diff options
| -rw-r--r-- | ed25519_32.dll | bin | 0 -> 127488 bytes | |||
| -rw-r--r-- | ed25519_64.dll | bin | 0 -> 112128 bytes | |||
| -rw-r--r-- | readme.md | 166 | ||||
| -rw-r--r-- | src/add_scalar.c | 56 | ||||
| -rw-r--r-- | src/ed25519.h | 38 | ||||
| -rw-r--r-- | src/fe.c | 1491 | ||||
| -rw-r--r-- | src/fe.h | 41 | ||||
| -rw-r--r-- | src/fixedint.h | 72 | ||||
| -rw-r--r-- | src/ge.c | 467 | ||||
| -rw-r--r-- | src/ge.h | 74 | ||||
| -rw-r--r-- | src/key_exchange.c | 79 | ||||
| -rw-r--r-- | src/keypair.c | 16 | ||||
| -rw-r--r-- | src/precomp_data.h | 1391 | ||||
| -rw-r--r-- | src/sc.c | 809 | ||||
| -rw-r--r-- | src/sc.h | 12 | ||||
| -rw-r--r-- | src/seed.c | 40 | ||||
| -rw-r--r-- | src/sha512.c | 275 | ||||
| -rw-r--r-- | src/sha512.h | 21 | ||||
| -rw-r--r-- | src/sign.c | 31 | ||||
| -rw-r--r-- | src/verify.c | 77 | ||||
| -rw-r--r-- | test.c | 150 |
21 files changed, 5306 insertions, 0 deletions
diff --git a/ed25519_32.dll b/ed25519_32.dll Binary files differnew file mode 100644 index 0000000..ac15a95 --- /dev/null +++ b/ed25519_32.dll diff --git a/ed25519_64.dll b/ed25519_64.dll Binary files differnew file mode 100644 index 0000000..f50647c --- /dev/null +++ b/ed25519_64.dll diff --git a/readme.md b/readme.md new file mode 100644 index 0000000..676a631 --- /dev/null +++ b/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 in the public domain. + +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/src/add_scalar.c b/src/add_scalar.c new file mode 100644 index 0000000..a4f2a55 --- /dev/null +++ b/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/src/ed25519.h b/src/ed25519.h new file mode 100644 index 0000000..8924659 --- /dev/null +++ b/src/ed25519.h @@ -0,0 +1,38 @@ +#ifndef ED25519_H +#define ED25519_H + +#include <stddef.h> + +#if defined(_WIN32) + #if defined(ED25519_BUILD_DLL) + #define ED25519_DECLSPEC __declspec(dllexport) + #elif defined(ED25519_DLL) + #define ED25519_DECLSPEC __declspec(dllimport) + #else + #define ED25519_DECLSPEC + #endif +#else + #define ED25519_DECLSPEC +#endif + + +#ifdef __cplusplus +extern "C" { +#endif + +#ifndef ED25519_NO_SEED +int ED25519_DECLSPEC ed25519_create_seed(unsigned char *seed); +#endif + +void ED25519_DECLSPEC ed25519_create_keypair(unsigned char *public_key, unsigned char *private_key, const unsigned char *seed); +void ED25519_DECLSPEC ed25519_sign(unsigned char *signature, const unsigned char *message, size_t message_len, const unsigned char *public_key, const unsigned char *private_key); +int ED25519_DECLSPEC ed25519_verify(const unsigned char *signature, const unsigned char *message, size_t message_len, const unsigned char *public_key); +void ED25519_DECLSPEC ed25519_add_scalar(unsigned char *public_key, unsigned char *private_key, const unsigned char *scalar); +void ED25519_DECLSPEC ed25519_key_exchange(unsigned char *shared_secret, const unsigned char *public_key, const unsigned char *private_key); + + +#ifdef __cplusplus +} +#endif + +#endif diff --git a/src/fe.c b/src/fe.c new file mode 100644 index 0000000..448e3e9 --- /dev/null +++ b/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<y<1. + + Write r=h-pq. + Have 0<=r<=p-1=2^255-20. + Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1. + + Write