don't consult NIS ever */
+  FILE_NIS,     /* Currently accessing file, use NIS if encountered */
+  IN_NIS,       /* Currently in a '+' entry; use NIS for getXXent */
+} FILE_STATE;
+
+struct t_pwent {        /* A single password file entry */
+  char * name;
+  struct t_num password;
+  struct t_num salt;
+  int index;
+};
+
+struct t_pw {           /* An open password file */
+  FILE * instream;
+  char close_on_exit;
+  FILE_STATE state;
+  char userbuf[MAXUSERLEN];
+  cstr * pwbuf;
+  unsigned char saltbuf[SALTLEN];
+  struct t_pwent pebuf;
+};
+
+/*
+ * The password manipulation routines are patterned after the getpw*
+ * standard C library function calls.
+ *
+ * "t_openpw" reads a stream as if it were a password file.
+ * "t_openpwbyname" opens the named file as a password file.
+ * "t_closepw" closes an open password file.
+ * "t_rewindpw" starts the internal file pointer from the beginning
+ *   of the password file.
+ * "t_getpwent" retrieves the next sequential password entry.
+ * "t_getpwbyname" looks up the password entry corresponding to the
+ *   specified user.
+ * "t_makepwent" constructs a password entry from a username, password,
+ *   numeric salt, and configuration entry.
+ * "t_putpwent" writes a password entry to a stream.
+ */
+_TYPE( struct t_pw * ) t_newpw();
+_TYPE( struct t_pw * ) t_openpw P((FILE *));
+_TYPE( struct t_pw * ) t_openpwbyname P((const char *));
+_TYPE( void ) t_closepw P((struct t_pw *));
+_TYPE( void ) t_rewindpw P((struct t_pw *));
+_TYPE( struct t_pwent * ) t_getpwent P((struct t_pw *));
+_TYPE( struct t_pwent * ) t_getpwbyname P((struct t_pw *, const char *));
+_TYPE( struct t_pwent * ) t_makepwent P((struct t_pw *, const char *,
+                                         const char *, const struct t_num *,
+                                         const struct t_confent *));
+_TYPE( void ) t_putpwent P((const struct t_pwent *, FILE *));
+
+struct t_passwd {
+  struct t_pwent tp;
+  struct t_confent tc;
+};
+
+/* libc-style system password file access */
+_TYPE( struct t_passwd * ) gettpent();
+_TYPE( struct t_passwd * ) gettpnam P((const char *));
+_TYPE( void ) settpent();
+_TYPE( void ) endtpent();
+
+#ifdef ENABLE_NSW
+extern struct t_passwd * _gettpent();
+extern struct t_passwd * _gettpnam P((const char *));
+extern void _settpent();
+extern void _endtpent();
+#endif
+
+/*
+ * Utility functions
+ *
+ * "t_verifypw" accepts a username and password, and checks against the
+ *   system password file to see if the password for that user is correct.
+ *   Returns > 0 if it is correct, 0 if not, and -1 if some error occurred
+ *   (i.e. the user doesn't exist on the system).  This is intended ONLY
+ *   for local authentication; for remote authentication, look at the
+ *   t_client and t_server source.  (That's the whole point of SRP!)
+ * "t_changepw" modifies the specified file, substituting the given password
+ *   entry for the one already in the file.  If no matching entry is found,
+ *   the new entry is simply appended to the file.
+ * "t_deletepw" removes the specified user from the specified file.
+ */
+_TYPE( int ) t_verifypw P((const char *, const char *));
+_TYPE( int ) t_changepw P((const char *, const struct t_pwent *));
+_TYPE( int ) t_deletepw P((const char *, const char *));
+
+/* Conversion utilities */
+
+/*
+ * All these calls accept output as the first parameter.  In the case of
+ * t_tohex and t_tob64, the last argument is the length of the byte-string
+ * input.
