diff --git a/src/libsodium/crypto_core/curve25519/ref10/curve25519_ref10.c b/src/libsodium/crypto_core/curve25519/ref10/curve25519_ref10.c index 59bbf7fa..aa315789 100644 --- a/src/libsodium/crypto_core/curve25519/ref10/curve25519_ref10.c +++ b/src/libsodium/crypto_core/curve25519/ref10/curve25519_ref10.c @@ -6,988 +6,992 @@ 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; + 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; + 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 -*/ + h = 0 + */ void fe_0(fe h) { - memset(&h[0], 0, 10 * sizeof h[0]); + memset(&h[0], 0, 10 * sizeof h[0]); } /* -h = 1 -*/ + h = 1 + */ void fe_1(fe h) { - h[0] = 1; - h[1] = 0; - memset(&h[2], 0, 8 * sizeof h[0]); + h[0] = 1; + h[1] = 0; + memset(&h[2], 0, 8 * sizeof h[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. -*/ + 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; + 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}. -*/ + 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); - 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; + 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); + 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; } /* -h = f -*/ + 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; + 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. -*/ + 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; + 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) (1L << 24)) >> 25; h0 += carry9 * 19; h9 -= carry9 * ((uint64_t) 1L << 25); - carry1 = (h1 + (int64_t) (1L << 24)) >> 25; h2 += carry1; h1 -= carry1 * ((uint64_t) 1L << 25); - carry3 = (h3 + (int64_t) (1L << 24)) >> 25; h4 += carry3; h3 -= carry3 * ((uint64_t) 1L << 25); - carry5 = (h5 + (int64_t) (1L << 24)) >> 25; h6 += carry5; h5 -= carry5 * ((uint64_t) 1L << 25); - carry7 = (h7 + (int64_t) (1L << 24)) >> 25; h8 += carry7; h7 -= carry7 * ((uint64_t) 1L << 25); + carry9 = (h9 + (int64_t) (1L << 24)) >> 25; h0 += carry9 * 19; h9 -= carry9 * ((uint64_t) 1L << 25); + carry1 = (h1 + (int64_t) (1L << 24)) >> 25; h2 += carry1; h1 -= carry1 * ((uint64_t) 1L << 25); + carry3 = (h3 + (int64_t) (1L << 24)) >> 25; h4 += carry3; h3 -= carry3 * ((uint64_t) 1L << 25); + carry5 = (h5 + (int64_t) (1L << 24)) >> 25; h6 += carry5; h5 -= carry5 * ((uint64_t) 1L << 25); + carry7 = (h7 + (int64_t) (1L << 24)) >> 25; h8 += carry7; h7 -= carry7 * ((uint64_t) 1L << 25); - carry0 = (h0 + (int64_t) (1L << 25)) >> 26; h1 += carry0; h0 -= carry0 * ((uint64_t) 1L << 26); - carry2 = (h2 + (int64_t) (1L << 25)) >> 26; h3 += carry2; h2 -= carry2 * ((uint64_t) 1L << 26); - carry4 = (h4 + (int64_t) (1L << 25)) >> 26; h5 += carry4; h4 -= carry4 * ((uint64_t) 1L << 26); - carry6 = (h6 + (int64_t) (1L << 25)) >> 26; h7 += carry6; h6 -= carry6 * ((uint64_t) 1L << 26); - carry8 = (h8 + (int64_t) (1L << 25)) >> 26; h9 += carry8; h8 -= carry8 * ((uint64_t) 1L << 26); + carry0 = (h0 + (int64_t) (1L << 25)) >> 26; h1 += carry0; h0 -= carry0 * ((uint64_t) 1L << 26); + carry2 = (h2 + (int64_t) (1L << 25)) >> 26; h3 += carry2; h2 -= carry2 * ((uint64_t) 1L << 26); + carry4 = (h4 + (int64_t) (1L << 25)) >> 26; h5 += carry4; h4 -= carry4 * ((uint64_t) 1L << 26); + carry6 = (h6 + (int64_t) (1L << 25)) >> 26; h7 += carry6; h6 -= carry6 * ((uint64_t) 1L << 26); + carry8 = (h8 + (int64_t) (1L << 25)) >> 26; h9 += carry8; h8 -= carry8 * ((uint64_t) 1L << 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[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: - |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. - -Write p=2^255-19; q=floor(h/p). -Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))). - -Proof: - Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4. - Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4. - - Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9). - Then 0> 25; - q = (h0 + q) >> 26; - q = (h1 + q) >> 25; - q = (h2 + q) >> 26; - q = (h3 + q) >> 25; - q = (h4 + q) >> 26; - q = (h5 + q) >> 25; - q = (h6 + q) >> 26; - q = (h7 + q) >> 25; - q = (h8 + q) >> 26; - q = (h9 + q) >> 25; + q = (19 * h9 + ((uint32_t) 1L << 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. */ + /* 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 * ((uint32_t) 1L << 26); - carry1 = h1 >> 25; h2 += carry1; h1 -= carry1 * ((uint32_t) 1L << 25); - carry2 = h2 >> 26; h3 += carry2; h2 -= carry2 * ((uint32_t) 1L << 26); - carry3 = h3 >> 25; h4 += carry3; h3 -= carry3 * ((uint32_t) 1L << 25); - carry4 = h4 >> 26; h5 += carry4; h4 -= carry4 * ((uint32_t) 1L << 26); - carry5 = h5 >> 25; h6 += carry5; h5 -= carry5 * ((uint32_t) 1L << 25); - carry6 = h6 >> 26; h7 += carry6; h6 -= carry6 * ((uint32_t) 1L << 26); - carry7 = h7 >> 25; h8 += carry7; h7 -= carry7 * ((uint32_t) 1L << 25); - carry8 = h8 >> 26; h9 += carry8; h8 -= carry8 * ((uint32_t) 1L << 26); - carry9 = h9 >> 25; h9 -= carry9 * ((uint32_t) 1L << 25); - /* h10 = carry9 */ + carry0 = h0 >> 26; h1 += carry0; h0 -= carry0 * ((uint32_t) 1L << 26); + carry1 = h1 >> 25; h2 += carry1; h1 -= carry1 * ((uint32_t) 1L << 25); + carry2 = h2 >> 26; h3 += carry2; h2 -= carry2 * ((uint32_t) 1L << 26); + carry3 = h3 >> 25; h4 += carry3; h3 -= carry3 * ((uint32_t) 1L << 25); + carry4 = h4 >> 26; h5 += carry4; h4 -= carry4 * ((uint32_t) 1L << 26); + carry5 = h5 >> 25; h6 += carry5; h5 -= carry5 * ((uint32_t) 1L << 25); + carry6 = h6 >> 26; h7 += carry6; h6 -= carry6 * ((uint32_t) 1L << 26); + carry7 = h7 >> 25; h8 += carry7; h7 -= carry7 * ((uint32_t) 1L << 25); + carry8 = h8 >> 26; h9 += carry8; h8 -= carry8 * ((uint32_t) 1L << 26); + carry9 = h9 >> 25; h9 -= carry9 * ((uint32_t) 1L << 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. - */ + /* + 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] = h0 >> 0; - s[1] = h0 >> 8; - s[2] = h0 >> 16; - s[3] = (h0 >> 24) | (h1 * ((uint32_t) 1 << 2)); - s[4] = h1 >> 6; - s[5] = h1 >> 14; - s[6] = (h1 >> 22) | (h2 * ((uint32_t) 1 << 3)); - s[7] = h2 >> 5; - s[8] = h2 >> 13; - s[9] = (h2 >> 21) | (h3 * ((uint32_t) 1 << 5)); - s[10] = h3 >> 3; - s[11] = h3 >> 11; - s[12] = (h3 >> 19) | (h4 * ((uint32_t) 1 << 6)); - s[13] = h4 >> 2; - s[14] = h4 >> 10; - s[15] = h4 >> 18; - s[16] = h5 >> 0; - s[17] = h5 >> 8; - s[18] = h5 >> 16; - s[19] = (h5 >> 24) | (h6 * ((uint32_t) 1 << 1)); - s[20] = h6 >> 7; - s[21] = h6 >> 15; - s[22] = (h6 >> 23) | (h7 * ((uint32_t) 1 << 3)); - s[23] = h7 >> 5; - s[24] = h7 >> 13; - s[25] = (h7 >> 21) | (h8 * ((uint32_t) 1 << 4)); - s[26] = h8 >> 4; - s[27] = h8 >> 12; - s[28] = (h8 >> 20) | (h9 * ((uint32_t) 1 << 6)); - s[29] = h9 >> 2; - s[30] = h9 >> 10; - s[31] = h9 >> 18; + s[0] = h0 >> 0; + s[1] = h0 >> 8; + s[2] = h0 >> 16; + s[3] = (h0 >> 24) | (h1 * ((uint32_t) 1 << 2)); + s[4] = h1 >> 6; + s[5] = h1 >> 14; + s[6] = (h1 >> 22) | (h2 * ((uint32_t) 1 << 3)); + s[7] = h2 >> 5; + s[8] = h2 >> 13; + s[9] = (h2 >> 21) | (h3 * ((uint32_t) 1 << 5)); + s[10] = h3 >> 3; + s[11] = h3 >> 11; + s[12] = (h3 >> 19) | (h4 * ((uint32_t) 1 << 6)); + s[13] = h4 >> 2; + s[14] = h4 >> 10; + s[15] = h4 >> 18; + s[16] = h5 >> 0; + s[17] = h5 >> 8; + s[18] = h5 >> 16; + s[19] = (h5 >> 24) | (h6 * ((uint32_t) 1 << 1)); + s[20] = h6 >> 7; + s[21] = h6 >> 15; + s[22] = (h6 >> 23) | (h7 * ((uint32_t) 1 << 3)); + s[23] = h7 >> 5; + s[24] = h7 >> 13; + s[25] = (h7 >> 21) | (h8 * ((uint32_t) 1 << 4)); + s[26] = h8 >> 4; + s[27] = h8 >> 12; + s[28] = (h8 >> 20) | (h9 * ((uint32_t) 1 << 6)); + s[29] = h9 >> 2; + s[30] = h9 >> 10; + s[31] = h9 >> 18; } /* -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. -*/ + 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; + 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. -*/ + 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. + */ static unsigned char zero[32]; int fe_isnonzero(const fe f) { - unsigned char s[32]; - fe_tobytes(s,f); - return crypto_verify_32(s,zero); + unsigned char s[32]; + fe_tobytes(s,f); + + return crypto_verify_32(s,zero); } /* -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. -*/ + 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. -*/ + 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; + 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; - /* - |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38)) - i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8 - |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19)) - i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9 - */ + /* + |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38)) + i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8 + |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19)) + i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9 + */ - carry0 = (h0 + (int64_t) (1L << 25)) >> 26; h1 += carry0; h0 -= carry0 * ((uint64_t) 1L << 26); - carry4 = (h4 + (int64_t) (1L << 25)) >> 26; h5 += carry4; h4 -= carry4 * ((uint64_t) 1L << 26); - /* |h0| <= 2^25 */ - /* |h4| <= 2^25 */ - /* |h1| <= 1.71*2^59 */ - /* |h5| <= 1.71*2^59 */ + carry0 = (h0 + (int64_t) (1L << 25)) >> 26; h1 += carry0; h0 -= carry0 * ((uint64_t) 1L << 26); + carry4 = (h4 + (int64_t) (1L << 25)) >> 26; h5 += carry4; h4 -= carry4 * ((uint64_t) 1L << 26); + /* |h0| <= 2^25 */ + /* |h4| <= 2^25 */ + /* |h1| <= 1.71*2^59 */ + /* |h5| <= 1.71*2^59 */ - carry1 = (h1 + (int64_t) (1L << 24)) >> 25; h2 += carry1; h1 -= carry1 * ((uint64_t) 1L << 25); - carry5 = (h5 + (int64_t) (1L << 24)) >> 25; h6 += carry5; h5 -= carry5 * ((uint64_t) 1L << 25); - /* |h1| <= 2^24; from now on fits into int32 */ - /* |h5| <= 2^24; from now on fits into int32 */ - /* |h2| <= 1.41*2^60 */ - /* |h6| <= 1.41*2^60 */ + carry1 = (h1 + (int64_t) (1L << 24)) >> 25; h2 += carry1; h1 -= carry1 * ((uint64_t) 1L << 25); + carry5 = (h5 + (int64_t) (1L << 24)) >> 25; h6 += carry5; h5 -= carry5 * ((uint64_t) 1L << 25); + /* |h1| <= 2^24; from now on fits into int32 */ + /* |h5| <= 2^24; from now on fits into int32 */ + /* |h2| <= 1.41*2^60 */ + /* |h6| <= 1.41*2^60 */ - carry2 = (h2 + (int64_t) (1L << 25)) >> 26; h3 += carry2; h2 -= carry2 * ((uint64_t) 1L << 26); - carry6 = (h6 + (int64_t) (1L << 25)) >> 26; h7 += carry6; h6 -= carry6 * ((uint64_t) 1L << 26); - /* |h2| <= 2^25; from now on fits into int32 unchanged */ - /* |h6| <= 2^25; from now on fits into int32 unchanged */ - /* |h3| <= 1.71*2^59 */ - /* |h7| <= 1.71*2^59 */ + carry2 = (h2 + (int64_t) (1L << 25)) >> 26; h3 += carry2; h2 -= carry2 * ((uint64_t) 1L << 26); + carry6 = (h6 + (int64_t) (1L << 25)) >> 26; h7 += carry6; h6 -= carry6 * ((uint64_t) 1L << 26); + /* |h2| <= 2^25; from now on fits into int32 unchanged */ + /* |h6| <= 2^25; from now on fits into int32 unchanged */ + /* |h3| <= 1.71*2^59 */ + /* |h7| <= 1.71*2^59 */ - carry3 = (h3 + (int64_t) (1L << 24)) >> 25; h4 += carry3; h3 -= carry3 * ((uint64_t) 1L << 25); - carry7 = (h7 + (int64_t) (1L << 24)) >> 25; h8 += carry7; h7 -= carry7 * ((uint64_t) 1L << 25); - /* |h3| <= 2^24; from now on fits into int32 