X-Git-Url: https://git.openssl.org/?p=openssl.git;a=blobdiff_plain;f=crypto%2Fec%2Fcurve25519.c;h=d1c725fa39749144626d3d2095055f6f7b698b85;hp=e535823c0f75ef52412341eb9bf35fd9d5256eff;hb=cfc32a1efb464205885e18e503bcb7051c307008;hpb=aa6bb1352b1026b20a23b49da4efdcf171926eb0 diff --git a/crypto/ec/curve25519.c b/crypto/ec/curve25519.c index e535823c0f..d1c725fa39 100644 --- a/crypto/ec/curve25519.c +++ b/crypto/ec/curve25519.c @@ -1,5 +1,5 @@ /* - * Copyright 2016 The OpenSSL Project Authors. All Rights Reserved. + * Copyright 2016-2017 The OpenSSL Project Authors. All Rights Reserved. * * Licensed under the OpenSSL license (the "License"). You may not use * this file except in compliance with the License. You can obtain a copy @@ -7,14 +7,489 @@ * https://www.openssl.org/source/license.html */ -/* This code is mostly taken from the ref10 version of Ed25519 in SUPERCOP - * 20141124 (http://bench.cr.yp.to/supercop.html). - * - * The field functions are shared by Ed25519 and X25519 where possible. */ - #include #include "ec_lcl.h" +#include + +#if !defined(PEDANTIC) && \ + (defined(__SIZEOF_INT128__) && __SIZEOF_INT128__==16) +/* + * Base 2^51 implementation. + */ +# define BASE_2_51_IMPLEMENTED + +typedef uint64_t fe51[5]; +typedef unsigned __int128 u128; + +static const uint64_t MASK51 = 0x7ffffffffffff; + +static uint64_t load_7(const uint8_t *in) +{ + uint64_t result; + + result = in[0]; + result |= ((uint64_t)in[1]) << 8; + result |= ((uint64_t)in[2]) << 16; + result |= ((uint64_t)in[3]) << 24; + result |= ((uint64_t)in[4]) << 32; + result |= ((uint64_t)in[5]) << 40; + result |= ((uint64_t)in[6]) << 48; + + return result; +} + +static uint64_t load_6(const uint8_t *in) +{ + uint64_t result; + + result = in[0]; + result |= ((uint64_t)in[1]) << 8; + result |= ((uint64_t)in[2]) << 16; + result |= ((uint64_t)in[3]) << 24; + result |= ((uint64_t)in[4]) << 32; + result |= ((uint64_t)in[5]) << 40; + + return result; +} + +static void fe51_frombytes(fe51 h, const uint8_t *s) +{ + uint64_t h0 = load_7(s); /* 56 bits */ + uint64_t h1 = load_6(s + 7) << 5; /* 53 bits */ + uint64_t h2 = load_7(s + 13) << 2; /* 58 bits */ + uint64_t h3 = load_6(s + 20) << 7; /* 55 bits */ + uint64_t h4 = (load_6(s + 26) & 0x7fffffffffff) << 4; /* 51 bits */ + + h1 |= h0 >> 51; h0 &= MASK51; + h2 |= h1 >> 51; h1 &= MASK51; + h3 |= h2 >> 51; h2 &= MASK51; + h4 |= h3 >> 51; h3 &= MASK51; + + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; +} + +static void fe51_tobytes(uint8_t *s, const fe51 h) +{ + uint64_t h0 = h[0]; + uint64_t h1 = h[1]; + uint64_t h2 = h[2]; + uint64_t h3 = h[3]; + uint64_t h4 = h[4]; + uint64_t q; + + /* compare to modulus */ + q = (h0 + 19) >> 51; + q = (h1 + q) >> 51; + q = (h2 + q) >> 51; + q = (h3 + q) >> 51; + q = (h4 + q) >> 51; + + /* full reduce */ + h0 += 19 * q; + h1 += h0 >> 51; h0 &= MASK51; + h2 += h1 >> 51; h1 &= MASK51; + h3 += h2 >> 51; h2 &= MASK51; + h4 += h3 >> 51; h3 &= MASK51; + h4 &= MASK51; + + /* smash */ + s[0] = h0 >> 0; + s[1] = h0 >> 8; + s[2] = h0 >> 16; + s[3] = h0 >> 24; + s[4] = h0 >> 32; + s[5] = h0 >> 40; + s[6] = (h0 >> 48) | ((uint32_t)h1 << 3); + s[7] = h1 >> 5; + s[8] = h1 >> 13; + s[9] = h1 >> 21; + s[10] = h1 >> 29; + s[11] = h1 >> 37; + s[12] = (h1 >> 45) | ((uint32_t)h2 << 6); + s[13] = h2 >> 2; + s[14] = h2 >> 10; + s[15] = h2 >> 18; + s[16] = h2 >> 26; + s[17] = h2 >> 34; + s[18] = h2 >> 42; + s[19] = (h2 >> 50) | ((uint32_t)h3 << 1); + s[20] = h3 >> 7; + s[21] = h3 >> 15; + s[22] = h3 >> 23; + s[23] = h3 >> 31; + s[24] = h3 >> 39; + s[25] = (h3 >> 47) | ((uint32_t)h4 << 4); + s[26] = h4 >> 4; + s[27] = h4 >> 12; + s[28] = h4 >> 20; + s[29] = h4 >> 28; + s[30] = h4 >> 36; + s[31] = h4 >> 44; +} + +static void fe51_mul(fe51 h, const fe51 f, const fe51 g) +{ + u128 h0, h1, h2, h3, h4; + uint64_t f_i, g0, g1, g2, g3, g4; + + f_i = f[0]; + h0 = (u128)f_i * (g0 = g[0]); + h1 = (u128)f_i * (g1 = g[1]); + h2 = (u128)f_i * (g2 = g[2]); + h3 = (u128)f_i * (g3 = g[3]); + h4 = (u128)f_i * (g4 = g[4]); + + f_i = f[1]; + h0 += (u128)f_i * (g4 *= 19); + h1 += (u128)f_i * g0; + h2 += (u128)f_i * g1; + h3 += (u128)f_i * g2; + h4 += (u128)f_i * g3; + + f_i = f[2]; + h0 += (u128)f_i * (g3 *= 19); + h1 += (u128)f_i * g4; + h2 += (u128)f_i * g0; + h3 += (u128)f_i * g1; + h4 += (u128)f_i * g2; + + f_i = f[3]; + h0 += (u128)f_i * (g2 *= 19); + h1 += (u128)f_i * g3; + h2 += (u128)f_i * g4; + h3 += (u128)f_i * g0; + h4 += (u128)f_i * g1; + + f_i = f[4]; + h0 += (u128)f_i * (g1 *= 19); + h1 += (u128)f_i * g2; + h2 += (u128)f_i * g3; + h3 += (u128)f_i * g4; + h4 += (u128)f_i * g0; + + /* partial [lazy] reduction */ + h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51; + h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51; + + h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51; + g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51; + + g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51; + g3 += g2 >> 51; g2 &= MASK51; + g1 += g0 >> 51; g0 &= MASK51; + + h[0] = g0; + h[1] = g1; + h[2] = g2; + h[3] = g3; + h[4] = g4; +} + +static void fe51_sq(fe51 h, const fe51 f) +{ +# if defined(OPENSSL_SMALL_FOOTPRINT) + fe51_mul(h, f, f); +# else + /* dedicated squaring gives 16-25% overall improvement */ + uint64_t g0 = f[0]; + uint64_t g1 = f[1]; + uint64_t g2 = f[2]; + uint64_t g3 = f[3]; + uint64_t g4 = f[4]; + u128 h0, h1, h2, h3, h4; + + h0 = (u128)g0 * g0; g0 *= 2; + h1 = (u128)g0 * g1; + h2 = (u128)g0 * g2; + h3 = (u128)g0 * g3; + h4 = (u128)g0 * g4; + + g0 = g4; /* borrow g0 */ + h3 += (u128)g0 * (g4 *= 19); + + h2 += (u128)g1 * g1; g1 *= 2; + h3 += (u128)g1 * g2; + h4 += (u128)g1 * g3; + h0 += (u128)g1 * g4; + + g0 = g3; /* borrow g0 */ + h1 += (u128)g0 * (g3 *= 19); + h2 += (u128)(g0 * 2) * g4; + + h4 += (u128)g2 * g2; g2 *= 2; + h0 += (u128)g2 * g3; + h1 += (u128)g2 * g4; + + /* partial [lazy] reduction */ + h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51; + h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51; + + h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51; + g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51; + + g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51; + g3 += g2 >> 51; g2 &= MASK51; + g1 += g0 >> 51; g0 &= MASK51; + + h[0] = g0; + h[1] = g1; + h[2] = g2; + h[3] = g3; + h[4] = g4; +# endif +} + +static void fe51_add(fe51 h, const fe51 f, const fe51 g) +{ + h[0] = f[0] + g[0]; + h[1] = f[1] + g[1]; + h[2] = f[2] + g[2]; + h[3] = f[3] + g[3]; + h[4] = f[4] + g[4]; +} + +static void fe51_sub(fe51 h, const fe51 f, const fe51 g) +{ + /* + * Add 2*modulus to ensure that result remains positive + * even if subtrahend is partially reduced. + */ + h[0] = (f[0] + 0xfffffffffffda) - g[0]; + h[1] = (f[1] + 0xffffffffffffe) - g[1]; + h[2] = (f[2] + 0xffffffffffffe) - g[2]; + h[3] = (f[3] + 0xffffffffffffe) - g[3]; + h[4] = (f[4] + 0xffffffffffffe) - g[4]; +} + +static void fe51_0(fe51 h) +{ + h[0] = 0; + h[1] = 0; + h[2] = 0; + h[3] = 0; + h[4] = 0; +} + +static void fe51_1(fe51 h) +{ + h[0] = 1; + h[1] = 0; + h[2] = 0; + h[3] = 0; + h[4] = 0; +} + +static void fe51_copy(fe51 h, const fe51 f) +{ + h[0] = f[0]; + h[1] = f[1]; + h[2] = f[2]; + h[3] = f[3]; + h[4] = f[4]; +} + +static void fe51_cswap(fe51 f, fe51 g, unsigned int b) +{ + int i; + uint64_t mask = 0 - (uint64_t)b; + + for (i = 0; i < 5; i++) { + int64_t x = f[i] ^ g[i]; + x &= mask; + f[i] ^= x; + g[i] ^= x; + } +} + +static void fe51_invert(fe51 out, const fe51 z) +{ + fe51 t0; + fe51 t1; + fe51 t2; + fe51 t3; + int i; + + /* + * Compute z ** -1 = z ** (2 ** 255 - 19 - 2) with the exponent as + * 2 ** 255 - 21 = (2 ** 5) * (2 ** 250 - 1) + 11. + */ + + /* t0 = z ** 2 */ + fe51_sq(t0, z); + + /* t1 = t0 ** (2 ** 2) = z ** 8 */ + fe51_sq(t1, t0); + fe51_sq(t1, t1); + + /* t1 = z * t1 = z ** 9 */ + fe51_mul(t1, z, t1); + /* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */ + fe51_mul(t0, t0, t1); + + /* t2 = t0 ** 2 = z ** 22 */ + fe51_sq(t2, t0); + + /* t1 = t1 * t2 = z ** (2 ** 5 - 1) */ + fe51_mul(t1, t1, t2); + + /* t2 = t1 ** (2 ** 5) = z ** ((2 ** 5) * (2 ** 5 - 