+ */
+_TYPE( char * ) t_tohex P((char *, const char *, unsigned));
+_TYPE( int ) t_fromhex P((char *, const char *));
+_TYPE( char * ) t_tob64 P((char *, const char *, unsigned));
+_TYPE( int ) t_fromb64 P((char *, const char *));
+
+/* These functions put their output in a cstr object */
+_TYPE( char * ) t_tohexcstr P((cstr *, const char *, unsigned));
+_TYPE( int ) t_cstrfromhex P((cstr *, const char *));
+_TYPE( char * ) t_tob64cstr P((cstr *, const char *, unsigned));
+_TYPE( int ) t_cstrfromb64 P((cstr *, const char *));
+
+/* Miscellaneous utilities (moved to t_defines.h) */
+
+#endif
diff --git a/3rd_party/libsrp6a-sha512/t_sha.c b/3rd_party/libsrp6a-sha512/t_sha.c
new file mode 100644
index 0000000..8e54cb6
--- /dev/null
+++ b/3rd_party/libsrp6a-sha512/t_sha.c
@@ -0,0 +1,314 @@
+#include "t_defines.h"
+#include "t_sha.h"
+
+#ifdef CRYPTOLIB_SHA
+
+/* A wrapper around CryptoLib's shsFinal that delivers output in octets */
+void
+shsFinalBytes(unsigned char digest[20], SHS_CTX* context)
+{
+  int i;
+  unsigned long r;
+  unsigned char *p = digest;
+
+  shsFinal(context);
+  for(i = 0; i < 5; ++i) {
+    r = context->h[i];
+    *p++ = (unsigned char)((r >> 24) & 0xff);
+    *p++ = (unsigned char)((r >> 16) & 0xff);
+    *p++ = (unsigned char)((r >> 8) & 0xff);
+    *p++ = (unsigned char)(r & 0xff);
+  }
+}
+
+#elif defined(GCRYPT_SHA)
+/* Wrappers for gcrypt's md interface */
+
+void
+SHA1Init_gcry(SHA1_CTX * ctx)
+{
+  gcry_md_open(ctx, GCRY_MD_SHA1, 0);
+}
+
+void
+SHA1Update_gcry(SHA1_CTX * ctx, const void *data, unsigned int len)
+{
+  gcry_md_write(*ctx, data, len);
+}
+
+void
+SHA1Final_gcry(unsigned char digest[20], SHA1_CTX * ctx)
+{
+  memcpy(digest, gcry_md_read(*ctx, GCRY_MD_SHA1), 20);
+  gcry_md_close(*ctx);
+}
+
+void
+SHA512Init_gcry(SHA512_CTX * ctx)
+{
+  gcry_md_open(ctx, GCRY_MD_SHA512, 0);
+}
+
+void
+SHA512Update_gcry(SHA512_CTX * ctx, const void *data, unsigned int len)
+{
+  gcry_md_write(*ctx, data, len);
+}
+
+void
+SHA512Final_gcry(unsigned char digest[64], SHA512_CTX * ctx)
+{
+  memcpy(digest, gcry_md_read(*ctx, GCRY_MD_SHA512), 64);
+  gcry_md_close(*ctx);
+}
+
+#elif defined(MBEDTLS_SHA)
+/* Wrappers for mbedtls's md interface */
+
+void
+SHA1Init_mbed(SHA1_CTX * ctx)
+{
+  mbedtls_md_init(ctx);
+  mbedtls_md_setup(ctx, mbedtls_md_info_from_type(MBEDTLS_MD_SHA1), 0);
+  mbedtls_md_starts(ctx);
+}
+
+void
+SHA1Update_mbed(SHA1_CTX * ctx, const void *data, unsigned int len)
+{
+  mbedtls_md_update(ctx, data, len);
+}
+
+void
+SHA1Final_mbed(unsigned char digest[20], SHA1_CTX * ctx)
+{
+  mbedtls_md_finish(ctx, digest);
+  mbedtls_md_free(ctx);
+}
+
+void
+SHA512Init_mbed(SHA512_CTX * ctx)
+{
+  mbedtls_md_init(ctx);