unchanged */ - /* |h7| <= 2^24; from now on fits into int32 unchanged */ - /* |h4| <= 1.72*2^34 */ - /* |h8| <= 1.41*2^60 */ + carry3 = (h3 + (int64_t) (1L << 24)) >> 25; h4 += carry3; h3 -= carry3 * ((uint64_t) 1L << 25); + carry7 = (h7 + (int64_t) (1L << 24)) >> 25; h8 += carry7; h7 -= carry7 * ((uint64_t) 1L << 25); + /* |h3| <= 2^24; from now on fits into int32 unchanged */ + /* |h7| <= 2^24; from now on fits into int32 unchanged */ + /* |h4| <= 1.72*2^34 */ + /* |h8| <= 1.41*2^60 */ - carry4 = (h4 + (int64_t) (1L << 25)) >> 26; h5 += carry4; h4 -= carry4 * ((uint64_t) 1L << 26); - carry8 = (h8 + (int64_t) (1L << 25)) >> 26; h9 += carry8; h8 -= carry8 * ((uint64_t) 1L << 26); - /* |h4| <= 2^25; from now on fits into int32 unchanged */ - /* |h8| <= 2^25; from now on fits into int32 unchanged */ - /* |h5| <= 1.01*2^24 */ - /* |h9| <= 1.71*2^59 */ + carry4 = (h4 + (int64_t) (1L << 25)) >> 26; h5 += carry4; h4 -= carry4 * ((uint64_t) 1L << 26); + carry8 = (h8 + (int64_t) (1L << 25)) >> 26; h9 += carry8; h8 -= carry8 * ((uint64_t) 1L << 26); + /* |h4| <= 2^25; from now on fits into int32 unchanged */ + /* |h8| <= 2^25; from now on fits into int32 unchanged */ + /* |h5| <= 1.01*2^24 */ + /* |h9| <= 1.71*2^59 */ - carry9 = (h9 + (int64_t) (1L << 24)) >> 25; h0 += carry9 * 19; h9 -= carry9 * ((uint64_t) 1L << 25); - /* |h9| <= 2^24; from now on fits into int32 unchanged */ - /* |h0| <= 1.1*2^39 */ + carry9 = (h9 + (int64_t) (1L << 24)) >> 25; h0 += carry9 * 19; h9 -= carry9 * ((uint64_t) 1L << 25); + /* |h9| <= 2^24; from now on fits into int32 unchanged */ + /* |h0| <= 1.1*2^39 */ - carry0 = (h0 + (int64_t) (1L << 25)) >> 26; h1 += carry0; h0 -= carry0 * ((uint64_t) 1L << 26); - /* |h0| <= 2^25; from now on fits into int32 unchanged */ - /* |h1| <= 1.01*2^24 */ + carry0 = (h0 + (int64_t) (1L << 25)) >> 26; h1 += carry0; h0 -= carry0 * ((uint64_t) 1L << 26); + /* |h0| <= 2^25; from now on fits into int32 unchanged */ + /* |h1| <= 1.01*2^24 */ - 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[0] = (int32_t) h0; + h[1] = (int32_t) h1; + h[2] = (int32_t) h2; + h[3] = (int32_t) h3; + h[4] = (int32_t) h4; + h[5] = (int32_t) h5; + h[6] = (int32_t) h6; + h[7] = (int32_t) h7; + h[8] = (int32_t) h8; + h[9] = (int32_t) h9; } /* -h = -f - -Preconditions: - |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. - -Postconditions: - |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. -*/ + 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; + 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; } /* -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. -*/ + 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. -*/ + 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; + 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) (1L << 25)) >> 26; h1 += carry0; h0 -= carry0 * ((uint64_t) 1L << 26); - carry4 = (h4 + (int64_t) (1L << 25)) >> 26; h5 += carry4; h4 -= carry4 * ((uint64_t) 1L << 26); + carry0 = (h0 + (int64_t) (1L << 25)) >> 26; h1 += carry0; h0 -= carry0 * ((uint64_t) 1L << 26); + carry4 = (h4 + (int64_t) (1L << 25)) >> 26; h5 += carry4; h4 -= carry4 * ((uint64_t) 1L << 26); - carry1 = (h1 + (int64_t) (1L << 24)) >> 25; h2 += carry1; h1 -= carry1 * ((uint64_t) 1L << 25); - carry5 = (h5 + (int64_t) (1L << 24)) >> 25; h6 += carry5; h5 -= carry5 * ((uint64_t) 1L << 25); + carry1 = (h1 + (int64_t) (1L << 24)) >> 25; h2 += carry1; h1 -= carry1 * ((uint64_t) 1L << 25); + carry5 = (h5 + (int64_t) (1L << 24)) >> 25; h6 += carry5; h5 -= carry5 * ((uint64_t) 1L << 25); - carry2 = (h2 + (int64_t) (1L << 25)) >> 26; h3 += carry2; h2 -= carry2 * ((uint64_t) 1L << 26); - carry6 = (h6 + (int64_t) (1L << 25)) >> 26; h7 += carry6; h6 -= carry6 * ((uint64_t) 1L << 26); + carry2 = (h2 + (int64_t) (1L << 25)) >> 26; h3 += carry2; h2 -= carry2 * ((uint64_t) 1L << 26); + carry6 = (h6 + (int64_t) (1L << 25)) >> 26; h7 += carry6; h6 -= carry6 * ((uint64_t) 1L << 26); - carry3 = (h3 + (int64_t) (1L << 24)) >> 25; h4 += carry3; h3 -= carry3 * ((uint64_t) 1L << 25); - carry7 = (h7 + (int64_t) (1L << 24)) >> 25; h8 += carry7; h7 -= carry7 * ((uint64_t) 1L << 25); + carry3 = (h3 + (int64_t) (1L << 24)) >> 25; h4 += carry3; h3 -= carry3 * ((uint64_t) 1L << 25); + carry7 = (h7 + (int64_t) (1L << 24)) >> 25; h8 += carry7; h7 -= carry7 * ((uint64_t) 1L << 25); - carry4 = (h4 + (int64_t) (1L << 25)) >> 26; h5 += carry4; h4 -= carry4 * ((uint64_t) 1L << 26); - carry8 = (h8 + (int64_t) (1L << 25)) >> 26; h9 += carry8; h8 -= carry8 * ((uint64_t) 1L << 26); + carry4 = (h4 + (int64_t) (1L << 25)) >> 26; h5 += carry4; h4 -= carry4 * ((uint64_t) 1L << 26); + carry8 = (h8 + (int64_t) (1L << 25)) >> 26; h9 += carry8; h8 -= carry8 * ((uint64_t) 1L << 26); - carry9 = (h9 + (int64_t) (1L << 24)) >> 25; h0 += carry9 * 19; h9 -= carry9 * ((uint64_t) 1L << 25); + carry9 = (h9 + (int64_t) (1L << 24)) >> 25; h0 += carry9 * 19; h9 -= carry9 * ((uint64_t) 1L << 25); - carry0 = (h0 + (int64_t) (1L << 25)) >> 26; h1 += carry0; h0 -= carry0 * ((uint64_t) 1L << 26); + carry0 = (h0 + (int64_t) (1L << 25)) >> 26; h1 += carry0; h0 -= carry0 * ((uint64_t) 1L << 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[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. -*/ + 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. -*/ + 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; + 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; + h0 += h0; + h1 += h1; + h2 += h2; + h3 += h3; + h4 += h4; + h5 += h5; + h6 += h6; + h7 += h7; + h8 += h8; + h9 += h9; - carry0 = (h0 + (int64_t) (1L << 25)) >> 26; h1 += carry0; h0 -= carry0 * ((uint64_t) 1L << 26); - carry4 = (h4 + (int64_t) (1L << 25)) >> 26; h5 += carry4; h4 -= carry4 * ((uint64_t) 1L << 26); + carry0 = (h0 + (int64_t) (1L << 25)) >> 26; h1 += carry0; h0 -= carry0 * ((uint64_t) 1L << 26); + carry4 = (h4 + (int64_t) (1L << 25)) >> 26; h5 += carry4; h4 -= carry4 * ((uint64_t) 1L << 26); - carry1 = (h1 + (int64_t) (1L << 24)) >> 25; h2 += carry1; h1 -= carry1 * ((uint64_t) 1L << 25); - carry5 = (h5 + (int64_t) (1L << 24)) >> 25; h6 += carry5; h5 -= carry5 * ((uint64_t) 1L << 25); + carry1 = (h1 + (int64_t) (1L << 24)) >> 25; h2 += carry1; h1 -= carry1 * ((uint64_t) 1L << 25); + carry5 = (h5 + (int64_t) (1L << 24)) >> 25; h6 += carry5; h5 -= carry5 * ((uint64_t) 1L << 25); - carry2 = (h2 + (int64_t) (1L << 25)) >> 26; h3 += carry2; h2 -= carry2 * ((uint64_t) 1L << 26); - carry6 = (h6 + (int64_t) (1L << 25)) >> 26; h7 += carry6; h6 -= carry6 * ((uint64_t) 1L << 26); + carry2 = (h2 + (int64_t) (1L << 25)) >> 26; h3 += carry2; h2 -= carry2 * ((uint64_t) 1L << 26); + carry6 = (h6 + (int64_t) (1L << 25)) >> 26; h7 += carry6; h6 -= carry6 * ((uint64_t) 1L << 26); - carry3 = (h3 + (int64_t) (1L << 24)) >> 25; h4 += carry3; h3 -= carry3 * ((uint64_t) 1L << 25); - carry7 = (h7 + (int64_t) (1L << 24)) >> 25; h8 += carry7; h7 -= carry7 * ((uint64_t) 1L << 25); + carry3 = (h3 + (int64_t) (1L << 24)) >> 25; h4 += carry3; h3 -= carry3 * ((uint64_t) 1L << 25); + carry7 = (h7 + (int64_t) (1L << 24)) >> 25; h8 += carry7; h7 -= carry7 * ((uint64_t) 1L << 25); - carry4 = (h4 + (int64_t) (1L << 25)) >> 26; h5 += carry4; h4 -= carry4 * ((uint64_t) 1L << 26); - carry8 = (h8 + (int64_t) (1L << 25)) >> 26; h9 += carry8; h8 -= carry8 * ((uint64_t) 1L << 26); + carry4 = (h4 + (int64_t) (1L << 25)) >> 26; h5 += carry4; h4 -= carry4 * ((uint64_t) 1L << 26); + carry8 = (h8 + (int64_t) (1L << 25)) >> 26; h9 += carry8; h8 -= carry8 * ((uint64_t) 1L << 26); - carry9 = (h9 + (int64_t) (1L << 24)) >> 25; h0 += carry9 * 19; h9 -= carry9 * ((uint64_t) 1L << 25); + carry9 = (h9 + (int64_t) (1L << 24)) >> 25; h0 += carry9 * 19; h9 -= carry9 * ((uint64_t) 1L << 25); - carry0 = (h0 + (int64_t) (1L << 25)) >> 26; h1 += carry0; h0 -= carry0 * ((uint64_t) 1L << 26); + carry0 = (h0 + (int64_t) (1L << 25)) >> 26; h1 += carry0; h0 -= carry0 * ((uint64_t) 1L << 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[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) @@ -1102,64 +1106,64 @@ void fe_pow22523(fe out,const fe z) } /* -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. -*/ + 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; + 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; } /* -r = p + q -*/ + r = p + q + */ void ge_add(ge_p1p1 *r,const ge_p3 *p,const ge_cached *q) { @@ -1180,33 +1184,33 @@ void ge_add(ge_p1p1 *r,const ge_p3 *p,const ge_cached *q) static void slide(signed char *r,const unsigned char *a) { - int i; - int b; - int k; + 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) + 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; + 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; + } } - } else - break; } - } - } } @@ -1226,48 +1230,51 @@ static const fe sqrtm1 = { int ge_frombytes_negate_vartime(ge_p3 *h,const unsigned char *s) { - fe u; - fe v; - fe v3; - fe vxx; - fe check; + 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_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_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_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); - } + 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); + if (fe_isnegative(h->X) == (s[31] >> 7)) { + fe_neg(h->X,h->X); + } + fe_mul(h->T,h->X,h->Y); - fe_mul(h->T,h->X,h->Y); - return 0; + return 0; } /* -r = p + q -*/ + r = p + q + */ void ge_madd(ge_p1p1 *r,const ge_p3 *p,const ge_precomp *q) { @@ -1286,8 +1293,8 @@ void ge_madd(ge_p1p1 *r,const ge_p3 *p,const ge_precomp *q) } /* -r = p - q -*/ + r = p - q + */ void ge_msub(ge_p1p1 *r,const ge_p3 *p,const ge_precomp *q) { @@ -1306,38 +1313,38 @@ void ge_msub(ge_p1p1 *r,const ge_p3 *p,const ge_precomp *q) } /* -r = p -*/ + r = p + */ extern 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); + 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 -*/ + r = p + */ extern 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); + 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); + fe_0(h->X); + fe_1(h->Y); + fe_1(h->Z); } /* -r = 2 * p -*/ + r = 2 * p + */ void ge_p2_dbl(ge_p1p1 *r,const ge_p2 *p) { @@ -1356,15 +1363,15 @@ void ge_p2_dbl(ge_p1p1 *r,const ge_p2 *p) void ge_p3_0(ge_p3 *h) { - fe_0(h->X); - fe_1(h->Y); - fe_1(h->Z); - fe_0(h->T); + fe_0(h->X); + fe_1(h->Y); + fe_1(h->Z); + fe_0(h->T); } /* -r = p -*/ + r = p + */ /* 2 * d = 16295367250680780974490674513165176452449235426866156013048779062215315747161 */ static const fe d2 = { @@ -1373,77 +1380,79 @@ static const fe d2 = { extern 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); + 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 -*/ + r = p + */ extern 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); + 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 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; + 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; } /* -r = 2 * p -*/ + 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); + ge_p2 