From df006700debd90dad9c09ff21a183f2d655ead71 Mon Sep 17 00:00:00 2001 From: agran Date: Mon, 11 May 2015 05:00:03 +0300 Subject: [PATCH] VanitygenQora --- .classpath | 11 + .gitignore | 1 + .project | 17 + .settings/org.eclipse.jdt.core.prefs | 12 + bin/.gitignore | 2 + libs/guava-15.0.jar | Bin 0 -> 2172168 bytes libs/native/Qora25519.windows.x64.dll | Bin 0 -> 186550 bytes libs/native/Qora25519.windows.x86.dll | Bin 0 -> 139837 bytes libs/native/ed25519/ed25519_32.dll | Bin 0 -> 127488 bytes libs/native/ed25519/ed25519_64.dll | Bin 0 -> 112128 bytes libs/native/ed25519/license.txt | 16 + libs/native/ed25519/readme.md | 166 +++ libs/native/ed25519/src/add_scalar.c | 56 + libs/native/ed25519/src/ed25519.h | 38 + libs/native/ed25519/src/fe.c | 1491 ++++++++++++++++++++++++ libs/native/ed25519/src/fe.h | 41 + libs/native/ed25519/src/fixedint.h | 72 ++ libs/native/ed25519/src/ge.c | 467 ++++++++ libs/native/ed25519/src/ge.h | 74 ++ libs/native/ed25519/src/key_exchange.c | 79 ++ libs/native/ed25519/src/keypair.c | 16 + libs/native/ed25519/src/precomp_data.h | 1391 ++++++++++++++++++++++ libs/native/ed25519/src/sc.c | 809 +++++++++++++ libs/native/ed25519/src/sc.h | 12 + libs/native/ed25519/src/seed.c | 40 + libs/native/ed25519/src/sha512.c | 275 +++++ libs/native/ed25519/src/sha512.h | 21 + libs/native/ed25519/src/sign.c | 31 + libs/native/ed25519/src/verify.c | 77 ++ libs/native/ed25519/test.c | 150 +++ libs/native/libQora25519.linux.x64.so | Bin 0 -> 83246 bytes libs/native/libQora25519.linux.x86.so | Bin 0 -> 97945 bytes libs/native/libQora25519.mac.dylib | Bin 0 -> 80668 bytes run.bat | 1 + src/Vanity.java | 111 ++ src/qora/crypto/Base58.java | 119 ++ src/qora/crypto/Crypto.java | 163 +++ src/qora/crypto/Ed25519.java | 85 ++ src/qora/crypto/RIPEMD160.java | 331 ++++++ src/utils/Pair.java | 38 + 40 files changed, 6213 insertions(+) create mode 100644 .classpath create mode 100644 .project create mode 100644 .settings/org.eclipse.jdt.core.prefs create mode 100644 bin/.gitignore create mode 100644 libs/guava-15.0.jar create mode 100644 libs/native/Qora25519.windows.x64.dll create mode 100644 libs/native/Qora25519.windows.x86.dll create mode 100644 libs/native/ed25519/ed25519_32.dll create mode 100644 libs/native/ed25519/ed25519_64.dll create mode 100644 libs/native/ed25519/license.txt create mode 100644 libs/native/ed25519/readme.md create mode 100644 libs/native/ed25519/src/add_scalar.c create mode 100644 libs/native/ed25519/src/ed25519.h create mode 100644 libs/native/ed25519/src/fe.c create mode 100644 libs/native/ed25519/src/fe.h create mode 100644 libs/native/ed25519/src/fixedint.h create mode 100644 libs/native/ed25519/src/ge.c create mode 100644 libs/native/ed25519/src/ge.h create mode 100644 libs/native/ed25519/src/key_exchange.c create mode 100644 libs/native/ed25519/src/keypair.c create mode 100644 libs/native/ed25519/src/precomp_data.h create mode 100644 libs/native/ed25519/src/sc.c create mode 100644 libs/native/ed25519/src/sc.h create mode 100644 libs/native/ed25519/src/seed.c create mode 100644 libs/native/ed25519/src/sha512.c create mode 100644 libs/native/ed25519/src/sha512.h create mode 100644 libs/native/ed25519/src/sign.c create mode 100644 libs/native/ed25519/src/verify.c create mode 100644 libs/native/ed25519/test.c create mode 100644 libs/native/libQora25519.linux.x64.so create mode 100644 libs/native/libQora25519.linux.x86.so create mode 100644 libs/native/libQora25519.mac.dylib create mode 100644 run.bat create mode 100644 src/Vanity.java create mode 100644 src/qora/crypto/Base58.java create mode 100644 src/qora/crypto/Crypto.java create mode 100644 src/qora/crypto/Ed25519.java create mode 100644 src/qora/crypto/RIPEMD160.java create mode 100644 src/utils/Pair.java diff --git a/.classpath b/.classpath new file mode 100644 index 0000000..32b8a26 --- /dev/null +++ b/.classpath @@ -0,0 +1,11 @@ + + + + + + + + + + + diff --git a/.gitignore b/.gitignore index 96374c4..15a0fc5 100644 --- a/.gitignore +++ b/.gitignore @@ -41,3 +41,4 @@ $RECYCLE.BIN/ Network Trash Folder Temporary Items .apdisk +*.class diff --git a/.project b/.project new file mode 100644 index 0000000..8dda715 --- /dev/null +++ b/.project @@ -0,0 +1,17 @@ + + + Vanitygen + + + + + + org.eclipse.jdt.core.javabuilder + + + + + + org.eclipse.jdt.core.javanature + + diff --git a/.settings/org.eclipse.jdt.core.prefs b/.settings/org.eclipse.jdt.core.prefs new file mode 100644 index 0000000..a698e59 --- /dev/null +++ b/.settings/org.eclipse.jdt.core.prefs @@ -0,0 +1,12 @@ +eclipse.preferences.version=1 +org.eclipse.jdt.core.compiler.codegen.inlineJsrBytecode=enabled +org.eclipse.jdt.core.compiler.codegen.methodParameters=do not generate +org.eclipse.jdt.core.compiler.codegen.targetPlatform=1.8 +org.eclipse.jdt.core.compiler.codegen.unusedLocal=preserve +org.eclipse.jdt.core.compiler.compliance=1.8 +org.eclipse.jdt.core.compiler.debug.lineNumber=generate 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z<)t&!!LAxW#yftHr5Yd?