+  mbedtls_md_setup(ctx, mbedtls_md_info_from_type(MBEDTLS_MD_SHA512), 0);
+  mbedtls_md_starts(ctx);
+}
+
+void
+SHA512Update_mbed(SHA512_CTX * ctx, const void *data, unsigned int len)
+{
+  mbedtls_md_update(ctx, data, len);
+}
+
+void
+SHA512Final_mbed(unsigned char digest[64], SHA512_CTX * ctx)
+{
+  mbedtls_md_finish(ctx, digest);
+  mbedtls_md_free(ctx);
+}
+
+#elif defined(OPENSSL_SHA)
+#if OPENSSL_VERSION_NUMBER >= 0x30000000L
+void
+SHA1Init_openssl(SHA1_CTX *ctx)
+{
+  *ctx = EVP_MD_CTX_new();
+  EVP_DigestInit(*ctx, EVP_sha1());
+}
+
+void SHA1Update_openssl(SHA1_CTX *ctx, const void *data, unsigned int len)
+{
+  EVP_DigestUpdate(*ctx, data, (size_t)len);
+}
+
+void SHA1Final_openssl(unsigned char digest[20], SHA1_CTX *ctx)
+{
+  EVP_DigestFinal(*ctx, digest, NULL);
+  EVP_MD_CTX_destroy(*ctx);
+}
+
+void
+SHA512Init_openssl(SHA512_CTX *ctx)
+{
+  *ctx = EVP_MD_CTX_new();
+  EVP_DigestInit(*ctx, EVP_sha512());
+}
+
+void SHA512Update_openssl(SHA512_CTX *ctx, const void *data, unsigned int len)
+{
+  EVP_DigestUpdate(*ctx, data, (size_t)len);
+}
+
+void SHA512Final_openssl(unsigned char digest[64], SHA512_CTX *ctx)
+{
+  EVP_DigestFinal(*ctx, digest, NULL);
+  EVP_MD_CTX_destroy(*ctx);
+}
+#endif
+#elif !defined(OPENSSL_SHA) && !defined(TOMCRYPT_SHA)
+/* Use the free SHA1 if the library doesn't have it */
+
+/*
+SHA-1 in C
+By Steve Reid <steve@edmweb.com>
+100% Public Domain
+
+Test Vectors (from FIPS PUB 180-1)
+"abc"
+  A9993E36 4706816A BA3E2571 7850C26C 9CD0D89D
+"abcdbcdecdefdefgefghfghighijhijkijkljklmklmnlmnomnopnopq"
+  84983E44 1C3BD26E BAAE4AA1 F95129E5 E54670F1
+A million repetitions of "a"
+  34AA973C D4C4DAA4 F61EEB2B DBAD2731 6534016F
+*/
+
+/* #define LITTLE_ENDIAN * This should be #define'd if true. */
+/* #define SHA1HANDSOFF * Copies data before messing with it. */
+
+#include <stdio.h>
+#include <string.h>
+
+static void SHA1Transform(uint32 state[5], const unsigned char buffer[64]);
+
+#define rol(value, bits) (((value) << (bits)) | ((value) >> (32 - (bits))))
+
+/* blk0() and blk() perform the initial expand. */
+/* I got the idea of expanding during the round function from SSLeay */
+#ifndef WORDS_BIGENDIAN
+#define blk0(i) (block->l[i] = (rol(block->l[i],24)&0xFF00FF00) \
+    |(rol(block->l[i],8)&0x00FF00FF))
+#else
+#define blk0(i) block->l[i]
+#endif
+#define blk(i) (block->l[i&15] = rol(block->l[(i+13)&15]^block->l[(i+8)&15] \
+    ^block->l[(i+2)&15]^block->l[i&15],1))
+
+/* (R0+R1), R2, R3, R4 are the different operations used in SHA1 */
+#define R0(v,w,x,y,z,i) z+=((w&(x^y))^y)+blk0(i)+0x5A827999+rol(v,5);w=rol(w,30);
+#define R1(v,w,x,y,z,i) z+=((w&(x^y))^y)+blk(i)+0x5A827999+rol(v,5);w=rol(w,30);