x=r+19(2^-255)r+y. + Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q. + + Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1)) + so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q. +*/ + +void fe_tobytes(unsigned char *s, const fe h) { + int32_t h0 = h[0]; + int32_t h1 = h[1]; + int32_t h2 = h[2]; + int32_t h3 = h[3]; + int32_t h4 = h[4]; + int32_t h5 = h[5]; + int32_t h6 = h[6]; + int32_t h7 = h[7]; + int32_t h8 = h[8]; + int32_t h9 = h[9]; + int32_t q; + int32_t carry0; + int32_t carry1; + int32_t carry2; + int32_t carry3; + int32_t carry4; + int32_t carry5; + int32_t carry6; + int32_t carry7; + int32_t carry8; + int32_t carry9; + q = (19 * h9 + (((int32_t) 1) << 24)) >> 25; + q = (h0 + q) >> 26; + q = (h1 + q) >> 25; + q = (h2 + q) >> 26; + q = (h3 + q) >> 25; + q = (h4 + q) >> 26; + q = (h5 + q) >> 25; + q = (h6 + q) >> 26; + q = (h7 + q) >> 25; + q = (h8 + q) >> 26; + q = (h9 + q) >> 25; + /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */ + h0 += 19 * q; + /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */ + carry0 = h0 >> 26; + h1 += carry0; + h0 -= carry0 << 26; + carry1 = h1 >> 25; + h2 += carry1; + h1 -= carry1 << 25; + carry2 = h2 >> 26; + h3 += carry2; + h2 -= carry2 << 26; + carry3 = h3 >> 25; + h4 += carry3; + h3 -= carry3 << 25; + carry4 = h4 >> 26; + h5 += carry4; + h4 -= carry4 << 26; + carry5 = h5 >> 25; + h6 += carry5; + h5 -= carry5 << 25; + carry6 = h6 >> 26; + h7 += carry6; + h6 -= carry6 << 26; + carry7 = h7 >> 25; + h8 += carry7; + h7 -= carry7 << 25; + carry8 = h8 >> 26; + h9 += carry8; + h8 -= carry8 << 26; + carry9 = h9 >> 25; + h9 -= carry9 << 25; + + /* h10 = carry9 */ + /* + Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20. + Have h0+...+2^230 h9 between 0 and 2^255-1; + evidently 2^255 h10-2^255 q = 0. + Goal: Output h0+...+2^230 h9. + */ + s[0] = (unsigned char) (h0 >> 0); + s[1] = (unsigned char) (h0 >> 8); + s[2] = (unsigned char) (h0 >> 16); + s[3] = (unsigned char) ((h0 >> 24) | (h1 << 2)); + s[4] = (unsigned char) (h1 >> 6); + s[5] = (unsigned char) (h1 >> 14); + s[6] = (unsigned char) ((h1 >> 22) | (h2 << 3)); + s[7] = (unsigned char) (h2 >> 5); + s[8] = (unsigned char) (h2 >> 13); + s[9] = (unsigned char) ((h2 >> 21) | (h3 << 5)); + s[10] = (unsigned char) (h3 >> 3); + s[11] = (unsigned char) (h3 >> 11); + s[12] = (unsigned char) ((h3 >> 19) | (h4 << 6)); + s[13] = (unsigned char) (h4 >> 2); + s[14] = (unsigned char) (h4 >> 10); + s[15] = (unsigned char) (h4 >> 18); + s[16] = (unsigned char) (h5 >> 0); + s[17] = (unsigned char) (h5 >> 8); + s[18] = (unsigned char) (h5 >> 16); + s[19] = (unsigned char) ((h5 >> 24) | (h6 << 1)); + s[20] = (unsigned char) (h6 >> 7); + s[21] = (unsigned char) (h6 >> 15); + s[22] = (unsigned char) ((h6 >> 23) | (h7 << 3)); + s[23] = (unsigned char) (h7 >> 5); + s[24] = (unsigned char) (h7 >> 13); + s[25] = (unsigned char) ((h7 >> 21) | (h8 << 4)); + s[26] = (unsigned char) (h8 >> 4); + s[27] = (unsigned char) (h8 >> 12); + s[28] = (unsigned char) ((h8 >> 20) | (h9 << 6)); + s[29] = (unsigned char) (h9 >> 2); + s[30] = (unsigned char) (h9 >> 10); + s[31] = (unsigned char) (h9 >> 18); +} diff --git a/src/fe.h b/src/fe.h new file mode 100644 index 0000000..b4b62d2 --- /dev/null +++ b/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/src/fixedint.h b/src/fixedint.h new file mode 100644 index 0000000..1a8745b --- /dev/null +++ b/src/fixedint.h @@ -0,0 +1,72 @@ +/* + Portable