q; + ge_p3_to_p2(&q,p); + ge_p2_dbl(r,&q); } void ge_precomp_0(ge_precomp *h) { - fe_1(h->yplusx); - fe_1(h->yminusx); - fe_0(h->xy2d); + fe_1(h->yplusx); + fe_1(h->yminusx); + fe_0(h->xy2d); } 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 */ - uint32_t y = x; /* 0: yes; 1..255: no */ - y -= 1; /* 4294967295: yes; 0..254: no */ - y >>= 31; /* 1: yes; 0: no */ - return y; + unsigned char ub = b; + unsigned char uc = c; + unsigned char x = ub ^ uc; /* 0: yes; 1..255: no */ + uint32_t y = x; /* 0: yes; 1..255: no */ + y -= 1; /* 4294967295: yes; 0..254: no */ + y >>= 31; /* 1: yes; 0: no */ + + return 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 x; + uint64_t x = b; /* 18446744073709551361..18446744073709551615: yes; 0..255: no */ + x >>= 63; /* 1: yes; 0: no */ + + return x; } static void cmov(ge_precomp *t,const ge_precomp *u,unsigned char b) { - fe_cmov(t->yplusx,u->yplusx,b); - fe_cmov(t->yminusx,u->yminusx,b); - fe_cmov(t->xy2d,u->xy2d,b); + fe_cmov(t->yplusx,u->yplusx,b); + fe_cmov(t->yminusx,u->yminusx,b); + fe_cmov(t->xy2d,u->xy2d,b); } /* base[i][j] = (j+1)*256^i*B */ @@ -1453,28 +1462,28 @@ static const ge_precomp base[32][8] = { static void ge_select(ge_precomp *t,int pos,signed char b) { - ge_precomp minust; - unsigned char bnegative = negative(b); - unsigned char babs = b - (((-bnegative) & b) * ((signed char) 1 << 1)); + ge_precomp minust; + unsigned char bnegative = negative(b); + unsigned char babs = b - (((-bnegative) & b) * ((signed char) 1 << 1)); - ge_precomp_0(t); - 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); + ge_precomp_0(t); + 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); } /* -r = p - q -*/ + r = p - q + */ void ge_sub(ge_p1p1 *r,const ge_p3 *p,const ge_cached *q) { @@ -1495,739 +1504,739 @@ void ge_sub(ge_p1p1 *r,const ge_p3 *p,const ge_cached *q) void ge_tobytes(unsigned char *s,const ge_p2 *h) { - fe recip; - fe x; - fe y; + 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; + 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; } /* -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 -*/ + 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 + */ /* -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. -*/ + 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; + 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); + 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_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); + 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]); + for (i = 255;i >= 0;--i) { + if (aslide[i] || bslide[i]) break; } - 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]); - } + for (;i >= 0;--i) { + ge_p2_dbl(&t,r); - ge_p1p1_to_p2(r,&t); - } + 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); + } } void ge_scalarmult_vartime(ge_p3 *r,const unsigned char *a,const ge_p3 *A) { - signed char aslide[256]; - ge_cached Ai[8]; - ge_p1p1 t; - ge_p3 u; - ge_p3 A2; - int i; + signed char aslide[256]; + ge_cached Ai[8]; + ge_p1p1 t; + ge_p3 u; + ge_p3 A2; + int i; - slide(aslide,a); + slide(aslide,a); - 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_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_p3_0(r); + ge_p3_0(r); - for (i = 255;i >= 0;--i) { - if (aslide[i]) break; - } - - for (;i >= 0;--i) { - ge_p3_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]); + for (i = 255;i >= 0;--i) { + if (aslide[i]) break; } - ge_p1p1_to_p3(r,&t); - } + for (;i >= 0;--i) { + ge_p3_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]); + } + + ge_p1p1_to_p3(r,&t); + } } 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; + 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 */ + 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 * ((signed char) 1 << 4); - } - e[63] += carry; - /* each e[i] is between -8 and 8 */ + carry = 0; + for (i = 0;i < 63;++i) { + e[i] += carry; + carry = e[i] + 8; + carry >>= 4; + e[i] -= carry * ((signed char) 1 << 4); + } + e[63] += carry; + /* each e[i] is between -8 and 8 */ - ge_p3_0(h); - for (i = 1;i < 64;i += 2) { - ge_select(&t,i / 2,e[i]); - ge_madd(&r,h,&t); ge_p1p1_to_p3(h,&r); - } + ge_p3_0(h); + for (i = 1;i < 64;i += 2) { + ge_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); + 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) { - ge_select(&t,i / 2,e[i]); - ge_madd(&r,h,&t); ge_p1p1_to_p3(h,&r); - } + for (i = 0;i < 64;i += 2) { + ge_select(&t,i / 2,e[i]); + ge_madd(&r,h,&t); ge_p1p1_to_p3(h,&r); + } } /* -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. -*/ + 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; + 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; + 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 + (int64_t) (1L << 20)) >> 21; s1 += carry0; s0 -= carry0 * ((uint64_t) 1L << 21); - carry2 = (s2 + (int64_t) (1L << 20)) >> 21; s3 += carry2; s2 -= carry2 * ((uint64_t) 1L << 21); - carry4 = (s4 + (int64_t) (1L << 20)) >> 21; s5 += carry4; s4 -= carry4 * ((uint64_t) 1L << 21); - carry6 = (s6 + (int64_t) (1L << 20)) >> 21; s7 += carry6; s6 -= carry6 * ((uint64_t) 1L << 21); - carry8 = (s8 + (int64_t) (1L << 20)) >> 21; s9 += carry8; s8 -= carry8 * ((uint64_t) 1L << 21); - carry10 = (s10 + (int64_t) (1L << 20)) >> 21; s11 += carry10; s10 -= carry10 * ((uint64_t) 1L << 21); - carry12 = (s12 + (int64_t) (1L << 20)) >> 21; s13 += carry12; s12 -= carry12 * ((uint64_t) 1L << 21); - carry14 = (s14 + (int64_t) (1L << 20)) >> 21; s15 += carry14; s14 -= carry14 * ((uint64_t) 1L << 21); - carry16 = (s16 + (int64_t) (1L << 20)) >> 21; s17 += carry16; s16 -= carry16 * ((uint64_t) 1L << 21); - carry18 = (s18 + (int64_t) (1L << 20)) >> 21; s19 += carry18; s18 -= carry18 * ((uint64_t) 1L << 21); - carry20 = (s20 + (int64_t) (1L << 20)) >> 21; s21 += carry20; s20 -= carry20 * ((uint64_t) 1L << 21); - carry22 = (s22 + (int64_t) (1L << 20)) >> 21; s23 += carry22; s22 -= carry22 * ((uint64_t) 1L << 21); + carry0 = (s0 + (int64_t) (1L << 20)) >> 21; s1 += carry0; s0 -= carry0 * ((uint64_t) 1L << 21); + carry2 = (s2 + (int64_t) (1L << 20)) >> 21; s3 += carry2; s2 -= carry2 * ((uint64_t) 1L << 21); + carry4 = (s4 + (int64_t) (1L << 20)) >> 21; s5 += carry4; s4 -= carry4 * ((uint64_t) 1L << 21); + carry6 = (s6 + (int64_t) (1L << 20)) >> 21; s7 += carry6; s6 -= carry6 * ((uint64_t) 1L << 21); + carry8 = (s8 + (int64_t) (1L << 20)) >> 21; s9 += carry8; s8 -= carry8 * ((uint64_t) 1L << 21); + carry10 = (s10 + (int64_t) (1L << 20)) >> 21; s11 += carry10; s10 -= carry10 * ((uint64_t) 1L << 21); + carry12 = (s12 + (int64_t) (1L << 20)) >> 21; s13 += carry12; s12 -= carry12 * ((uint64_t) 1L << 21); + carry14 = (s14 + (int64_t) (1L << 20)) >> 21; s15 += carry14; s14 -= carry14 * ((uint64_t) 1L << 21); + carry16 = (s16 + (int64_t) (1L << 20)) >> 21; s17 += carry16; s16 -= carry16 * ((uint64_t) 1L << 21); + carry18 = (s18 + (int64_t) (1L << 20)) >> 21; s19 += carry18; s18 -= carry18 * ((uint64_t) 1L << 21); + carry20 = (s20 + (int64_t) (1L << 20)) >> 21; s21 += carry20; s20 -= carry20 * ((uint64_t) 1L << 21); + carry22 = (s22 + (int64_t) (1L << 20)) >> 21; s23 += carry22; s22 -= carry22 * ((uint64_t) 1L << 21); - carry1 = (s1 + (int64_t) (1L << 20)) >> 21; s2 += carry1; s1 -= carry1 * ((uint64_t) 1L << 21); - carry3 = (s3 + (int64_t) (1L << 20)) >> 21; s4 += carry3; s3 -= carry3 * ((uint64_t) 1L << 21); - carry5 = (s5 + (int64_t) (1L << 20)) >> 21; s6 += carry5; s5 -= carry5 * ((uint64_t) 1L << 21); - carry7 = (s7 + (int64_t) (1L << 20)) >> 21; s8 += carry7; s7 -= carry7 * ((uint64_t) 1L << 21); - carry9 = (s9 + (int64_t) (1L << 20)) >> 21; s10 += carry9; s9 -= carry9 * ((uint64_t) 1L << 21); - carry11 = (s11 + (int64_t) (1L << 20)) >> 21; s12 += carry11; s11 -= carry11 * ((uint64_t) 1L << 21); - carry13 = (s13 + (int64_t) (1L << 20)) >> 21; s14 += carry13; s13 -= carry13 * ((uint64_t) 1L << 21); - carry15 = (s15 + (int64_t) (1L << 20)) >> 21; s16 += carry15; s15 -= carry15 * ((uint64_t) 1L << 21); - carry17 = (s17 + (int64_t) (1L << 20)) >> 21; s18 += carry17; s17 -= carry17 * ((uint64_t) 1L << 21); - carry19 = (s19 + (int64_t) (1L << 20)) >> 21; s20 += carry19; s19 -= carry19 * ((uint64_t) 1L << 21); - carry21 = (s21 + (int64_t) (1L << 20)) >> 21; s22 += carry21; s21 -= carry21 * ((uint64_t) 1L << 21); + carry1 = (s1 + (int64_t) (1L << 20)) >> 21; s2 += carry1; s1 -= carry1 * ((uint64_t) 1L << 21); + carry3 = (s3 + (int64_t) (1L << 20)) >> 21; s4 += carry3; s3 -= carry3 * ((uint64_t) 1L << 21); + carry5 = (s5 + (int64_t) (1L << 20)) >> 21; s6 += carry5; s5 -= carry5 * ((uint64_t) 1L << 21); + carry7 = (s7 + (int64_t) (1L << 20)) >> 21; s8 += carry7; s7 -= carry7 * ((uint64_t) 1L << 21); + carry9 = (s9 + (int64_t) (1L << 20)) >> 21; s10 += carry9; s9 -= carry9 * ((uint64_t) 1L << 21); + carry11 = (s11 + (int64_t) (1L << 20)) >> 21; s12 += carry11; s11 -= carry11 * ((uint64_t) 1L << 21); + carry13 = (s13 + (int64_t) (1L << 20)) >> 21; s14 += carry13; s13 -= carry13 * ((uint64_t) 1L << 21); + carry15 = (s15 + (int64_t) (1L << 20)) >> 21; s16 += carry15; s15 -= carry15 * ((uint64_t) 1L << 21); + carry17 = (s17 + (int64_t) (1L << 20)) >> 21; s18 += carry17; s17 -= carry17 * ((uint64_t) 1L << 21); + carry19 = (s19 + (int64_t) (1L << 20)) >> 21; s20 += carry19; s19 -= carry19 * ((uint64_t) 1L << 21); + carry21 = (s21 + (int64_t) (1L << 20)) >> 21; s22 += carry21; s21 -= carry21 * ((uint64_t) 1L << 21); - s11 += s23 * 666643; - s12 += s23 * 470296; - s13 += s23 * 654183; - s14 -= s23 * 997805; - s15 += s23 * 136657; - s16 -= s23 * 683901; + s11 += s23 * 666643; + s12 += s23 * 470296; + s13 += s23 * 654183; + s14 -= s23 * 997805; + s15 += s23 * 136657; + s16 -= s23 * 683901; - s10 += s22 * 666643; - s11 += s22 * 470296; - s12 += s22 * 654183; - s13 -= s22 * 997805; - s14 += s22 * 136657; - s15 -= s22 * 683901; + s10 += s22 * 666643; + s11 += s22 * 470296; + s12 += s22 * 654183; + s13 -= s22 * 997805; + s14 += s22 * 136657; + s15 -= s22 * 683901; - s9 += s21 * 666643; - s10 += s21 * 470296; - s11 += s21 * 654183; - s12 -= s21 * 997805; - s13 += s21 * 136657; - s14 -= s21 * 683901; + s9 += s21 * 666643; + s10 += s21 * 470296; + s11 += s21 * 654183; + s12 -= s21 * 997805; + s13 += s21 * 136657; + s14 -= s21 * 683901; - s8 += s20 * 666643; - s9 += s20 * 470296; - s10 += s20 * 654183; - s11 -= s20 * 997805; - s12 += s20 * 136657; - s13 -= s20 * 683901; + s8 += s20 * 666643; + s9 += s20 * 470296; + s10 += s20 * 654183; + s11 -= s20 * 997805; + s12 += s20 * 136657; + s13 -= s20 * 683901; - s7 += s19 * 666643; - s8 += s19 * 470296; - s9 += s19 * 654183; - s10 -= s19 * 997805; - s11 += s19 * 136657; - s12 -= s19 * 683901; + s7 += s19 * 666643; + s8 += s19 * 470296; + s9 += s19 * 654183; + s10 -= s19 * 997805; + s11 += s19 * 136657; + s12 -= s19 * 683901; - s6 += s18 * 666643; - s7 += s18 * 470296; - s8 += s18 * 654183; - s9 -= s18 * 997805; - s10 += s18 * 136657; - s11 -= s18 * 683901; + s6 += s18 * 666643; + s7 += s18 * 