+#define R2(v,w,x,y,z,i) z+=(w^x^y)+blk(i)+0x6ED9EBA1+rol(v,5);w=rol(w,30);
+#define R3(v,w,x,y,z,i) z+=(((w|x)&y)|(w&x))+blk(i)+0x8F1BBCDC+rol(v,5);w=rol(w,30);
+#define R4(v,w,x,y,z,i) z+=(w^x^y)+blk(i)+0xCA62C1D6+rol(v,5);w=rol(w,30);
+
+/* Hash a single 512-bit block. This is the core of the algorithm. */
+
+static void SHA1Transform(uint32 state[5], const unsigned char buffer[64])
+{
+uint32 a, b, c, d, e;
+typedef union {
+    unsigned char c[64];
+    uint32 l[16];
+} CHAR64LONG16;
+CHAR64LONG16* block;
+#ifdef SHA1HANDSOFF
+static unsigned char workspace[64];
+    block = (CHAR64LONG16*)workspace;
+    memcpy(block, buffer, 64);
+#else
+    block = (CHAR64LONG16*)buffer;
+#endif
+    /* Copy context->state[] to working vars */
+    a = state[0];
+    b = state[1];
+    c = state[2];
+    d = state[3];
+    e = state[4];
+    /* 4 rounds of 20 operations each. Loop unrolled. */
+    R0(a,b,c,d,e, 0); R0(e,a,b,c,d, 1); R0(d,e,a,b,c, 2); R0(c,d,e,a,b, 3);
+    R0(b,c,d,e,a, 4); R0(a,b,c,d,e, 5); R0(e,a,b,c,d, 6); R0(d,e,a,b,c, 7);
+    R0(c,d,e,a,b, 8); R0(b,c,d,e,a, 9); R0(a,b,c,d,e,10); R0(e,a,b,c,d,11);
+    R0(d,e,a,b,c,12); R0(c,d,e,a,b,13); R0(b,c,d,e,a,14); R0(a,b,c,d,e,15);
+    R1(e,a,b,c,d,16); R1(d,e,a,b,c,17); R1(c,d,e,a,b,18); R1(b,c,d,e,a,19);
+    R2(a,b,c,d,e,20); R2(e,a,b,c,d,21); R2(d,e,a,b,c,22); R2(c,d,e,a,b,23);
+    R2(b,c,d,e,a,24); R2(a,b,c,d,e,25); R2(e,a,b,c,d,26); R2(d,e,a,b,c,27);
+    R2(c,d,e,a,b,28); R2(b,c,d,e,a,29); R2(a,b,c,d,e,30); R2(e,a,b,c,d,31);
+    R2(d,e,a,b,c,32); R2(c,d,e,a,b,33); R2(b,c,d,e,a,34); R2(a,b,c,d,e,35);
+    R2(e,a,b,c,d,36); R2(d,e,a,b,c,37); R2(c,d,e,a,b,38); R2(b,c,d,e,a,39);
+    R3(a,b,c,d,e,40); R3(e,a,b,c,d,41); R3(d,e,a,b,c,42); R3(c,d,e,a,b,43);
+    R3(b,c,d,e,a,44); R3(a,b,c,d,e,45); R3(e,a,b,c,d,46); R3(d,e,a,b,c,47);
+    R3(c,d,e,a,b,48); R3(b,c,d,e,a,49); R3(a,b,c,d,e,50); R3(e,a,b,c,d,51);
+    R3(d,e,a,b,c,52); R3(c,d,e,a,b,53); R3(b,c,d,e,a,54); R3(a,b,c,d,e,55);
+    R3(e,a,b,c,d,56); R3(d,e,a,b,c,57); R3(c,d,e,a,b,58); R3(b,c,d,e,a,59);
+    R4(a,b,c,d,e,60); R4(e,a,b,c,d,61); R4(d,e,a,b,c,62); R4(c,d,e,a,b,63);
+    R4(b,c,d,e,a,64); R4(a,b,c,d,e,65); R4(e,a,b,c,d,66); R4(d,e,a,b,c,67);
+    R4(c,d,e,a,b,68); R4(b,c,d,e,a,69); R4(a,b,c,d,e,70); R4(e,a,b,c,d,71);
+    R4(d,e,a,b,c,72); R4(c,d,e,a,b,73); R4(b,c,d,e,a,74); R4(a,b,c,d,e,75);
+    R4(e,a,b,c,d,76); R4(d,e,a,b,c,77); R4(c,d,e,a,b,78); R4(b,c,d,e,a,79);
+    /* Add the working vars back into context.state[] */
+    state[0] += a;
+    state[1] += b;
+    state[2] += c;
+    state[3] += d;
+    state[4] += e;
+    /* Wipe variables */
+    a = b = c = d = e = 0;
+}
+
+
+/* SHA1Init - Initialize new context */