(-%*kY9Q5bDYZ4;s0yZP60x65aD7q@QC`7SL&PC|^!-Yu zMvN?gXe?EY;DAMO#s)Z@!enC`kO$A2xEYx9hflI_v084>M{X#-vl3Ju+ zSdAY&e}wn5Qu;fM>hC_t(xT@3olZ3-|NomZ#M#5m+4Yb3O(_2V8xj&0;U`zrrn>g+ z^bh`T%K^PV&m*V}w|0Jk`!DkhYR~_J|Fv?!UT;}VD{i0?TPWv+n8OeM|5~Z}=WhS= zIY9kbbkU-;_%w*7cL(wO)RNSB^wAn L{~Z5?bKt)L+YBFb literal 0 HcmV?d00001 diff --git a/libs/native/ed25519/license.txt b/libs/native/ed25519/license.txt new file mode 100644 index 0000000..c1503f9 --- /dev/null +++ b/libs/native/ed25519/license.txt @@ -0,0 +1,16 @@ +Copyright (c) 2015 Orson Peters + +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/libs/native/ed25519/readme.md b/libs/native/ed25519/readme.md new file mode 100644 index 0000000..14d575a --- /dev/null +++ b/libs/native/ed25519/readme.md @@ -0,0 +1,166 @@ +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. A +windows DLL is pre-built. + +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 in the public domain. diff --git a/libs/native/ed25519/src/add_scalar.c b/libs/native/ed25519/src/add_scalar.c new file mode 100644 index 0000000..a4f2a55 --- /dev/null +++ b/libs/native/ed25519/src/add_scalar.c @@ -0,0 +1,56 @@ +#include "ed25519.h" +#include "ge.h" +#include "sc.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; + + 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); + } + + /* 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/libs/native/ed25519/src/ed25519.h b/libs/native/ed25519/src/ed25519.h new file mode 100644 index 0000000..8924659 --- /dev/null +++ b/libs/native/ed25519/src/ed25519.h @@ -0,0 +1,38 @@ +#ifndef ED25519_H +#define ED25519_H + +#include + +#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/libs/native/ed25519/src/fe.c b/libs/native/ed25519/src/fe.c new file mode 100644 index 0000000..448e3e9 --- /dev/null +++ b/libs/native/ed25519/src/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 = -b; + 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] = 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; +} + + +/* +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> 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/libs/native/ed25519/src/fe.h b/libs/native/ed25519/src/fe.h new file mode 100644 index 0000000..b4b62d2 --- /dev/null +++ b/libs/native/ed25519/src/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/libs/native/ed25519/src/fixedint.h b/libs/native/ed25519/src/fixedint.h new file mode 100644 index 0000000..1a8745b --- /dev/null +++ b/libs/native/ed25519/src/fixedint.h @@ -0,0 +1,72 @@ +/* + Portable header to provide the 32 and 64 bits type. + + Not a compatible replacement for , 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 + #define FIXEDINT_H_INCLUDED + + #if defined(__WATCOMC__) && __WATCOMC__ >= 1250 && !defined(UINT64_C) + #include + #define UINT64_C(x) (x + (UINT64_MAX - UINT64_MAX)) + #endif +#endif + + +#ifndef FIXEDINT_H_INCLUDED + #define FIXEDINT_H_INCLUDED + + #include + + /* (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/libs/native/ed25519/src/ge.c b/libs/native/ed25519/src/ge.c new file mode 100644 index 0000000..3c342b1 --- /dev/null +++ b/libs/native/ed25519/src/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, 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/libs/native/ed25519/src/ge.h b/libs/native/ed25519/src/ge.h new file mode 100644 index 0000000..17fde2d --- /dev/null +++ b/libs/native/ed25519/src/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/libs/native/ed25519/src/key_exchange.c b/libs/native/ed25519/src/key_exchange.c new file mode 100644 index 0000000..abd75da --- /dev/null +++ b/libs/native/ed25519/src/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/libs/native/ed25519/src/keypair.c b/libs/native/ed25519/src/keypair.c new file mode 100644 index 0000000..dc1b8ec --- /dev/null +++ b/libs/native/ed25519/src/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/libs/native/ed25519/src/precomp_data.h b/libs/native/ed25519/src/precomp_data.h new file mode 100644 index 0000000..776b84f --- /dev/null +++ b/libs/native/ed25519/src/precomp_data.h @@ -0,0 +1,1391 @@ +static 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 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, 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-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 }, + }, + }, +}; \ No newline at end of file diff --git a/libs/native/ed25519/src/sc.c b/libs/native/ed25519/src/sc.c new file mode 100644 index 0000000..ca5bad2 --- /dev/null +++ b/libs/native/ed25519/src/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/libs/native/ed25519/src/sc.h b/libs/native/ed25519/src/sc.h new file mode 100644 index 0000000..8fa727e --- /dev/null +++ b/libs/native/ed25519/src/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 \ No newline at end of file diff --git a/libs/native/ed25519/src/seed.c b/libs/native/ed25519/src/seed.c new file mode 100644 index 0000000..25e5182 --- /dev/null +++ b/libs/native/ed25519/src/seed.c @@ -0,0 +1,40 @@ +#include "ed25519.h" + +#ifndef ED25519_NO_SEED + +#ifdef _WIN32 +#include +#include +#else +#include +#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; + } + + fread(seed, 1, 32, f); + fclose(f); +#endif + + return 0; +} + +#endif \ No newline at end of file diff --git a/libs/native/ed25519/src/sha512.c b/libs/native/ed25519/src/sha512.c new file mode 100644 index 0000000..cb8ae71 --- /dev/null +++ b/libs/native/ed25519/src/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/libs/native/ed25519/src/sha512.h b/libs/native/ed25519/src/sha512.h new file mode 100644 index 0000000..e56b00e --- /dev/null +++ b/libs/native/ed25519/src/sha512.h @@ -0,0 +1,21 @@ +#ifndef SHA512_H +#define SHA512_H + +#include + +#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 \ No newline at end of file diff --git a/libs/native/ed25519/src/sign.c b/libs/native/ed25519/src/sign.c new file mode 100644 index 0000000..199a839 --- /dev/null +++ b/libs/native/ed25519/src/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/libs/native/ed25519/src/verify.c b/libs/native/ed25519/src/verify.c new file mode 100644 index 0000000..32f988e --- /dev/null +++ b/libs/native/ed25519/src/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/libs/native/ed25519/test.c b/libs/native/ed25519/test.c new file mode 100644 index 0000000..e2159a9 --- /dev/null +++ b/libs/native/ed25519/test.c @@ -0,0 +1,150 @@ +#include +#include +#include +#include + +/* #define ED25519_DLL */ +#include "src/ed25519.h" + +#include "src/ge.h" +#include "src/sc.h" + + +int main() { + unsigned char public_key[32], private_key[64], seed[32], scalar[32]; + unsigned char other_public_key[32], other_private_key[64]; + unsigned char shared_secret[32], other_shared_secret[32]; + unsigned char signature[64]; + + clock_t start; + clock_t end; + int i; + + const unsigned char message[] = "Hello, world!"; + const int message_len = strlen((char*) message); + + /* create a random seed, and a keypair out of that seed */ + ed25519_create_seed(seed); + ed25519_create_keypair(public_key, private_key, seed); + + /* create signature on the message with the keypair */ + ed25519_sign(signature, message, message_len, public_key, private_key); + + /* verify the signature */ + if (ed25519_verify(signature, message, message_len, public_key)) { + printf("valid signature\n"); + } else { + printf("invalid signature\n"); + } + + /* create scalar and add it to the keypair */ + ed25519_create_seed(scalar); + ed25519_add_scalar(public_key, private_key, scalar); + + /* create signature with the new keypair */ + ed25519_sign(signature, message, message_len, public_key, private_key); + + /* verify the signature with the new keypair */ + if (ed25519_verify(signature, message, message_len, public_key)) { + printf("valid signature\n"); + } else { + printf("invalid signature\n"); + } + + /* make a slight adjustment and verify again */ + signature[44] ^= 0x10; + if (ed25519_verify(signature, message, message_len, public_key)) { + printf("did not detect signature change\n"); + } else { + printf("correctly detected signature change\n"); + } + + /* generate two keypairs for testing key exchange */ + ed25519_create_seed(seed); + ed25519_create_keypair(public_key, private_key, seed); + ed25519_create_seed(seed); + ed25519_create_keypair(other_public_key, other_private_key, seed); + + /* create two shared secrets - from both perspectives - and check if they're equal */ + ed25519_key_exchange(shared_secret, other_public_key, private_key); + ed25519_key_exchange(other_shared_secret, public_key, other_private_key); + + for (i = 0; i < 32; ++i) { + if (shared_secret[i] != other_shared_secret[i]) { + printf("key exchange was incorrect\n"); + break; + } + } + + if (i == 32) { + printf("key exchange was correct\n"); + } + + /* test performance */ + printf("testing seed generation performance: "); + start = clock(); + for (i = 0; i < 10000; ++i) { + ed25519_create_seed(seed); + } + end = clock(); + + printf("%fus per seed\n", ((double) ((end - start) * 1000)) / CLOCKS_PER_SEC / i * 1000); + + + printf("testing key generation performance: "); + start = clock(); + for (i = 0; i < 10000; ++i) { + ed25519_create_keypair(public_key, private_key, seed); + } + end = clock(); + + printf("%fus per keypair\n", ((double) ((end - start) * 1000)) / CLOCKS_PER_SEC / i * 1000); + + printf("testing sign performance: "); + start = clock(); + for (i = 0; i < 10000; ++i) { + ed25519_sign(signature, message, message_len, public_key, private_key); + } + end = clock(); + + printf("%fus per signature\n", ((double) ((end - start) * 1000)) / CLOCKS_PER_SEC / i * 1000); + + printf("testing verify performance: "); + start = clock(); + for (i = 0; i < 10000; ++i) { + ed25519_verify(signature, message, message_len, public_key); + } + end = clock(); + + printf("%fus per signature\n", ((double) ((end - start) * 1000)) / CLOCKS_PER_SEC / i * 1000); + + + printf("testing keypair scalar addition performance: "); + start = clock(); + for (i = 0; i < 10000; ++i) { + ed25519_add_scalar(public_key, private_key, scalar); + } + end = clock(); + + printf("%fus per keypair\n", ((double) ((end - start) * 1000)) / CLOCKS_PER_SEC / i * 1000); + + printf("testing public key scalar addition performance: "); + start = clock(); + for (i = 0; i < 10000; ++i) { + ed25519_add_scalar(public_key, NULL, scalar); + } + end = clock(); + + printf("%fus per key\n", ((double) 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zLsF9^g?%&u5gL#-~O;j=LPW98uhV&OG>DVC2As{r&S*Q`s@Q z6VPF8YzK2kF%R31$nd*3+jx1~*~-c;T*M%7{(s~)`FnZWyDnVuM{cATIl;J*vzv|} z02b}}2MeA217XStX7R+|QvTxUqj+ZOUo10<4M*|(Q5-OeCD`}@`|IlG5;@K z%y#41_eWX&#a5$OfyFbAYys?Vr2Sj+2m%7$@8^wn1e{t|APO|!oqepS$nZG#UANhp8_|hm=i2jSOkK(FP z{D5J0yR7`Xz4#Bzs5bsv`^fKO$zM@zHMSqYGr`i!-o@V5o9+L+2rX^hT|GSQy}ZEE zj@9k*^mbKbhe}|%7A#jdgXN!ByXF5ly#IYo|NHj+p9M!=-v;nMxBq>wGl_qcivJh@ z{;mHr4*ZKohXYHdl_$9# zf3B15|7R6pMC#uw{ZGYUq|x=CbGZKb0#@Vkk4nJ4_rF5rzfftUr$*|PEJu`tKZnZy z)G7bhI;K{PDhs1RBYMW@NtOTGef$^Q=I;Z;&i~Kl{CmG%wj;gw=W^NM=;%B89RB+} l{vBKYc{=}$y#IjF@%O)JwSRQe|5o!?&;5T?+`m7B{{x{BTv7l4 literal 0 HcmV?d00001 diff --git a/run.bat b/run.bat new file mode 100644 index 0000000..fa14862 --- /dev/null +++ b/run.bat @@ -0,0 +1 @@ +start "Qora" java -Xmx512m -Djava.library.path=libs/native -jar VanitygenQora.jar \ No newline at end of file diff --git a/src/Vanity.java b/src/Vanity.java new file mode 100644 index 0000000..c907d69 --- /dev/null +++ b/src/Vanity.java @@ -0,0 +1,111 @@ +import java.security.SecureRandom; +import java.util.Scanner; +import java.util.Random; + +import qora.crypto.Base58; +import qora.crypto.Crypto; +import qora.crypto.Ed25519; +import utils.Pair; + +import com.google.common.primitives.Bytes; +import com.google.common.primitives.Ints; + + +public class Vanity { + + public static boolean done = false; + public static String pattern = ""; + + + public static void main(String args[]) + { + Ed25519.load(); + + + Scanner scanner = new Scanner(System.in); + + System.out.print("Enter the beginning of the address (with letter Q): "); + String command = scanner.nextLine(); + + if(command.equals("quit")) + { + scanner.close(); + System.exit(0); + } + + boolean check = true; + for (int m=0; m<=command.length()-1; m++){ + String sub_str = command.substring(m, m+1); + if(Base58.ALPHABET.indexOf(sub_str) == -1) + { + check = false; + } + } + + if(!check) + { + System.out.println("\"" + command + "\" contains invalid characters."); + new java.util.Scanner(System.in).nextLine(); + scanner.close(); + System.exit(0); + } + + pattern = command; + + int availableProcessors = Runtime.getRuntime().availableProcessors(); + for (int m=0; m<=availableProcessors-1; m++){ + Runnable r = new MyRunnable(); + Thread t = new Thread(r); + t.start(); + } + + } + + private static byte[] generateAccountSeed(byte[] seed, int nonce) + { + byte[] nonceBytes = Ints.toByteArray(nonce); + byte[] accountSeed = Bytes.concat(nonceBytes, seed, nonceBytes); + return Crypto.getInstance().doubleDigest(accountSeed); + } + + public static class MyRunnable implements Runnable { + public void run() { + String doneseed = ""; + String doneaddr = ""; + + byte[] seed = new byte[32]; + Random random = new SecureRandom(); + int nonce = 0; + + while(!done) + { + random.nextBytes(seed); + + nonce = 0; + + while(nonce<10) + { + byte[] accountSeed = generateAccountSeed(seed, nonce); + + Pair keyPair = Crypto.getInstance().createKeyPair(accountSeed); + byte[] publicKey = keyPair.getB(); + String address = Crypto.getInstance().getAddress(publicKey); + + if(address.startsWith(pattern)) + { + doneseed = Base58.encode(seed); + doneaddr = address; + done = true; + } + nonce ++; + } + } + if(doneaddr != "") + { + System.out.println("address: " + doneaddr + " seed: " + doneseed); + new java.util.Scanner(System.in).nextLine(); + } + } + } +} + diff --git a/src/qora/crypto/Base58.java b/src/qora/crypto/Base58.java new file mode 100644 index 0000000..d55f0e2 --- /dev/null +++ b/src/qora/crypto/Base58.java @@ -0,0 +1,119 @@ +/** + * Copyright 2011 Google Inc. + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +package qora.crypto; + +import java.math.BigInteger; +import java.util.Arrays; + + +/** + * A custom form of base58 is used to encode BitCoin addresses. + */ +public class Base58 { + public static final String ALPHABET = "123456789ABCDEFGHJKLMNPQRSTUVWXYZabcdefghijkmnopqrstuvwxyz"; + private static final BigInteger BASE = BigInteger.valueOf(58); + + public static String encode(byte[] input) { + BigInteger bi = new BigInteger(1, input); + StringBuffer s = new StringBuffer(); + while (bi.compareTo(BASE) >= 0) { + BigInteger mod = bi.mod(BASE); + s.insert(0, ALPHABET.charAt(mod.intValue())); + bi = bi.subtract(mod).divide(BASE); + } + s.insert(0, ALPHABET.charAt(bi.intValue())); + // Convert leading zeros too. + for (byte anInput : input) { + if (anInput == 0) + s.insert(0, ALPHABET.charAt(0)); + else + break; + } + return s.toString(); + } + + public static byte[] decode(String input) { + if(input.length() == 0) { + return null; + } + BigInteger decoded = decodeToBigInteger(input); + if(decoded == null) { + return null; + } + byte[] bytes = decoded.toByteArray(); + // We may have got one more byte than we wanted, if the high bit of the + // next-to-last byte was not zero. This + // is because BigIntegers are represented with twos-compliment notation, + // thus if the high bit of the last + // byte happens to be 1 another 8 zero bits will be added to ensure the + // number parses as positive. Detect + // that case here and chop it off. + boolean stripSignByte = bytes.length > 1 && bytes[0] == 0 && bytes[1] < 0; + // Count the leading zeros, if any. + int leadingZeros = 0; + for (int i = 0; i < input.length() && input.charAt(i) == ALPHABET.charAt(0); i++) { + leadingZeros++; + } + // Now cut/pad correctly. Java 6 has a convenience for this, but Android + // can't use it. + byte[] tmp = new byte[bytes.length - (stripSignByte ? 1 : 0) + + leadingZeros]; + System.arraycopy(bytes, stripSignByte ? 1 : 0, tmp, leadingZeros, + tmp.length - leadingZeros); + return tmp; + } + + private static BigInteger decodeToBigInteger(String input) { + BigInteger bi = BigInteger.valueOf(0); + // Work backwards through the string. + for (int i = input.length() - 1; i >= 0; i--) { + int alphaIndex = ALPHABET.indexOf(input.charAt(i)); + if (alphaIndex == -1) { + return null; + } + bi = bi.add(BigInteger.valueOf(alphaIndex).multiply( + BASE.pow(input.length() - 1 - i))); + } + return bi; + } + + /** + * Uses the checksum in the last 4 bytes of the decoded data to verify the + * rest are correct. The checksum is removed from the returned data. + * @param input The base58 encoded string to decode and verify. + * @return The decoded and verified input as an array of bytes. + */ + public static byte[] decodeChecked(String input) { + byte[] tmp = decode(input); + if (tmp == null) { + return null; + } + if (tmp.length < 4) { + return null; + } + byte[] checksum = new byte[4]; + System.arraycopy(tmp, tmp.length - 4, checksum, 0, 4); + byte[] bytes = new byte[tmp.length - 4]; + System.arraycopy(tmp, 0, bytes, 0, tmp.length - 4); + tmp = Crypto.getInstance().doubleDigest(bytes); + byte[] hash = new byte[4]; + System.arraycopy(tmp, 0, hash, 0, 4); + if (!Arrays.equals(hash, checksum)) + return null; + return bytes; + } +} \ No newline at end of file diff --git a/src/qora/crypto/Crypto.java b/src/qora/crypto/Crypto.java new file mode 100644 index 0000000..9f9b1c5 --- /dev/null +++ b/src/qora/crypto/Crypto.java @@ -0,0 +1,163 @@ +package qora.crypto; + +import java.security.MessageDigest; +import java.security.NoSuchAlgorithmException; +import