470296; + s8 += s18 * 654183; + s9 -= s18 * 997805; + s10 += s18 * 136657; + s11 -= s18 * 683901; - carry6 = (s6 + (int64_t) (1L << 20)) >> 21; s7 += carry6; s6 -= carry6 * ((uint64_t) 1L << 21); - carry8 = (s8 + (int64_t) (1L << 20)) >> 21; s9 += carry8; s8 -= carry8 * ((uint64_t) 1L << 21); - carry10 = (s10 + (int64_t) (1L << 20)) >> 21; s11 += carry10; s10 -= carry10 * ((uint64_t) 1L << 21); - carry12 = (s12 + (int64_t) (1L << 20)) >> 21; s13 += carry12; s12 -= carry12 * ((uint64_t) 1L << 21); - carry14 = (s14 + (int64_t) (1L << 20)) >> 21; s15 += carry14; s14 -= carry14 * ((uint64_t) 1L << 21); - carry16 = (s16 + (int64_t) (1L << 20)) >> 21; s17 += carry16; s16 -= carry16 * ((uint64_t) 1L << 21); + carry6 = (s6 + (int64_t) (1L << 20)) >> 21; s7 += carry6; s6 -= carry6 * ((uint64_t) 1L << 21); + carry8 = (s8 + (int64_t) (1L << 20)) >> 21; s9 += carry8; s8 -= carry8 * ((uint64_t) 1L << 21); + carry10 = (s10 + (int64_t) (1L << 20)) >> 21; s11 += carry10; s10 -= carry10 * ((uint64_t) 1L << 21); + carry12 = (s12 + (int64_t) (1L << 20)) >> 21; s13 += carry12; s12 -= carry12 * ((uint64_t) 1L << 21); + carry14 = (s14 + (int64_t) (1L << 20)) >> 21; s15 += carry14; s14 -= carry14 * ((uint64_t) 1L << 21); + carry16 = (s16 + (int64_t) (1L << 20)) >> 21; s17 += carry16; s16 -= carry16 * ((uint64_t) 1L << 21); - carry7 = (s7 + (int64_t) (1L << 20)) >> 21; s8 += carry7; s7 -= carry7 * ((uint64_t) 1L << 21); - carry9 = (s9 + (int64_t) (1L << 20)) >> 21; s10 += carry9; s9 -= carry9 * ((uint64_t) 1L << 21); - carry11 = (s11 + (int64_t) (1L << 20)) >> 21; s12 += carry11; s11 -= carry11 * ((uint64_t) 1L << 21); - carry13 = (s13 + (int64_t) (1L << 20)) >> 21; s14 += carry13; s13 -= carry13 * ((uint64_t) 1L << 21); - carry15 = (s15 + (int64_t) (1L << 20)) >> 21; s16 += carry15; s15 -= carry15 * ((uint64_t) 1L << 21); + carry7 = (s7 + (int64_t) (1L << 20)) >> 21; s8 += carry7; s7 -= carry7 * ((uint64_t) 1L << 21); + carry9 = (s9 + (int64_t) (1L << 20)) >> 21; s10 += carry9; s9 -= carry9 * ((uint64_t) 1L << 21); + carry11 = (s11 + (int64_t) (1L << 20)) >> 21; s12 += carry11; s11 -= carry11 * ((uint64_t) 1L << 21); + carry13 = (s13 + (int64_t) (1L << 20)) >> 21; s14 += carry13; s13 -= carry13 * ((uint64_t) 1L << 21); + carry15 = (s15 + (int64_t) (1L << 20)) >> 21; s16 += carry15; s15 -= carry15 * ((uint64_t) 1L << 21); - s5 += s17 * 666643; - s6 += s17 * 470296; - s7 += s17 * 654183; - s8 -= s17 * 997805; - s9 += s17 * 136657; - s10 -= s17 * 683901; + s5 += s17 * 666643; + s6 += s17 * 470296; + s7 += s17 * 654183; + s8 -= s17 * 997805; + s9 += s17 * 136657; + s10 -= s17 * 683901; - s4 += s16 * 666643; - s5 += s16 * 470296; - s6 += s16 * 654183; - s7 -= s16 * 997805; - s8 += s16 * 136657; - s9 -= s16 * 683901; + s4 += s16 * 666643; + s5 += s16 * 470296; + s6 += s16 * 654183; + s7 -= s16 * 997805; + s8 += s16 * 136657; + s9 -= s16 * 683901; - s3 += s15 * 666643; - s4 += s15 * 470296; - s5 += s15 * 654183; - s6 -= s15 * 997805; - s7 += s15 * 136657; - s8 -= s15 * 683901; + s3 += s15 * 666643; + s4 += s15 * 470296; + s5 += s15 * 654183; + s6 -= s15 * 997805; + s7 += s15 * 136657; + s8 -= s15 * 683901; - s2 += s14 * 666643; - s3 += s14 * 470296; - s4 += s14 * 654183; - s5 -= s14 * 997805; - s6 += s14 * 136657; - s7 -= s14 * 683901; + s2 += s14 * 666643; + s3 += s14 * 470296; + s4 += s14 * 654183; + s5 -= s14 * 997805; + s6 += s14 * 136657; + s7 -= s14 * 683901; - s1 += s13 * 666643; - s2 += s13 * 470296; - s3 += s13 * 654183; - s4 -= s13 * 997805; - s5 += s13 * 136657; - s6 -= s13 * 683901; + s1 += s13 * 666643; + s2 += s13 * 470296; + s3 += s13 * 654183; + s4 -= s13 * 997805; + s5 += s13 * 136657; + s6 -= s13 * 683901; - s0 += s12 * 666643; - s1 += s12 * 470296; - s2 += s12 * 654183; - s3 -= s12 * 997805; - s4 += s12 * 136657; - s5 -= s12 * 683901; - s12 = 0; + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + s12 = 0; - carry0 = (s0 + (int64_t) (1L << 20)) >> 21; s1 += carry0; s0 -= carry0 * ((uint64_t) 1L << 21); - carry2 = (s2 + (int64_t) (1L << 20)) >> 21; s3 += carry2; s2 -= carry2 * ((uint64_t) 1L << 21); - carry4 = (s4 + (int64_t) (1L << 20)) >> 21; s5 += carry4; s4 -= carry4 * ((uint64_t) 1L << 21); - carry6 = (s6 + (int64_t) (1L << 20)) >> 21; s7 += carry6; s6 -= carry6 * ((uint64_t) 1L << 21); - carry8 = (s8 + (int64_t) (1L << 20)) >> 21; s9 += carry8; s8 -= carry8 * ((uint64_t) 1L << 21); - carry10 = (s10 + (int64_t) (1L << 20)) >> 21; s11 += carry10; s10 -= carry10 * ((uint64_t) 1L << 21); + carry0 = (s0 + (int64_t) (1L << 20)) >> 21; s1 += carry0; s0 -= carry0 * ((uint64_t) 1L << 21); + carry2 = (s2 + (int64_t) (1L << 20)) >> 21; s3 += carry2; s2 -= carry2 * ((uint64_t) 1L << 21); + carry4 = (s4 + (int64_t) (1L << 20)) >> 21; s5 += carry4; s4 -= carry4 * ((uint64_t) 1L << 21); + carry6 = (s6 + (int64_t) (1L << 20)) >> 21; s7 += carry6; s6 -= carry6 * ((uint64_t) 1L << 21); + carry8 = (s8 + (int64_t) (1L << 20)) >> 21; s9 += carry8; s8 -= carry8 * ((uint64_t) 1L << 21); + carry10 = (s10 + (int64_t) (1L << 20)) >> 21; s11 += carry10; s10 -= carry10 * ((uint64_t) 1L << 21); - carry1 = (s1 + (int64_t) (1L << 20)) >> 21; s2 += carry1; s1 -= carry1 * ((uint64_t) 1L << 21); - carry3 = (s3 + (int64_t) (1L << 20)) >> 21; s4 += carry3; s3 -= carry3 * ((uint64_t) 1L << 21); - carry5 = (s5 + (int64_t) (1L << 20)) >> 21; s6 += carry5; s5 -= carry5 * ((uint64_t) 1L << 21); - carry7 = (s7 + (int64_t) (1L << 20)) >> 21; s8 += carry7; s7 -= carry7 * ((uint64_t) 1L << 