+
+void SHA1Init(SHA1_CTX* context)
+{
+    /* SHA1 initialization constants */
+    context->state[0] = 0x67452301;
+    context->state[1] = 0xEFCDAB89;
+    context->state[2] = 0x98BADCFE;
+    context->state[3] = 0x10325476;
+    context->state[4] = 0xC3D2E1F0;
+    context->count[0] = context->count[1] = 0;
+}
+
+
+/* Run your data through this. */
+
+void SHA1Update(SHA1_CTX* context, const unsigned char* data, unsigned int len)
+{
+unsigned int i, j;
+
+    j = (context->count[0] >> 3) & 63;
+    if ((context->count[0] += len << 3) < (len << 3)) context->count[1]++;
+    context->count[1] += (len >> 29);
+    if ((j + len) > 63) {
+        memcpy(&context->buffer[j], data, (i = 64-j));
+        SHA1Transform(context->state, context->buffer);
+        for ( ; i + 63 < len; i += 64) {
+            SHA1Transform(context->state, &data[i]);
+        }
+        j = 0;
+    }
+    else i = 0;
+    memcpy(&context->buffer[j], &data[i], len - i);
+}
+
+
+/* Add padding and return the message digest. */
+
+void SHA1Final(unsigned char digest[20], SHA1_CTX* context)
+{
+uint32 i, j;
+unsigned char finalcount[8];
+
+    for (i = 0; i < 8; i++) {
+        finalcount[i] = (unsigned char)((context->count[(i >= 4 ? 0 : 1)]
+         >> ((3-(i & 3)) * 8) ) & 255);  /* Endian independent */
+    }
+    SHA1Update(context, (unsigned char *)"\200", 1);
+    while ((context->count[0] & 504) != 448) {
+        SHA1Update(context, (unsigned char *)"\0", 1);
+    }
+    SHA1Update(context, finalcount, 8);  /* Should cause a SHA1Transform() */
+    for (i = 0; i < 20; i++) {
+        digest[i] = (unsigned char)
+         ((context->state[i>>2] >> ((3-(i & 3)) * 8) ) & 255);
+    }
+    /* Wipe variables */
+    i = j = 0;
+    memset(context->buffer, 0, 64);
+    memset(context->state, 0, 20);
+    memset(context->count, 0, 8);
+    memset(&finalcount, 0, 8);
+#ifdef SHA1HANDSOFF  /* make SHA1Transform overwrite it's own static vars */
+    SHA1Transform(context->state, context->buffer);
+#endif
+}
+#endif
diff --git a/3rd_party/libsrp6a-sha512/t_sha.h b/3rd_party/libsrp6a-sha512/t_sha.h
new file mode 100644
index 0000000..2e38067
--- /dev/null
+++ b/3rd_party/libsrp6a-sha512/t_sha.h
@@ -0,0 +1,147 @@
+#ifndef T_SHA_H
+#define T_SHA_H
+
+#if     !defined(P)
+#ifdef  __STDC__
+#define P(x)    x
+#else
+#define P(x)    ()
+#endif
+#endif
+
+#define SHA_DIGESTSIZE 20
+
+#ifdef OPENSSL
+#define OPENSSL_SHA 1
+#endif
+
+#ifdef TOMCRYPT
+# include <tomcrypt.h>
+# ifdef SHA1
+#  define TOMCRYPT_SHA 1
+# endif
+#endif
+
+#ifdef CRYPTOLIB
+/* The SHA (shs) implementation in CryptoLib 1.x breaks when Update
+ * is called multiple times, so we still use our own code.