1)) */ + fe51_sq(t2, t1); + for (i = 1; i < 5; ++i) + fe51_sq(t2, t2); + + /* t1 = t1 * t2 = z ** ((2 ** 5 + 1) * (2 ** 5 - 1)) = z ** (2 ** 10 - 1) */ + fe51_mul(t1, t2, t1); + + /* Continuing similarly... */ + + /* t2 = z ** (2 ** 20 - 1) */ + fe51_sq(t2, t1); + for (i = 1; i < 10; ++i) + fe51_sq(t2, t2); + + fe51_mul(t2, t2, t1); + + /* t2 = z ** (2 ** 40 - 1) */ + fe51_sq(t3, t2); + for (i = 1; i < 20; ++i) + fe51_sq(t3, t3); + + fe51_mul(t2, t3, t2); + + /* t2 = z ** (2 ** 10) * (2 ** 40 - 1) */ + for (i = 0; i < 10; ++i) + fe51_sq(t2, t2); + + /* t1 = z ** (2 ** 50 - 1) */ + fe51_mul(t1, t2, t1); + + /* t2 = z ** (2 ** 100 - 1) */ + fe51_sq(t2, t1); + for (i = 1; i < 50; ++i) + fe51_sq(t2, t2); + + fe51_mul(t2, t2, t1); + + /* t2 = z ** (2 ** 200 - 1) */ + fe51_sq(t3, t2); + for (i = 1; i < 100; ++i) + fe51_sq(t3, t3); + + fe51_mul(t2, t3, t2); + + /* t2 = z ** ((2 ** 50) * (2 ** 200 - 1) */ + for (i = 0; i < 50; ++i) + fe51_sq(t2, t2); + + /* t1 = z ** (2 ** 250 - 1) */ + fe51_mul(t1, t2, t1); + + /* t1 = z ** ((2 ** 5) * (2 ** 250 - 1)) */ + for (i = 0; i < 5; ++i) + fe51_sq(t1, t1); + + /* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */ + fe51_mul(out, t1, t0); +} + +static void fe51_mul121666(fe51 h, fe51 f) +{ + u128 h0 = f[0] * (u128)121666; + u128 h1 = f[1] * (u128)121666; + u128 h2 = f[2] * (u128)121666; + u128 h3 = f[3] * (u128)121666; + u128 h4 = f[4] * (u128)121666; + uint64_t g0, g1, g2, g3, g4; + + h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51; + h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51; + + h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51; + g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51; + + g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51; + g3 += g2 >> 51; g2 &= MASK51; + g1 += g0 >> 51; g0 &= MASK51; + + h[0] = g0; + h[1] = g1; + h[2] = g2; + h[3] = g3; + h[4] = g4; +} + +/* + * Duplicate of original x25519_scalar_mult_generic, but using + * fe51_* subroutines. + */ +static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32], + const uint8_t point[32]) +{ + fe51 x1, x2, z2, x3, z3, tmp0, tmp1; + uint8_t e[32]; + unsigned swap = 0; + int pos; + + memcpy(e, scalar, 32); + e[0] &= 0xf8; + e[31] &= 0x7f; + e[31] |= 0x40; + fe51_frombytes(x1, point); + fe51_1(x2); + fe51_0(z2); + fe51_copy(x3, x1); + fe51_1(z3); + for (pos = 254; pos >= 0; --pos) { + unsigned int b = 1 & (e[pos / 8] >> (pos & 7)); + + swap ^= b; + fe51_cswap(x2, x3, swap); + fe51_cswap(z2, z3, swap); + swap = b; + fe51_sub(tmp0, x3, z3); + fe51_sub(tmp1, x2, z2); + fe51_add(x2, x2, z2); + fe51_add(z2, x3, z3); + fe51_mul(z3, tmp0, x2); + fe51_mul(z2, z2, tmp1); + fe51_sq(tmp0, tmp1); + fe51_sq(tmp1, x2); + fe51_add(x3, z3, z2); + fe51_sub(z2, z3, z2); + fe51_mul(x2, tmp1, tmp0); + fe51_sub(tmp1, tmp1, tmp0); + fe51_sq(z2, z2); + fe51_mul121666(z3, tmp1); + fe51_sq(x3, x3); + fe51_add(tmp0, tmp0, z3); + fe51_mul(z3, x1, z2); + fe51_mul(z2, tmp1, tmp0); + } + fe51_cswap(x2, x3, swap); + fe51_cswap(z2, z3, swap); + + fe51_invert(z2, z2); + fe51_mul(x2, x2, z2); + fe51_tobytes(out, x2); + + OPENSSL_cleanse(e, sizeof(e)); +} +#endif + +/* + * Reference base 2^25.5 implementation. + */ +/* + * This code is mostly taken from the ref10 version of Ed25519 in SUPERCOP + * 20141124 (http://bench.cr.yp.to/supercop.html). + * + * The field functions are shared by Ed25519 and X25519 where possible. + */ /* 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 @@ -79,16 +554,16 @@ static void fe_frombytes(fe h, const uint8_t *s) { carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; - 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[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; } /* Preconditions: @@ -470,16 +945,16 @@ static void fe_mul(fe h, const fe f, const fe g) { /* |h0| <= 2^25; from now on fits into int32 unchanged */ /* |h1| <= 1.01*2^24 */ - 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[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 * f @@ -611,16 +1086,16 @@ static void fe_sq(fe