java.util.ArrayList; +import java.util.Arrays; +import java.util.List; + +import utils.Pair; + +import com.google.common.primitives.Bytes; + +public class Crypto { + + public static final byte ADDRESS_VERSION = 58; + + private static Crypto instance; + + public static Crypto getInstance() + { + if(instance == null) + { + instance = new Crypto(); + } + + return instance; + } + + private Crypto() + { + + } + + public byte[] digest(byte[] input) + { + try + { + //SHA256 + MessageDigest sha256 = MessageDigest.getInstance("SHA-256"); + return sha256.digest(input); + } + catch (NoSuchAlgorithmException e) + { + return null; + } + } + + public byte[] doubleDigest(byte[] input) + { + //DOUBLE SHA256 + return this.digest(this.digest(input)); + } + + public Pair createKeyPair(byte[] seed) + { + try + { + //GENERATE PUBLIC KEY + return Ed25519.createKeyPair(seed); + } + catch (Exception e) + { + e.printStackTrace(); + return null; + } + } + + public String getAddress(byte[] publicKey) + { + //SHA256 PUBLICKEY FOR PROTECTION + byte[] publicKeyHash = this.digest(publicKey); + + //RIPEMD160 TO CREATE A SHORTER ADDRESS + RIPEMD160 ripEmd160 = new RIPEMD160(); + publicKeyHash = ripEmd160.digest(publicKeyHash); + + //CONVERT TO LIST + List addressList = new ArrayList(); + + //ADD VERSION BYTE + Byte versionByte = Byte.valueOf(ADDRESS_VERSION); + addressList.add(versionByte); + + addressList.addAll(Bytes.asList(publicKeyHash)); + + //GENERATE CHECKSUM + byte[] checkSum = this.doubleDigest(Bytes.toArray(addressList)); + + //ADD FIRST 4 BYTES OF CHECKSUM TO ADDRESS + addressList.add(checkSum[0]); + addressList.add(checkSum[1]); + addressList.add(checkSum[2]); + addressList.add(checkSum[3]); + + //BASE58 ENCODE ADDRESS + String address = Base58.encode(Bytes.toArray(addressList)); + + return address; + } + + public boolean isValidAddress(String address) + { + try + { + //BASE 58 DECODE + byte[] addressBytes = Base58.decode(address); + + //CHECK BYTES + if(addressBytes.length != 25) + { + return false; + } + + //CHECK VERSION + if(addressBytes[0] != ADDRESS_VERSION) + { + return false; + } + + //CONVERT TO LIST + List addressList = new ArrayList(); + addressList.addAll(Bytes.asList(addressBytes)); + + //REMOVE CHECKSUM + byte[] checkSum = new byte[4]; + checkSum[3] = addressList.remove(addressList.size() - 1); + checkSum[2] = addressList.remove(addressList.size() - 1); + checkSum[1] = addressList.remove(addressList.size() - 1); + checkSum[0] = addressList.remove(addressList.size() - 1); + + //GENERATE ADDRESS CHECKSUM + byte[] digest = this.doubleDigest(Bytes.toArray(addressList)); + byte[] checkSumTwo = new byte[4]; + checkSumTwo[0] = digest[0]; + checkSumTwo[1] = digest[1]; + checkSumTwo[2] = digest[2]; + checkSumTwo[3] = digest[3]; + + //CHECK IF CHECKSUMS ARE THE SAME + return Arrays.equals(checkSum, checkSumTwo); + } + catch(Exception e) + { + //ERROR DECODING + return false; + } + } + + public boolean verify(byte[] publicKey, byte[] signature, byte[] message) + { + try + { + //VERIFY SIGNATURE + return Ed25519.verify(signature, message, publicKey); + } + catch(Exception e) + { + e.printStackTrace(); + return false; + } + } + +} diff --git a/src/qora/crypto/Ed25519.java b/src/qora/crypto/Ed25519.java new file mode 100644 index 0000000..c7821e0 --- /dev/null +++ b/src/qora/crypto/Ed25519.java @@ -0,0 +1,85 @@ +package qora.crypto; + +import java.util.Arrays; + +import utils.Pair; + +public class Ed25519 { + + private native static byte[] createKeyPairN(byte[] seed); + private native static byte[] signN(byte[] privateKey, byte[] publicKey, byte[] message, int messageLength); + private native static int verifyN(byte[] signature, byte[] message, int messageLength, byte[] publicKey); + + + public static boolean load() + { + try + { + String arch = System.getProperty("os.arch").toLowerCase(); + String os = System.getProperty("os.name").toLowerCase(); + + //WINDOWS + if(os.contains("windows")) + { + //32BIT + if(arch.contains("x86") || arch.contains("i386")) + { + System.loadLibrary("Qora25519.windows.x86"); + } + //64BIT + else + { + System.loadLibrary("Qora25519.windows.x64"); + } + } + + //LINUX + if(os.contains("linux")) + { + //32BIT + if(arch.contains("x86") || arch.contains("i386")) + { + System.loadLibrary("Qora25519.linux.x86"); + } + //64BIT + else + { + System.loadLibrary("Qora25519.linux.x64"); + } + } + + //OSX + if(os.contains("mac")) + { + System.loadLibrary("Qora25519.mac"); + } + } + catch(Exception e) + { + return false; + } + + return