+ * Uncomment below if you think your copy of CryptoLib is fixed. */
+/*#define CRYPTOLIB_SHA 1*/
+#endif
+
+#ifdef GCRYPT
+# define GCRYPT_SHA 1
+#endif
+
+#ifdef MBEDTLS
+# define MBEDTLS_SHA 1
+#endif
+
+#ifdef OPENSSL_SHA
+#include <openssl/err.h>
+#if OPENSSL_VERSION_NUMBER >= 0x30000000L
+#include <openssl/evp.h>
+
+typedef EVP_MD_CTX* SHA1_CTX;
+#define SHA1Init SHA1Init_openssl
+#define SHA1Update SHA1Update_openssl
+#define SHA1Final SHA1Final_openssl
+
+typedef EVP_MD_CTX* SHA512_CTX;
+#define SHA512Init SHA512Init_openssl
+#define SHA512Update SHA512Update_openssl
+#define SHA512Final SHA512Final_openssl
+
+void SHA1Init_openssl(SHA1_CTX *ctx);
+void SHA1Update_openssl(SHA1_CTX *ctx, const void *data, unsigned int len);
+void SHA1Final_openssl(unsigned char digest[20], SHA1_CTX *ctx);
+
+void SHA512Init_openssl(SHA512_CTX *ctx);
+void SHA512Update_openssl(SHA512_CTX *ctx, const void *data, unsigned int len);
+void SHA512Final_openssl(unsigned char digest[64], SHA1_CTX *ctx);
+#else /* for OpenSSL < 3.0 */
+#include <openssl/sha.h>
+
+typedef SHA_CTX SHA1_CTX;
+#define SHA1Init SHA1_Init
+#define SHA1Update SHA1_Update
+#define SHA1Final SHA1_Final
+
+#define SHA512Init SHA512_Init
+#define SHA512Update SHA512_Update
+#define SHA512Final SHA512_Final
+#endif /* for OpenSSL < 3.0 */
+#elif defined(TOMCRYPT_SHA)
+/* mycrypt.h already included above */
+
+typedef hash_state SHA1_CTX;
+#define SHA1Init sha1_init
+#define SHA1Update sha1_process
+#define SHA1Final(D,C) sha1_done(C,D)
+
+#elif defined(GCRYPT_SHA)
+#include "gcrypt.h"
+
+typedef gcry_md_hd_t SHA1_CTX;
+#define SHA1Init SHA1Init_gcry
+#define SHA1Update SHA1Update_gcry
+#define SHA1Final SHA1Final_gcry
+typedef gcry_md_hd_t SHA512_CTX;
+#define SHA512Init SHA512Init_gcry
+#define SHA512Update SHA512Update_gcry
+#define SHA512Final SHA512Final_gcry
+
+void SHA1Init_gcry(SHA1_CTX * ctx);
+void SHA1Update_gcry(SHA1_CTX * ctx, const void *data, unsigned int len);
+void SHA1Final_gcry(unsigned char digest[20], SHA1_CTX * ctx);
+
+void SHA512Init_gcry(SHA512_CTX * ctx);
+void SHA512Update_gcry(SHA512_CTX * ctx, const void *data, unsigned int len);
+void SHA512Final_gcry(unsigned char digest[64], SHA512_CTX * ctx);
+
+#elif defined(MBEDTLS_SHA)
+#include <mbedtls/md.h>
+
+typedef mbedtls_md_context_t SHA1_CTX;
+#define SHA1Init SHA1Init_mbed
+#define SHA1Update SHA1Update_mbed
+#define SHA1Final SHA1Final_mbed
+
+typedef mbedtls_md_context_t SHA512_CTX;
+#define SHA512Init SHA512Init_mbed
+#define SHA512Update SHA512Update_mbed
+#define SHA512Final SHA512Final_mbed
+
+void SHA1Init_mbed(SHA1_CTX * ctx);
+void SHA1Update_mbed(SHA1_CTX * ctx, const void *data, unsigned int len);
+void SHA1Final_mbed(unsigned char digest[20], SHA1_CTX * ctx);
+
+void SHA512Init_mbed(SHA512_CTX * ctx);
+void SHA512Update_mbed(SHA512_CTX * ctx, const void *data, unsigned int len);
+void SHA512Final_mbed(unsigned char digest[64], SHA512_CTX * ctx);
+
+#elif defined(CRYPTOLIB_SHA)
+#include "libcrypt.h"
+
+typedef SHS_CTX SHA1_CTX;
+#define SHA1Init shsInit
+#define SHA1Update shsUpdate
+#define SHA1Final shsFinalBytes
+