header to provide the 32 and 64 bits type. + + Not a compatible replacement for <stdint.h>, do not blindly use it as such. +*/ + +#if ((defined(__STDC__) && __STDC__ && __STDC_VERSION__ >= 199901L) || (defined(__WATCOMC__) && (defined(_STDINT_H_INCLUDED) || __WATCOMC__ >= 1250)) || (defined(__GNUC__) && (defined(_STDINT_H) || defined(_STDINT_H_) || defined(__UINT_FAST64_TYPE__)) )) && !defined(FIXEDINT_H_INCLUDED) + #include <stdint.h> + #define FIXEDINT_H_INCLUDED + + #if defined(__WATCOMC__) && __WATCOMC__ >= 1250 && !defined(UINT64_C) + #include <limits.h> + #define UINT64_C(x) (x + (UINT64_MAX - UINT64_MAX)) + #endif +#endif + + +#ifndef FIXEDINT_H_INCLUDED + #define FIXEDINT_H_INCLUDED + + #include <limits.h> + + /* (u)int32_t */ + #ifndef uint32_t + #if (ULONG_MAX == 0xffffffffUL) + typedef unsigned long uint32_t; + #elif (UINT_MAX == 0xffffffffUL) + typedef unsigned int uint32_t; + #elif (USHRT_MAX == 0xffffffffUL) + typedef unsigned short uint32_t; + #endif + #endif + + + #ifndef int32_t + #if (LONG_MAX == 0x7fffffffL) + typedef signed long int32_t; + #elif (INT_MAX == 0x7fffffffL) + typedef signed int int32_t; + #elif (SHRT_MAX == 0x7fffffffL) + typedef signed short int32_t; + #endif + #endif + + + /* (u)int64_t */ + #if (defined(__STDC__) && defined(__STDC_VERSION__) && __STDC__ && __STDC_VERSION__ >= 199901L) + typedef long long int64_t; + typedef unsigned long long uint64_t; + + #define UINT64_C(v) v ##ULL + #define INT64_C(v) v ##LL + #elif defined(__GNUC__) + __extension__ typedef long long int64_t; + __extension__ typedef unsigned long long uint64_t; + + #define UINT64_C(v) v ##ULL + #define INT64_C(v) v ##LL + #elif defined(__MWERKS__) || defined(__SUNPRO_C) || defined(__SUNPRO_CC) || defined(__APPLE_CC__) || defined(_LONG_LONG) || defined(_CRAYC) + typedef long long int64_t; + typedef unsigned long long uint64_t; + + #define UINT64_C(v) v ##ULL + #define INT64_C(v) v ##LL + #elif (defined(__WATCOMC__) && defined(__WATCOM_INT64__)) || (defined(_MSC_VER) && _INTEGRAL_MAX_BITS >= 64) || (defined(__BORLANDC__) && __BORLANDC__ > 0x460) || defined(__alpha) || defined(__DECC) + typedef __int64 int64_t; + typedef unsigned __int64 uint64_t; + + #define UINT64_C(v) v ##UI64 + #define INT64_C(v) v ##I64 + #endif +#endif diff --git a/src/ge.c b/src/ge.c new file mode 100644 index 0000000..3c342b1 --- /dev/null +++ b/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/src/ge.h b/src/ge.h new file mode 100644 index 0000000..17fde2d --- /dev/null +++ b/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/src/key_exchange.c b/src/key_exchange.c new file mode 100644 index 0000000..abd75da --- /dev/null +++ b/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/src/keypair.c b/src/keypair.c new file mode 100644 index 0000000..dc1b8ec --- /dev/null +++ b/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/src/precomp_data.h b/src/precomp_data.h new file mode 100644 index 0000000..776b84f --- /dev/null +++ b/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, 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-11233159, 26961357, 1640861, -32413112, -16737940, 12248509, -5240639, 13735342, 1934062 }, + { 25089769, 6742589, 17081145, -13406266, 21909293, -16067981, -15136294, -3765346, -21277997, 5473616 }, + { 31883677, -7961101, 1083432, -11572403, 22828471, 13290673, -7125085, 