true; + } + + public static Pair createKeyPair(byte[] seed) + { + byte[] rawPair = createKeyPairN(seed); + + byte[] privateKey = Arrays.copyOfRange(rawPair, 0, 64); + byte[] publicKey = Arrays.copyOfRange(rawPair, 64, 96); + + return new Pair(privateKey, publicKey); + } + + public static byte[] sign(Pair keyPair, byte[] message) + { + return signN(keyPair.getA(), keyPair.getB(), message, message.length); + } + + public static boolean verify(byte[] signature, byte[] message, byte[] publicKey) + { + int valid = verifyN(signature, message, message.length, publicKey); + return valid == 1; + } +} diff --git a/src/qora/crypto/RIPEMD160.java b/src/qora/crypto/RIPEMD160.java new file mode 100644 index 0000000..49c28ff --- /dev/null +++ b/src/qora/crypto/RIPEMD160.java @@ -0,0 +1,331 @@ +package qora.crypto; + +public class RIPEMD160 { + + private static final int[][] ArgArray = {{11, 14, 15, 12, 5, 8, 7, 9, 11, 13, 14, 15, 6, 7, 9, 8, + 7, 6, 8, 13, 11, 9, 7, 15, 7, 12, 15, 9, 11, 7, 13, 12, + 11, 13, 6, 7, 14, 9, 13, 15, 14, 8, 13, 6, 5, 12, 7, 5, + 11, 12, 14, 15, 14, 15, 9, 8, 9, 14, 5, 6, 8, 6, 5, 12, + 9, 15, 5, 11, 6, 8, 13, 12, 5, 12, 13, 14, 11, 8, 5, 6}, + {8, 9, 9, 11, 13, 15, 15, 5, 7, 7, 8, 11, 14, 14, 12, 6, + 9, 13, 15, 7, 12, 8, 9, 11, 7, 7, 12, 7, 6, 15, 13, 11, + 9, 7, 15, 11, 8, 6, 6, 14, 12, 13, 5, 14, 13, 13, 7, 5, + 15, 5, 8, 11, 14, 14, 6, 14, 6, 9, 12, 9, 12, 5, 15, 8, + 8, 5, 12, 9, 12, 5, 14, 6, 8, 13, 6, 5, 15, 13, 11, 11}}; + private static final int[][] IndexArray = {{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, + 7, 4, 13, 1, 10, 6, 15, 3, 12, 0, 9, 5, 2, 14, 11, 8, + 3, 10, 14, 4, 9, 15, 8, 1, 2, 7, 0, 6, 13, 11, 5, 12, + 1, 9, 11, 10, 0, 8, 12, 4, 13, 3, 7, 15, 14, 5, 6, 2, + 4, 0, 5, 9, 7, 12, 2, 10, 14, 1, 3, 8, 11, 6, 15, 13}, + {5, 14, 7, 0, 9, 2, 11, 4, 13, 6, 15, 8, 1, 10, 3, 12, + 6, 11, 3, 7, 0, 13, 5, 10, 14, 15, 8, 12, 4, 9, 1, 2, + 15, 5, 1, 3, 7, 14, 6, 9, 11, 8, 12, 2, 10, 0, 4, 13, + 8, 6, 4, 1, 3, 11, 15, 0, 5, 12, 2, 13, 9, 7, 10, 14, + 12, 15, 10, 4, 1, 5, 8, 7, 6, 2, 13, 14, 0, 3, 9, 11}}; + private int[] MDbuf; + + public RIPEMD160() { + MDbuf = new int[5]; + MDbuf[0] = 0x67452301; + MDbuf[1] = 0xefcdab89; + MDbuf[2] = 0x98badcfe; + MDbuf[3] = 0x10325476; + MDbuf[4] = 0xc3d2e1f0; + working = new int[16]; + working_ptr = 0; + msglen = 0; + } + + public void reset() { + MDbuf = new int[5]; + MDbuf[0] = 0x67452301; + MDbuf[1] = 0xefcdab89; + MDbuf[2] = 0x98badcfe; + MDbuf[3] = 0x10325476; + MDbuf[4] = 0xc3d2e1f0; + working = new int[16]; + working_ptr = 0; + msglen = 0; + } + + private void compress(int[] X) { + int index = 0; + + int a, b, c, d, e; + int A, B, C, D, E; + int temp, s; + + A = a = MDbuf[0]; + B = b = MDbuf[1]; + C = c = MDbuf[2]; + D = d = MDbuf[3]; + E = e = MDbuf[4]; + + for (; index < 16; index++) { + // The 16 FF functions - round 1 */ + temp = a + (b ^ c ^ d) + X[IndexArray[0][index]]; + a = e; + e = d; + d = (c << 10) | (c >>> 22); + c = b; + s = ArgArray[0][index]; + b = ((temp << s) | (temp >>> (32 - s))) + a; + + // The 16 JJJ functions - parallel round 1 */ + temp = A + (B ^ (C | ~D)) + X[IndexArray[1][index]] + 0x50a28be6; + A = E; + E = D; + D = (C << 10) | (C >>> 22); + C = B; + s = ArgArray[1][index]; + B = ((temp << s) | (temp >>> (32 - s))) + A; + } + + for (; index < 32; index++) { + // The 16 GG functions - round 2 */ + temp = a + ((b & c) | (~b & d)) + X[IndexArray[0][index]] + 0x5a827999; + a = e; + e = d; + d = (c << 10) | (c >>> 22); + c = b; + s = ArgArray[0][index]; + b = ((temp << s) | (temp >>> (32 - s))) + a; + + // The 16 III functions - parallel round 2 */ + temp = A + ((B & D) | (C & ~D)) + X[IndexArray[1][index]] + 0x5c4dd124; + A = E; + E = D; + D = (C << 10) | (C >>> 22); + C = B; + s = ArgArray[1][index]; + B = ((temp << s) | (temp >>> (32 - s))) + A; + } + + for (; index < 48; index++) { + // The 16 HH functions - round 3 */ + temp = a + ((b | ~c) ^ d) + X[IndexArray[0][index]] + 0x6ed9eba1; + a = e; + e = d; + d = (c << 10) | (c >>> 22); + c = b; + s = ArgArray[0][index]; + b = ((temp << s) | (temp >>> (32 - s))) + a; + + // The 16 HHH functions - parallel round 3 */ + temp = A + ((B | ~C) ^ D) + X[IndexArray[1][index]] + 0x6d703ef3; + A = E; + E = D; + D = (C << 10) | (C >>> 22); + C = B; + s = ArgArray[1][index]; + B = ((temp << s) | (temp >>> (32 - s))) + A; + } + + for (; index < 64; index++) { + // The 16 II functions - round 4 */ + temp = a + ((b & d) | (c & ~d)) + X[IndexArray[0][index]] + 0x8f1bbcdc; + a = e; + e = d; + d = (c << 10) | (c >>> 22); + c = b; + s = ArgArray[0][index]; + b = ((temp << s) | (temp >>> (32 - s))) + a; + + // The 16 GGG functions - parallel round 4 */ + temp = A + ((B & C) | (~B & D)) + X[IndexArray[1][index]] + 0x7a6d76e9; + A = E; + E = D; + D = (C << 10) | (C >>> 22); + C = B; + s = ArgArray[1][index]; + B = ((temp << s) | (temp >>> (32 - s))) + A; + } + + for (; index < 80; index++) { + // The 16 JJ functions - round 5 */ + temp = a + (b ^ (c | ~d)) + X[IndexArray[0][index]] + 0xa953fd4e; + a = e; + e = d; + d = (c << 10) | (c >>> 22); + c = b; + s = ArgArray[0][index]; + b = ((temp << s) | (temp >>> (32 - s))) + a; + + // The 16 FFF functions - parallel round 5 */ + temp = A + (B ^ C ^ D) + X[IndexArray[1][index]]; + A = E; + E = D; + D = (C << 10) | (C >>> 22); + C = B; + s = ArgArray[1][index]; + B = ((temp << s) | (temp >>> (32 - s))) + A; + } + + /* combine results */ + D += c + MDbuf[1]; /* final result for MDbuf[0] */ + MDbuf[1] = MDbuf[2] + d + E; + MDbuf[2] = MDbuf[3] + e + A; + MDbuf[3] = MDbuf[4] + a + B; + MDbuf[4] = MDbuf[0] + b + C; + MDbuf[0] = D; + } + + private void MDfinish(int[] array, int lswlen, int mswlen) { + int[] X = array; /* message words */ + + /* append the bit m_n == 1 */ + X[(lswlen >> 2) & 15] ^= 1 << (((lswlen & 3) << 3) + 7); + + if ((lswlen & 63) > 55) { + /* length goes to next block */ + compress(X); + for (int i = 0; i < 14; i++) { + X[i] = 0; + } + } + + /* append length in bits*/ + X[14] = lswlen << 3; + X[15] = (lswlen >> 29) | (mswlen << 3); + compress(X); + } + private int[] working; + private int working_ptr; + private int msglen; + + public void update(byte input) { + working[working_ptr >> 2] ^= ((int) input) << ((working_ptr & 3) << 3); + working_ptr++; + if (working_ptr == 64) { + compress(working); + for (int j = 0; j < 16; j++) { + working[j] = 0; + } + working_ptr = 0; + } + msglen++; + } + + public void update(byte[] input) { + for (int i = 0; i < input.length; i++) { + working[working_ptr >> 2] ^= ((int) input[i]) << ((working_ptr & 3) << 3); + working_ptr++; + if (working_ptr == 64) { + compress(working); + for (int j = 0; j < 16; j++) { + working[j] = 0; + } + working_ptr = 0; + } + } + msglen += input.length; + } + + public void update(byte[] input, int offset, int len) { + if (offset + len >= input.length) { + for (int i = offset; i < input.length; i++) { + working[working_ptr >> 2] ^= ((int) input[i]) << ((working_ptr & 3) << 3); + working_ptr++; + if (working_ptr == 64) { + compress(working); + for (int j = 0; j < 16; j++) { + working[j] = 0; + } + working_ptr = 0; + } + } + msglen += input.length - offset; + } else { + for (int i = offset; i < offset + len; i++) { + working[working_ptr >> 2] ^= ((int) input[i]) << ((working_ptr & 3) << 3); + working_ptr++; + if (working_ptr == 64) { + compress(working); + for (int j = 0; j < 16; j++) { + working[j] = 0; + } + working_ptr = 0; + } + } + msglen += len; + } + } + + public void update(String s) { + byte[] bytearray = new byte[s.length()]; + for (int i = 0; i < bytearray.length; i++) { + bytearray[i] = (byte) s.charAt(i); + } + update(bytearray); + } + + public byte[] digestBin() { + MDfinish(working, msglen, 0); + byte[] res = new byte[20]; + for (int i = 0; i < 20; i++) { + res[i] = (byte) ((MDbuf[i >> 2] >>> ((i & 3) << 3)) & 0x000000FF); + } + return res; + } + + public byte[] digest(byte[] input) { + update(input); + return digestBin(); + } + + public String digest() + { + MDfinish(working, msglen, 0); + byte[] res = new byte[20]; + for (int i = 0; i < 20; i++) { + res[i] = (byte) ((MDbuf[i >> 2] >>> ((i & 3) << 3)) & 0x000000FF); + } + + String hex = ""; + for (int i=0; i 9) { + res = "" + (char) ('a' + (top - 10)); + } else { + res = "" + (char) ('0' + top); + } + if (bottom > 9) { + res += (char) ('a' + (bottom - 10)); + } else { + res += (char) ('0' + bottom); + } + return res; + } + + public static String RIPEMD160String(String txt) + { + RIPEMD160 r = new RIPEMD160(); + r.update(txt); + return r.digest(); + + } +} \ No newline at end of file diff --git a/src/utils/Pair.java b/src/utils/Pair.java new file mode 100644 index 0000000..89c1754 --- /dev/null +++ b/src/utils/Pair.java @@ -0,0 +1,38 @@ +package utils; + +public class Pair { + + private T a; + private U b; + + public Pair() + { + } + + public Pair(T a, U b) + { + this.a = a; + this.b = b; + } + + public void setA(T a) + { + this.a = a; + } + + public T getA() + { + return a; + } + + public void setB(U b) + { + this.b = b; + } + + public U getB() + { + return b; + } + +}