h, const fe f) { carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; - 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[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; } static void fe_invert(fe out, const fe z) { @@ -746,6 +1221,30 @@ static void fe_cmov(fe f, const fe g, unsigned b) { } } +/* return 0 if f == 0 + * return 1 if f != 0 + * + * Preconditions: + * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ +static int fe_isnonzero(const fe f) { + uint8_t s[32]; + static const uint8_t zero[32] = {0}; + fe_tobytes(s, f); + + return CRYPTO_memcmp(s, zero, sizeof(zero)) != 0; +} + +/* 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. */ +static int fe_isnegative(const fe f) { + uint8_t s[32]; + fe_tobytes(s, f); + return s[0] & 1; +} + /* h = 2 * f * f * Can overlap h with f. * @@ -886,16 +1385,73 @@ static void fe_sq2(fe h, const fe f) { carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; - 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[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; +} + +static void fe_pow22523(fe out, const fe z) { + fe t0; + fe t1; + fe t2; + int i; + + fe_sq(t0, z); + 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); + 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); } /* ge means group element. @@ -943,6 +1499,85 @@ typedef struct { fe T2d; } ge_cached; +static void ge_tobytes(uint8_t *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; +} + +static void ge_p3_tobytes(uint8_t *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 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}; + +static int ge_frombytes_vartime(ge_p3 *h, const uint8_t *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; +} + +static void ge_p2_0(ge_p2 *h) { + fe_0(h->X); + fe_1(h->Y); + fe_1(h->Z); +} + static void ge_p3_0(ge_p3 *h) { fe_0(h->X); fe_1(h->Y); @@ -963,6 +1598,17 @@ static void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p) { fe_copy(r->Z, p->Z); } +static const fe d2 = {-21827239, -5839606, -30745221, 13898782, 229458, + 15978800, -12551817, -6495438, 29715968, 9444199}; + +/* r = p */ +static 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 */ static void ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p) { fe_mul(r->X, p->X, p->T); @@ -1016,6 +1662,56 @@ static void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) { fe_sub(r->T, t0, r->T); } +/* r = p - q */ +static 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 + q */ +static 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); +} + +/* r = p - q */ +static 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); +} + static uint8_t equal(signed char b, signed char c) { uint8_t ub = b; uint8_t uc = c; @@ -3226,8 +3922,11 @@ static void ge_scalarmult_base(ge_p3 *h, const uint8_t *a) { ge_madd(&r, h, &t); ge_p1p1_to_p3(h, &r); } + + OPENSSL_cleanse(e, sizeof(e)); } +#if !defined(BASE_2_51_IMPLEMENTED) /* Replace (f,g) with (g,f) if b == 1; * replace (f,g) with (f,g) if b == 0. * @@ -3295,16 +3994,16 @@ static void fe_mul121666(fe h, fe f) { carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; - 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[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; } static void x25519_scalar_mult_generic(uint8_t out[32], @@ -3356,12 +4055,1115 @@ static void x25519_scalar_mult_generic(uint8_t out[32], fe_invert(z2, z2); fe_mul(x2, x2, z2); fe_tobytes(out, x2); + + OPENSSL_cleanse(e, sizeof(e)); } static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32], const uint8_t point[32]) { x25519_scalar_mult_generic(out, scalar, point); } +#endif + +static void slide(signed char *r, const uint8_t *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; + } + } + } + } + } +} + +static const ge_precomp Bi[8] = { + { + {25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, + -11754271, -6079156, 2047605}, + {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, + 5043384, 19500929, -15469378}, + {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, + 