12469656, 29111212, -5451014 }, + }, + { + { 24244947, -15050407, -26262976, 2791540, -14997599, 16666678, 24367466, 6388839, -10295587, 452383 }, + { -25640782, -3417841, 5217916, 16224624, 19987036, -4082269, -24236251, -5915248, 15766062, 8407814 }, + { -20406999, 13990231, 15495425, 16395525, 5377168, 15166495, -8917023, -4388953, -8067909, 2276718 }, + }, + { + { 30157918, 12924066, -17712050, 9245753, 19895028, 3368142, -23827587, 5096219, 22740376, -7303417 }, + { 2041139, -14256350, 7783687, 13876377, -25946985, -13352459, 24051124, 13742383, -15637599, 13295222 }, + { 33338237, -8505733, 12532113, 7977527, 9106186, -1715251, -17720195, -4612972, -4451357, -14669444 }, + }, + { + { -20045281, 5454097, -14346548, 6447146, 28862071, 1883651, -2469266, -4141880, 7770569, 9620597 }, + { 23208068, 7979712, 33071466, 8149229, 1758231, -10834995, 30945528, -1694323, -33502340, -14767970 }, + { 1439958, -16270480, -1079989, -793782, 4625402, 10647766, -5043801, 1220118, 30494170, -11440799 }, + }, + { + { -5037580, -13028295, -2970559, -3061767, 15640974, -6701666, -26739026, 926050, -1684339, -13333647 }, + { 13908495, -3549272, 30919928, -6273825, -21521863, 7989039, 9021034, 9078865, 3353509, 4033511 }, + { -29663431, -15113610, 32259991, -344482, 24295849, -12912123, 23161163, 8839127, 27485041, 7356032 }, + }, + }, + { + { + { 9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142, 2625015, 28431036, -16771834 }, + { -23839233, -8311415, -25945511, 7480958, -17681669, -8354183, -22545972, 14150565, 15970762, 4099461 }, + { 29262576, 16756590, 26350592, -8793563, 8529671, -11208050, 13617293, -9937143, 11465739, 8317062 }, + }, + { + { -25493081, -6962928, 32500200, -9419051, -23038724, -2302222, 14898637, 3848455, 20969334, -5157516 }, + { -20384450, -14347713, -18336405, 13884722, -33039454, 2842114, -21610826, -3649888, 11177095, 14989547 }, + { -24496721, -11716016, 16959896, 2278463, 12066309, 10137771, 13515641, 2581286, -28487508, 9930240 }, + }, + { + { -17751622, -2097826, 16544300, -13009300, -15914807, -14949081, 18345767, -13403753, 16291481, -5314038 }, + { -33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774, 6957617, 4368891, 9788741 }, + { 16660756, 7281060, -10830758, 12911820, 20108584, -8101676, -21722536, -8613148, 16250552, -11111103 }, + }, + { + { -19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584, 10604807, -30190403, 4782747 }, + { -1354539, 14736941, -7367442, -13292886, 7710542, -14155590, -9981571, 4383045, 22546403, 437323 }, + { 31665577, -12180464, -16186830, 1491339, -18368625, 3294682, 27343084, 2786261, -30633590, -14097016 }, + }, + { + { -14467279, -683715, -33374107, 7448552, 19294360, 14334329, -19690631, 2355319, -19284671, -6114373 }, + { 15121312, -15796162, 6377020, -6031361, -10798111, -12957845, 18952177, 15496498, -29380133, 11754228 }, + { -2637277, -13483075, 8488727, -14303896, 12728761, -1622493, 7141596, 11724556, 22761615, -10134141 }, + }, + { + { 16918416, 11729663, -18083579, 3022987, -31015732, -13339659, -28741185, -12227393, 32851222, 11717399 }, + { 11166634, 7338049, -6722523, 4531520, -29468672, -7302055, 31474879, 3483633, -1193175, -4030831 }, + { -185635, 9921305, 31456609, -13536438, -12013818, 13348923, 33142652, 6546660, -19985279, -3948376 }, + }, + { + { -32460596, 11266712, -11197107, -7899103, 