+void shsFinalBytes P((unsigned char digest[20], SHS_CTX* context));
+
+#else
+typedef unsigned int uint32;
+
+typedef struct {
+    uint32 state[5];
+    uint32 count[2];
+    unsigned char buffer[64];
+} SHA1_CTX;
+
+void SHA1Init P((SHA1_CTX* context));
+void SHA1Update P((SHA1_CTX* context, const unsigned char* data, unsigned int len));
+void SHA1Final P((unsigned char digest[20], SHA1_CTX* context));
+#endif /* !OPENSSL && !CRYPTOLIB */
+
+#endif /* T_SHA_H */
diff --git a/3rd_party/libsrp6a-sha512/t_truerand.c b/3rd_party/libsrp6a-sha512/t_truerand.c
new file mode 100644
index 0000000..f995ed7
--- /dev/null
+++ b/3rd_party/libsrp6a-sha512/t_truerand.c
@@ -0,0 +1,241 @@
+/*
+ *      Physically random numbers (very nearly uniform)
+ *      D. P. Mitchell 
+ *      Modified by Matt Blaze 7/95
+ */
+/*
+ * The authors of this software are Don Mitchell and Matt Blaze.
+ *              Copyright (c) 1995 by AT&T.
+ * Permission to use, copy, and modify this software without fee
+ * is hereby granted, provided that this entire notice is included in
+ * all copies of any software which is or includes a copy or
+ * modification of this software and in all copies of the supporting
+ * documentation for such software.
+ *
+ * This software may be subject to United States export controls.
+ *
+ * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
+ * WARRANTY.  IN PARTICULAR, NEITHER THE AUTHORS NOR AT&T MAKE ANY
+ * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
+ * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
+ */
+
+/*
+ * WARNING: depending on the particular platform, raw_truerand()
+ * output may be biased or correlated.  In general, you can expect
+ * about 16 bits of "pseudo-entropy" out of each 32 bit word returned
+ * by truerand(), but it may not be uniformly diffused.  You should
+ * raw_therefore run the output through some post-whitening function
+ * (like MD5 or DES or whatever) before using it to generate key
+ * material.  (RSAREF's random package does this for you when you feed
+ * raw_truerand() bits to the seed input function.)
+ *
+ * The application interface, for 8, 16, and 32 bit properly "whitened"
+ * random numbers, can be found in trand8(), trand16(), and trand32().
+ * Use those instead of calling raw_truerand() directly.
+ *
+ * The basic idea here is that between clock "skew" and various
+ * hard-to-predict OS event arrivals, counting a tight loop will yield
+ * a little (maybe a third of a bit or so) of "good" randomness per
+ * interval clock tick.  This seems to work well even on unloaded
+ * machines.  If there is a human operator at the machine, you should
+ * augment truerand with other measure, like keyboard event timing.
+ * On server machines (e.g., when you need to generate a
+ * Diffie-Hellman secret) truerand alone may be good enough.
+ *
+ * Test these assumptions on your own platform before fielding a
+ * system based on this software or these techniques.
+ *
+ * This software seems to work well (at 10 or so bits per
+ * raw_truerand() call) on a Sun Sparc-20 under SunOS 4.1.3 and on a
+ * P100 under BSDI 2.0.  You're on your own elsewhere.