11864899, -24514362, -4438546}, + }, + { + {15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, + -14772189, 28944400, -1550024}, + {16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, + -11775962, 7689662, 11199574}, + {30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, + 10017326, -17749093, -9920357}, + }, + { + {10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, + 14515107, -15438304, 10819380}, + {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, + 12483688, -12668491, 5581306}, + {19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, + 13850243, -23678021, -15815942}, + }, + { + {5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, + 5230134, -23952439, -15175766}, + {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, + 16520125, 30598449, 7715701}, + {28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, + 1370708, 29794553, -1409300}, + }, + { + {-22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211, + -1361450, -13062696, 13821877}, + {-6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028, + -7212327, 18853322, -14220951}, + {4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358, + -10431137, 2207753, -3209784}, + }, + { + {-25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364, + -663000, -31111463, -16132436}, + {25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789, + 15725684, 171356, 6466918}, + {23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339, + -14088058, -30714912, 16193877}, + }, + { + {-33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398, + 4729455, -18074513, 9256800}, + {-25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405, + 9761698, -19827198, 630305}, + {-13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551, + -15960994, -2449256, -14291300}, + }, + { + {-3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575, + 15033784, 25105118, -7894876}, + {-24326370, 15950226, -31801215, -14592823, -11662737, -5090925, + 1573892, -2625887, 2198790, -15804619}, + {-3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022, + -16236442, -32461234, -12290683}, + }, +}; + +/* 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. */ +static void ge_double_scalarmult_vartime(ge_p2 *r, const uint8_t *a, + const ge_p3 *A, const uint8_t *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); + } +} + +/* The set of scalars is \Z/l + * where l = 2^252 + 27742317777372353535851937790883648493. */ + +/* 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. */ +static void x25519_sc_reduce(uint8_t *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 * (1 << 21); + carry8 = (s8 + (1 << 20)) >> 21; + s9 += carry8; + s8 -= carry8 * (1 << 21); + carry10 = (s10 + (1 << 20)) >> 21; + s11 += carry10; + s10 -= carry10 * (1 << 21); + carry12 = (s12 + (1 << 20)) >> 21; + s13 += carry12; + s12 -= carry12 * (1 << 21); + carry14 = (s14 + (1 << 20)) >> 21; + s15 += carry14; + s14 -= carry14 * (1 << 21); + carry16 = (s16 + (1 << 20)) >> 21; + s17 += carry16; + s16 -= carry16 * (1 << 21); + + carry7 = (s7 + (1 << 20)) >> 21; + s8 += carry7; + s7 -= carry7 * (1 << 21); + carry9 = (s9 + (1 << 20)) >> 21; + s10 += carry9; + s9 -= carry9 * (1 << 21); + carry11 = (s11 + (1 << 20)) >> 21; + s12 += carry11; + s11 -= carry11 * (1 << 21); + carry13 = (s13 + (1 << 20)) >> 21; + s14 += carry13; + s13 -= carry13 * (1 << 21); + carry15 = (s15 + (1 << 20)) >> 21; + s16 += carry15; + s15 -= carry15 * (1 << 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 * (1 << 21); + carry2 = (s2 + (1 << 20)) >> 21; + s3 += carry2; + s2 -= carry2 * (1 << 21); + carry4 = (s4 + (1 << 20)) >> 21; + s5 += carry4; + s4 -= carry4 * (1 << 21); + carry6 = (s6 + (1 << 20)) >> 21; + s7 += carry6; + s6 -= carry6 * (1 << 21); + carry8 = (s8 + (1 << 20)) >> 21; + s9 += carry8; + s8 -= carry8 * (1 << 21); + carry10 = (s10 + (1 << 20)) >> 21; + s11 += carry10; + s10 -= carry10 * (1 << 21); + + carry1 = (s1 + (1 << 20)) >> 21; + s2 += carry1; + s1 -= carry1 * (1 << 21); + carry3 = (s3 + (1 << 20)) >> 21; + s4 += carry3; + s3 -= carry3 * (1 << 21); + carry5 = (s5 + (1 << 20)) >> 21; + s6 += carry5; + s5 -= carry5 * (1 << 21); + carry7 = (s7 + (1 << 20)) >> 21; + s8 += carry7; + s7 -= carry7 * (1 << 21); + carry9 = (s9 + (1 << 20)) >> 21; + s10 += carry9; + s9 -= carry9 * (1 << 21); + carry11 = (s11 + (1 << 20)) >> 21; + s12 += carry11; + s11 -= carry11 * (1 << 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 * (1 << 21); + carry1 = s1 >> 21; + s2 += carry1; + s1 -= carry1 * (1 << 21); + carry2 = s2 >> 21; + s3 += carry2; + s2 -= carry2 * (1 << 21); + carry3 = s3 >> 21; + s4 += carry3; + s3 -= carry3 * (1 << 21); + carry4 = s4 >> 21; + s5 += carry4; + s4 -= carry4 * (1 << 21); + carry5 = s5 >> 21; + s6 += carry5; + s5 -= carry5 * (1 << 21); + carry6 = s6 >> 21; + s7 += carry6; + s6 -= carry6 * (1 << 21); + carry7 = s7 >> 21; + s8 += carry7; + s7 -= carry7 * (1 << 21); + carry8 = s8 >> 21; + s9 += carry8; + s8 -= carry8 * (1 << 21); + carry9 = s9 >> 21; + s10 += carry9; + s9 -= carry9 * (1 << 21); + carry10 = s10 >> 21; + s11 += carry10; + s10 -= carry10 * (1 << 21); + carry11 = s11 >> 21; + s12 += carry11; + s11 -= carry11 * (1 << 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 * (1 << 21); + carry1 = s1 >> 21; + s2 += carry1; + s1 -= carry1 * (1 << 21); + carry2 = s2 >> 21; + s3 += carry2; + s2 -= carry2 * (1 << 21); + carry3 = s3 >> 21; + s4 += carry3; + s3 -= carry3 * (1 << 21); + carry4 = s4 >> 21; + s5 += carry4; + s4 -= carry4 * (1 << 21); + carry5 = s5 >> 21; + s6 += carry5; + s5 -= carry5 * (1 << 21); + carry6 = s6 >> 21; + s7 += carry6; + s6 -= carry6 * (1 << 21); + carry7 = s7 >> 21; + s8 += carry7; + s7 -= carry7 * (1 << 21); + carry8 = s8 >> 21; + s9 += carry8; + s8 -= carry8 * (1 << 21); + carry9 = s9 >> 21; + s10 += carry9; + s9 -= carry9 * (1 << 21); + carry10 = s10 >> 21; + s11 += carry10; + s10 -= carry10 * (1 << 21); + + s[0] = (uint8_t)(s0 >> 0); + s[1] = (uint8_t)(s0 >> 8); + s[2] = (uint8_t)((s0 >> 16) | (s1 << 5)); + s[3] = (uint8_t)(s1 >> 3); + s[4] = (uint8_t)(s1 >> 11); + s[5] = (uint8_t)((s1 >> 19) | (s2 << 2)); + s[6] = (uint8_t)(s2 >> 6); + s[7] = (uint8_t)((s2 >> 14) | (s3 << 7)); + s[8] = (uint8_t)(s3 >> 1); + s[9] = (uint8_t)(s3 >> 9); + s[10] = (uint8_t)((s3 >> 17) | (s4 << 4)); + s[11] = (uint8_t)(s4 >> 4); + s[12] = (uint8_t)(s4 >> 12); + s[13] = (uint8_t)((s4 >> 20) | (s5 << 1)); + s[14] = (uint8_t)(s5 >> 7); + s[15] = (uint8_t)((s5 >> 15) | (s6 << 6)); + s[16] = (uint8_t)(s6 >> 2); + s[17] = (uint8_t)(s6 >> 10); + s[18] = (uint8_t)((s6 >> 18) | (s7 << 3)); + s[19] = (uint8_t)(s7 >> 5); + s[20] = (uint8_t)(s7 >> 13); + s[21] = (uint8_t)(s8 >> 0); + s[22] = (uint8_t)(s8 >> 8); + s[23] = (uint8_t)((s8 >> 16) | (s9 << 5)); + s[24] = (uint8_t)(s9 >> 3); + s[25] = (uint8_t)(s9 >> 11); + s[26] = (uint8_t)((s9 >> 19) | (s10 << 2)); + s[27] = (uint8_t)(s10 >> 6); + s[28] = (uint8_t)((s10 >> 14) | (s11 << 7)); + s[29] = (uint8_t)(s11 >> 1); + s[30] = (uint8_t)(s11 >> 9); + s[31] = (uint8_t)(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. */ +static void sc_muladd(uint8_t *s, const uint8_t *a, const uint8_t *b, + const uint8_t *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 * (1 << 21); + carry2 = (s2 + (1 << 20)) >> 21; + s3 += carry2; + s2 -= carry2 * (1 << 21); + carry4 = (s4 + (1 << 20)) >> 21; + s5 += carry4; + s4 -= carry4 * (1 << 21); + carry6 = (s6 + (1 << 20)) >> 21; + s7 += carry6; + s6 -= carry6 * (1 << 21); + carry8 = (s8 + (1 << 20)) >> 21; + s9 += carry8; + s8 -= carry8 * (1 << 21); + carry10 = (s10 + (1 << 20)) >> 21; + s11 += carry10; + s10 -= carry10 * (1 << 21); + carry12 = (s12 + (1 << 20)) >> 21; + s13 += carry12; + s12 -= carry12 * (1 << 21); + carry14 = (s14 + (1 << 20)) >> 21; + s15 += carry14; + s14 -= carry14 * (1 << 21); + carry16 = (s16 + (1 << 20)) >> 21; + s17 += carry16; + s16 -= carry16 * (1 << 21); + carry18 = (s18 + (1 << 20)) >> 21; + s19 += carry18; + s18 -= carry18 * (1 << 21); + carry20 = (s20 + (1 << 20)) >> 21; + s21 += carry20; + s20 -= carry20 * (1 << 21); + carry22 = (s22 + (1 << 20)) >> 