#include #include #include "../scalarmult_curve25519.h" #include "export.h" #include "private/ed25519_ref10.h" #include "utils.h" #include "x25519_ref10.h" /* * Reject small order points early to mitigate the implications of * unexpected optimizations that would affect the ref10 code. * See https://eprint.iacr.org/2017/806.pdf for reference. */ static int has_small_order(const unsigned char s[32]) { CRYPTO_ALIGN(16) static const unsigned char blocklist[][32] = { /* 0 (order 4) */ { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 }, /* 1 (order 1) */ { 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 }, /* 325606250916557431795983626356110631294008115727848805560023387167927233504 (order 8) */ { 0xe0, 0xeb, 0x7a, 0x7c, 0x3b, 0x41, 0xb8, 0xae, 0x16, 0x56, 0xe3, 0xfa, 0xf1, 0x9f, 0xc4, 0x6a, 0xda, 0x09, 0x8d, 0xeb, 0x9c, 0x32, 0xb1, 0xfd, 0x86, 0x62, 0x05, 0x16, 0x5f, 0x49, 0xb8, 0x00 }, /* 39382357235489614581723060781553021112529911719440698176882885853963445705823 (order 8) */ { 0x5f, 0x9c, 0x95, 0xbc, 0xa3, 0x50, 0x8c, 0x24, 0xb1, 0xd0, 0xb1, 0x55, 0x9c, 0x83, 0xef, 0x5b, 0x04, 0x44, 0x5c, 0xc4, 0x58, 0x1c, 0x8e, 0x86, 0xd8, 0x22, 0x4e, 0xdd, 0xd0, 0x9f, 0x11, 0x57 }, /* p-1 (order 2) */ { 0xec, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f }, /* p (=0, order 4) */ { 0xed, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f }, /* p+1 (=1, order 1) */ { 0xee, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f } }; unsigned char c[7] = { 0 }; unsigned int k; size_t i, j; COMPILER_ASSERT(7 == sizeof blocklist / sizeof blocklist[0]); for (j = 0; j < 31; j++) { for (i = 0; i < sizeof blocklist / sizeof blocklist[0]; i++) { c[i] |= s[j] ^ blocklist[i][j]; } } for (i = 0; i < sizeof blocklist / sizeof blocklist[0]; i++) { c[i] |= (s[j] & 0x7f) ^ blocklist[i][j]; } k = 0; for (i = 0; i < sizeof blocklist / sizeof blocklist[0]; i++) { k |= (c[i] - 1); } return (int) ((k >> 8) & 1); } static int crypto_scalarmult_curve25519_ref10(unsigned char *q, const unsigned char *n, const unsigned char *p) { unsigned char t[32]; unsigned int i; fe25519 x1, x2, x3, z2, z3; fe25519 a, b, aa, bb, e, da, cb; int pos; unsigned int swap; unsigned int bit; if (has_small_order(p)) { return -1; } for (i = 0; i < 32; i++) { t[i] = n[i]; } t[0] &= 248; t[31] &= 127; t[31] |= 64; fe25519_frombytes(x1, p); fe25519_1(x2); fe25519_0(z2); fe25519_copy(x3, x1); fe25519_1(z3); swap = 0; for (pos = 254; pos >= 0; --pos) { bit = t[pos / 8] >> (pos & 7); bit &= 1; swap ^= bit; fe25519_cswap(x2, x3, swap); fe25519_cswap(z2, z3, swap); swap = bit; fe25519_add(a, x2, z2); fe25519_sub(b, x2, z2); fe25519_sq(aa, a); fe25519_sq(bb, b); fe25519_mul(x2, aa, bb); fe25519_sub(e, aa, bb); fe25519_sub(da, x3, z3); fe25519_mul(da, da, a); fe25519_add(cb, x3, z3); fe25519_mul(cb, cb, b); fe25519_add(x3, da, cb); fe25519_sq(x3, x3); fe25519_sub(z3, da, cb); fe25519_sq(z3, z3); fe25519_mul(z3, z3, x1); fe25519_mul32(z2, e, 121666); fe25519_add(z2, z2, bb); fe25519_mul(z2, z2, e); } fe25519_cswap(x2, x3, swap); fe25519_cswap(z2, z3, swap); fe25519_invert(z2, z2); fe25519_mul(x2, x2, z2); fe25519_tobytes(q, x2); sodium_memzero(t, sizeof t); return 0; } static void edwards_to_montgomery(fe25519 montgomeryX, const fe25519 edwardsY, const fe25519 edwardsZ) { fe25519 tempX; fe25519 tempZ; fe25519_add(tempX, edwardsZ, edwardsY); fe25519_sub(tempZ, edwardsZ, edwardsY); fe25519_invert(tempZ, tempZ); fe25519_mul(montgomeryX, tempX, tempZ); } static int crypto_scalarmult_curve25519_ref10_base(unsigned char *q, const unsigned char *n) { unsigned char *t = q; ge25519_p3 A; fe25519 pk; unsigned int i; for (i = 0; i < 32; i++) { t[i] = n[i]; } t[0] &= 248; t[31] &= 127; t[31] |= 64; ge25519_scalarmult_base(&A, t); edwards_to_montgomery(pk, A.Y, A.Z); fe25519_tobytes(q, pk); return 0; } struct crypto_scalarmult_curve25519_implementation crypto_scalarmult_curve25519_ref10_implementation = { SODIUM_C99(.mult =) crypto_scalarmult_curve25519_ref10, SODIUM_C99(.mult_base =) crypto_scalarmult_curve25519_ref10_base };