31703694, 3855903, -8537131, -12833048, -30772034, -15486313 }, + { -18006477, 12709068, 3991746, -6479188, -21491523, -10550425, -31135347, -16049879, 10928917, 3011958 }, + { -6957757, -15594337, 31696059, 334240, 29576716, 14796075, -30831056, -12805180, 18008031, 10258577 }, + }, + { + { -22448644, 15655569, 7018479, -4410003, -30314266, -1201591, -1853465, 1367120, 25127874, 6671743 }, + { 29701166, -14373934, -10878120, 9279288, -17568, 13127210, 21382910, 11042292, 25838796, 4642684 }, + { -20430234, 14955537, -24126347, 8124619, -5369288, -5990470, 30468147, -13900640, 18423289, 4177476 }, + }, + }, +};
\ No newline at end of file diff --git a/src/sc.c b/src/sc.c new file mode 100644 index 0000000..ca5bad2 --- /dev/null +++ b/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/src/sc.h b/src/sc.h new file mode 100644 index 0000000..8fa727e --- /dev/null +++ b/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/src/seed.c b/src/seed.c new file mode 100644 index 0000000..25e5182 --- /dev/null +++ b/src/seed.c @@ -0,0 +1,40 @@ +#include "ed25519.h" + +#ifndef ED25519_NO_SEED + +#ifdef _WIN32 +#include <Windows.h> +#include <Wincrypt.h> +#else +#include <stdio.h> +#endif + +int ed25519_create_seed(unsigned char *seed) { +#ifdef _WIN32 + HCRYPTPROV prov; + + if (!CryptAcquireContext(&prov, NULL, NULL, PROV_RSA_FULL, CRYPT_VERIFYCONTEXT)) { + return 1; + } + + if (!CryptGenRandom(prov, 32, seed)) { + CryptReleaseContext(prov, 0); + return 1; + } + + CryptReleaseContext(prov, 0); +#else + FILE *f = fopen("/dev/urandom", "rb"); + + if (f == NULL) { + return 1; + } + + fread(seed, 1, 32, f); + fclose(f); +#endif + + return 0; +} + +#endif
\ No newline at end of file diff --git a/src/sha512.c b/src/sha512.c new file mode 100644 index 0000000..cb8ae71 --- /dev/null +++ b/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/src/sha512.h b/src/sha512.h new file mode 100644 index 0000000..e56b00e --- /dev/null +++ b/src/sha512.h @@ -0,0 +1,21 @@ +#ifndef SHA512_H +#define SHA512_H + +#include <stddef.h> + +#include "fixedint.h" + +/* state */ +typedef struct sha512_context_ { + uint64_t length, state[8]; + size_t curlen; + unsigned char buf[128]; +} sha512_context; + + +int sha512_init(sha512_context * md); +int sha512_final(sha512_context * md, unsigned char *out); +int sha512_update(sha512_context * md, const unsigned char *in, size_t inlen); +int sha512(const unsigned char *message, size_t message_len, unsigned char *out); + +#endif
\ No newline at end of file diff --git a/src/sign.c b/src/sign.c new file mode 100644 index 0000000..199a839 --- /dev/null +++ b/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/src/verify.c b/src/verify.c new file mode 100644 index 0000000..32f988e --- /dev/null +++ b/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; +} @@ -0,0 +1,150 @@ +#include <stdlib.h> +#include <stdio.h> +#include <string.h> +#include <time.h> + +/* #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) ((end - start) * 1000)) / CLOCKS_PER_SEC / i * 1000); + + printf("testing key exchange performance: "); + start = clock(); + for (i = 0; i < 10000; ++i) { + ed25519_key_exchange(shared_secret, other_public_key, private_key); + } + end = clock(); + + printf("%fus per shared secret\n", ((double) ((end - start) * 1000)) / CLOCKS_PER_SEC / i * 1000); + + return 0; +} |