+ *
+ */
+
+#include "t_defines.h"
+
+#ifdef WIN32
+
+# ifdef CRYPTOLIB
+
+/* Cryptolib contains its own truerand() on both UNIX and Windows. */
+/* Only use cryptolib's truerand under Windows */
+
+#  include "libcrypt.h"
+
+unsigned long
+raw_truerand()
+{
+        return truerand();
+}
+
+# else /* !CRYPTOLIB && WIN32 */
+
+#include <windows.h>
+#include <wtypes.h>
+#include <winbase.h>
+#include <windef.h>
+#include <winnt.h>
+#include <winuser.h>
+#include <process.h>
+
+volatile unsigned long count, ocount, randbuf;
+volatile int dontstop;
+char outbuf[1024], *bufp;
+
+static void counter() {
+        while (dontstop)
+                count++;
+        _endthread();
+}
+
+
+static unsigned long roulette() {
+        unsigned long thread;
+
+        count = 0;
+        dontstop= 1;
+        while ((thread = _beginthread((void *)counter, 1024, NULL)) < 0)
+                ;
+
+        Sleep(16);
+        dontstop = 0;
+        Sleep(1);
+
+        count ^= (count>>3) ^ (count>>6) ^ (ocount);
+        count &= 0x7;
+        ocount = count;
+        randbuf = (randbuf<<3) ^ count;
+        return randbuf;
+}
+
+
+unsigned long
+raw_truerand() {
+
+        roulette();
+        roulette();
+        roulette();
+        roulette();
+        roulette();
+        roulette();
+        roulette();
+        roulette();
+        roulette();
+        roulette();
+        return roulette();
+}
+
+# endif /* CRYPTOLIB */
+
+#else /* !WIN32 */
+
+#include <signal.h>
+#include <setjmp.h>
+#include <sys/time.h>
+#include <math.h>
+#include <stdio.h>
+
+#ifdef OLD_TRUERAND
+static jmp_buf env;
+#endif
+static unsigned volatile count
+#ifndef OLD_TRUERAND
+  , done = 0
+#endif
+;
+
+static unsigned ocount;
+static unsigned buffer;
+
+static void
+tick()
+{
+        struct itimerval it, oit;
+
+        it.it_interval.tv_sec = 0;
+        it.it_interval.tv_usec = 0;
+        it.it_value.tv_sec = 0;
+        it.it_value.tv_usec = 16665;
+        if (setitimer(ITIMER_REAL, &it, &oit) < 0)
+                perror("tick");
+}
+
+static void
+interrupt()
+{
+        if (count) {
+#ifdef OLD_TRUERAND
+                longjmp(env, 1);
+#else
+                ++done;
+                return;
+#endif
+        }
+
+        (void) signal(SIGALRM, interrupt);
+        tick();
+}
+
+static unsigned long
+roulette()
+{
+#ifdef OLD_TRUERAND
+        if (setjmp(env)) {
+                count ^= (count>>3) ^ (count>>6) ^ ocount;
+                count &= 0x7;
+                ocount=count;
+                buffer = (buffer<<3) ^ count;
+                return buffer;
+        }
+#else
+        done = 0;
+#endif
+        (void) signal(SIGALRM, interrupt);
+        count = 0;
+        tick();
+#ifdef OLD_TRUERAND
+        for (;;)
+#else
+        while(done == 0)
+#endif
+                count++;        /* about 1 MHz on VAX 11/780 */
+#ifndef OLD_TRUERAND
+        count ^= (count>>3) ^ (count>>6) ^ ocount;
+        count &= 0x7;
+        ocount=count;
+        buffer = (buffer<<3) ^ count;
+        return buffer;
+#endif
+}
+
+unsigned long
+raw_truerand()
+{
+        count=0;
+        (void) roulette();
+        (void) roulette();
+        (void) roulette();
+        (void) roulette();
+        (void) roulette();
+        (void) roulette();
+        (void) roulette();
+        (void) roulette();
+        (void) roulette();
+        (void) roulette();
+        return roulette();
+}
+
+int
+raw_n_truerand(int n)
+{
+        int slop, v;
+
+        slop = 0x7FFFFFFF % n;
+        do {
+                v = raw_truerand() >> 1;
+        } while (v <= slop);
+        return v % n;
+}
+
+#endif /* !CRYPTOLIB || !WIN32 */