21; + s23 += carry22; + s22 -= carry22 * (1 << 21); + + carry1 = (s1 + (1 << 20)) >> 21; + s2 += carry1; + s1 -= carry1 * (1 << 21); + carry3 = (s3 + (1 << 20)) >> 21; + s4 += carry3; + s3 -= carry3 * (1 << 21); + carry5 = (s5 + (1 << 20)) >> 21; + s6 += carry5; + s5 -= carry5 * (1 << 21); + carry7 = (s7 + (1 << 20)) >> 21; + s8 += carry7; + s7 -= carry7 * (1 << 21); + carry9 = (s9 + (1 << 20)) >> 21; + s10 += carry9; + s9 -= carry9 * (1 << 21); + carry11 = (s11 + (1 << 20)) >> 21; + s12 += carry11; + s11 -= carry11 * (1 << 21); + carry13 = (s13 + (1 << 20)) >> 21; + s14 += carry13; + s13 -= carry13 * (1 << 21); + carry15 = (s15 + (1 << 20)) >> 21; + s16 += carry15; + s15 -= carry15 * (1 << 21); + carry17 = (s17 + (1 << 20)) >> 21; + s18 += carry17; + s17 -= carry17 * (1 << 21); + carry19 = (s19 + (1 << 20)) >> 21; + s20 += carry19; + s19 -= carry19 * (1 << 21); + carry21 = (s21 + (1 << 20)) >> 21; + s22 += carry21; + s21 -= carry21 * (1 << 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 * (1 << 21); + carry8 = (s8 + (1 << 20)) >> 21; + s9 += carry8; + s8 -= carry8 * (1 << 21); + carry10 = (s10 + (1 << 20)) >> 21; + s11 += carry10; + s10 -= carry10 * (1 << 21); + carry12 = (s12 + (1 << 20)) >> 21; + s13 += carry12; + s12 -= carry12 * (1 << 21); + carry14 = (s14 + (1 << 20)) >> 21; + s15 += carry14; + s14 -= carry14 * (1 << 21); + carry16 = (s16 + (1 << 20)) >> 21; + s17 += carry16; + s16 -= carry16 * (1 << 21); + + carry7 = (s7 + (1 << 20)) >> 21; + s8 += carry7; + s7 -= carry7 * (1 << 21); + carry9 = (s9 + (1 << 20)) >> 21; + s10 += carry9; + s9 -= carry9 * (1 << 21); + carry11 = (s11 + (1 << 20)) >> 21; + s12 += carry11; + s11 -= carry11 * (1 << 21); + carry13 = (s13 + (1 << 20)) >> 21; + s14 += carry13; + s13 -= carry13 * (1 << 21); + carry15 = (s15 + (1 << 20)) >> 21; + s16 += carry15; + s15 -= carry15 * (1 << 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 * (1 << 21); + carry2 = (s2 + (1 << 20)) >> 21; + s3 += carry2; + s2 -= carry2 * (1 << 21); + carry4 = (s4 + (1 << 20)) >> 21; + s5 += carry4; + s4 -= carry4 * (1 << 21); + carry6 = (s6 + (1 << 20)) >> 21; + s7 += carry6; + s6 -= carry6 * (1 << 21); + carry8 = (s8 + (1 << 20)) >> 21; + s9 += carry8; + s8 -= carry8 * (1 << 21); + carry10 = (s10 + (1 << 20)) >> 21; + s11 += carry10; + s10 -= carry10 * (1 << 21); + + carry1 = (s1 + (1 << 20)) >> 21; + s2 += carry1; + s1 -= carry1 * (1 << 21); + carry3 = (s3 + (1 << 20)) >> 21; + s4 += carry3; + s3 -= carry3 * (1 << 21); + carry5 = (s5 + (1 << 20)) >> 21; + s6 += carry5; + s5 -= carry5 * (1 << 21); + carry7 = (s7 + (1 << 20)) >> 21; + s8 += carry7; + s7 -= carry7 * (1 << 21); + carry9 = (s9 + (1 << 20)) >> 21; + s10 += carry9; + s9 -= carry9 * (1 << 21); + carry11 = (s11 + (1 << 20)) >> 21; + s12 += carry11; + s11 -= carry11 * (1 << 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 * (1 << 21); + carry1 = s1 >> 21; + s2 += carry1; + s1 -= carry1 * (1 << 21); + carry2 = s2 >> 21; + s3 += carry2; + s2 -= carry2 * (1 << 21); + carry3 = s3 >> 21; + s4 += carry3; + s3 -= carry3 * (1 << 21); + carry4 = s4 >> 21; + s5 += carry4; + s4 -= carry4 * (1 << 21); + carry5 = s5 >> 21; + s6 += carry5; + s5 -= carry5 * (1 << 21); + carry6 = s6 >> 21; + s7 += carry6; + s6 -= carry6 * (1 << 21); + carry7 = s7 >> 21; + s8 += carry7; + s7 -= carry7 * (1 << 21); + carry8 = s8 >> 21; + s9 += carry8; + s8 -= carry8 * (1 << 21); + carry9 = s9 >> 21; + s10 += carry9; + s9 -= carry9 * (1 << 21); + carry10 = s10 >> 21; + s11 += carry10; + s10 -= carry10 * (1 << 21); + carry11 = s11 >> 21; + s12 += carry11; + s11 -= carry11 * (1 << 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 * (1 << 21); + carry1 = s1 >> 21; + s2 += carry1; + s1 -= carry1 * (1 << 21); + carry2 = s2 >> 21; + s3 += carry2; + s2 -= carry2 * (1 << 21); + carry3 = s3 >> 21; + s4 += carry3; + s3 -= carry3 * (1 << 21); + carry4 = s4 >> 21; + s5 += carry4; + s4 -= carry4 * (1 << 21); + carry5 = s5 >> 21; + s6 += carry5; + s5 -= carry5 * (1 << 21); + carry6 = s6 >> 21; + s7 += carry6; + s6 -= carry6 * (1 << 21); + carry7 = s7 >> 21; + s8 += carry7; + s7 -= carry7 * (1 << 21); + carry8 = s8 >> 21; + s9 += carry8; + s8 -= carry8 * (1 << 21); + carry9 = s9 >> 21; + s10 += carry9; + s9 -= carry9 * (1 << 21); + carry10 = s10 >> 21; + s11 += carry10; + s10 -= carry10 * (1 << 21); + + s[0] = (uint8_t)(s0 >> 0); + s[1] = (uint8_t)(s0 >> 8); + s[2] = (uint8_t)((s0 >> 16) | (s1 << 5)); + s[3] = (uint8_t)(s1 >> 3); + s[4] = (uint8_t)(s1 >> 11); + s[5] = (uint8_t)((s1 >> 19) | (s2 << 2)); + s[6] = (uint8_t)(s2 >> 6); + s[7] = (uint8_t)((s2 >> 14) | (s3 << 7)); + s[8] = (uint8_t)(s3 >> 1); + s[9] = (uint8_t)(s3 >> 9); + s[10] = (uint8_t)((s3 >> 17) | (s4 << 4)); + s[11] = (uint8_t)(s4 >> 4); + s[12] = (uint8_t)(s4 >> 12); + s[13] = (uint8_t)((s4 >> 20) | (s5 << 1)); + s[14] = (uint8_t)(s5 >> 7); + s[15] = (uint8_t)((s5 >> 15) | (s6 << 6)); + s[16] = (uint8_t)(s6 >> 2); + s[17] = (uint8_t)(s6 >> 10); + s[18] = (uint8_t)((s6 >> 18) | (s7 << 3)); + s[19] = (uint8_t)(s7 >> 5); + s[20] = (uint8_t)(s7 >> 13); + s[21] = (uint8_t)(s8 >> 0); + s[22] = (uint8_t)(s8 >> 8); + s[23] = (uint8_t)((s8 >> 16) | (s9 << 5)); + s[24] = (uint8_t)(s9 >> 3); + s[25] = (uint8_t)(s9 >> 11); + s[26] = (uint8_t)((s9 >> 19) | (s10 << 2)); + s[27] = (uint8_t)(s10 >> 6); + s[28] = (uint8_t)((s10 >> 14) | (s11 << 7)); + s[29] = (uint8_t)(s11 >> 1); + s[30] = (uint8_t)(s11 >> 9); + s[31] = (uint8_t)(s11 >> 17); +} + +int ED25519_sign(uint8_t *out_sig, const uint8_t *message, size_t message_len, + const uint8_t public_key[32], const uint8_t private_key[32]) { + uint8_t az[SHA512_DIGEST_LENGTH]; + uint8_t nonce[SHA512_DIGEST_LENGTH]; + ge_p3 R; + uint8_t hram[SHA512_DIGEST_LENGTH]; + SHA512_CTX hash_ctx; + + SHA512_Init(&hash_ctx); + SHA512_Update(&hash_ctx, private_key, 32); + SHA512_Final(az, &hash_ctx); + + az[0] &= 248; + az[31] &= 63; + az[31] |= 64; + + SHA512_Init(&hash_ctx); + SHA512_Update(&hash_ctx, az + 32, 32); + SHA512_Update(&hash_ctx, message, message_len); + SHA512_Final(nonce, &hash_ctx); + + x25519_sc_reduce(nonce); + ge_scalarmult_base(&R, nonce); + ge_p3_tobytes(out_sig, &R); + + SHA512_Init(&hash_ctx); + SHA512_Update(&hash_ctx, out_sig, 32); + SHA512_Update(&hash_ctx, public_key, 32); + SHA512_Update(&hash_ctx, message, message_len); + SHA512_Final(hram, &hash_ctx); + + x25519_sc_reduce(hram); + sc_muladd(out_sig + 32, hram, az, nonce); + + OPENSSL_cleanse(&hash_ctx, sizeof(hash_ctx)); + OPENSSL_cleanse(nonce, sizeof(nonce)); + OPENSSL_cleanse(az, sizeof(az)); + + return 1; +} + +int ED25519_verify(const uint8_t *message, size_t message_len, + const uint8_t signature[64], const uint8_t public_key[32]) { + ge_p3 A; + uint8_t rcopy[32]; + uint8_t scopy[32]; + SHA512_CTX hash_ctx; + ge_p2 R; + uint8_t rcheck[32]; + uint8_t h[SHA512_DIGEST_LENGTH]; + + if ((signature[63] & 224) != 0 || + ge_frombytes_vartime(&A, public_key) != 0) { + return 0; + } + + fe_neg(A.X, A.X); + fe_neg(A.T, A.T); + + memcpy(rcopy, signature, 32); + memcpy(scopy, signature + 32, 32); + + SHA512_Init(&hash_ctx); + SHA512_Update(&hash_ctx, signature, 32); + SHA512_Update(&hash_ctx, public_key, 32); + SHA512_Update(&hash_ctx, message, message_len); + SHA512_Final(h, &hash_ctx); + + x25519_sc_reduce(h); + + ge_double_scalarmult_vartime(&R, h, &A, scopy); + + ge_tobytes(rcheck, &R); + + return CRYPTO_memcmp(rcheck, rcopy, sizeof(rcheck)) == 0; +} + +void ED25519_public_from_private(uint8_t out_public_key[32], + const uint8_t private_key[32]) { + uint8_t az[SHA512_DIGEST_LENGTH]; + ge_p3 A; + + SHA512(private_key, 32, az); + + az[0] &= 248; + az[31] &= 63; + az[31] |= 64; + + ge_scalarmult_base(&A, az); + ge_p3_tobytes(out_public_key, &A); + + OPENSSL_cleanse(az, sizeof(az)); +} int X25519(uint8_t out_shared_key[32], const uint8_t private_key[32], const uint8_t peer_public_value[32]) { @@ -3391,4 +5193,6 @@ void X25519_public_from_private(uint8_t out_public_value[32], fe_invert(zminusy_inv, zminusy); fe_mul(zplusy, zplusy, zminusy_inv); fe_tobytes(out_public_value, zplusy); + + OPENSSL_cleanse(e, sizeof(e)); }