21); - carry9 = (s9 + (int64_t) (1L << 20)) >> 21; s10 += carry9; s9 -= carry9 * ((uint64_t) 1L << 21); - carry11 = (s11 + (int64_t) (1L << 20)) >> 21; s12 += carry11; s11 -= carry11 * ((uint64_t) 1L << 21); + carry1 = (s1 + (int64_t) (1L << 20)) >> 21; s2 += carry1; s1 -= carry1 * ((uint64_t) 1L << 21); + carry3 = (s3 + (int64_t) (1L << 20)) >> 21; s4 += carry3; s3 -= carry3 * ((uint64_t) 1L << 21); + carry5 = (s5 + (int64_t) (1L << 20)) >> 21; s6 += carry5; s5 -= carry5 * ((uint64_t) 1L << 21); + carry7 = (s7 + (int64_t) (1L << 20)) >> 21; s8 += carry7; s7 -= carry7 * ((uint64_t) 1L << 21); + carry9 = (s9 + (int64_t) (1L << 20)) >> 21; s10 += carry9; s9 -= carry9 * ((uint64_t) 1L << 21); + carry11 = (s11 + (int64_t) (1L << 20)) >> 21; s12 += carry11; s11 -= carry11 * ((uint64_t) 1L << 21); - s0 += s12 * 666643; - s1 += s12 * 470296; - s2 += s12 * 654183; - s3 -= s12 * 997805; - s4 += s12 * 136657; - s5 -= s12 * 683901; - s12 = 0; + 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 * ((uint64_t) 1L << 21); - carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 * ((uint64_t) 1L << 21); - carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 * ((uint64_t) 1L << 21); - carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 * ((uint64_t) 1L << 21); - carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 * ((uint64_t) 1L << 21); - carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 * ((uint64_t) 1L << 21); - carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 * ((uint64_t) 1L << 21); - carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 * ((uint64_t) 1L << 21); - carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 * ((uint64_t) 1L << 21); - carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 * ((uint64_t) 1L << 21); - carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 * ((uint64_t) 1L << 21); - carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 * ((uint64_t) 1L << 21); + carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 * ((uint64_t) 1L << 21); + carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 * ((uint64_t) 1L << 21); + carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 * ((uint64_t) 1L << 21); + carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 * ((uint64_t) 1L << 21); + carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 * ((uint64_t) 1L << 21); + carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 * ((uint64_t) 1L << 21); + carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 * ((uint64_t) 1L << 21); + carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 * ((uint64_t) 1L << 21); + carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 * ((uint64_t) 1L << 21); + carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 * ((uint64_t) 1L << 21); + carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 * ((uint64_t) 1L << 21); + carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 * ((uint64_t) 1L << 21); - s0 += s12 * 666643; - s1 += s12 * 470296; - s2 += s12 * 654183; - s3 -= s12 * 997805; - s4 += s12 * 136657; - s5 -= s12 * 683901; + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; - carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 * ((uint64_t) 1L << 21); - carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 * ((uint64_t) 1L << 21); - carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 * ((uint64_t) 1L << 21); - carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 * ((uint64_t) 1L << 21); - carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 * ((uint64_t) 1L << 21); - carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 * ((uint64_t) 1L << 21); - carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 * ((uint64_t) 1L << 21); - carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 * ((uint64_t) 1L << 21); - carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 * ((uint64_t) 1L << 21); - carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 * ((uint64_t) 1L << 21); - carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 * ((uint64_t) 1L << 21); + carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 * ((uint64_t) 1L << 21); + carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 * ((uint64_t) 1L << 21); + carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 * ((uint64_t) 1L << 21); + carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 * ((uint64_t) 1L << 21); + carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 * ((uint64_t) 1L << 21); + carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 * ((uint64_t) 1L << 21); + carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 * ((uint64_t) 1L << 21); + carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 * ((uint64_t) 1L << 21); + carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 * ((uint64_t) 1L << 21); + carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 * ((uint64_t) 1L << 21); + carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 * ((uint64_t) 1L << 21); - s[0] = s0 >> 0; - s[1] = s0 >> 8; - s[2] = (s0 >> 16) | (s1 * ((uint64_t) 1 << 5)); - s[3] = s1 >> 3; - s[4] = s1 >> 11; - s[5] = (s1 >> 19) | (s2 * ((uint64_t) 1 << 2)); - s[6] = s2 >> 6; - s[7] = (s2 >> 14) | (s3 * ((uint64_t) 1 << 7)); - s[8] = s3 >> 1; - s[9] = s3 >> 9; - s[10] = (s3 >> 17) | (s4 * ((uint64_t) 1 << 4)); - s[11] = s4 >> 4; - s[12] = s4 >> 12; - s[13] = (s4 >> 20) | (s5 * ((uint64_t) 1 << 1)); - s[14] = s5 >> 7; - s[15] = (s5 >> 15) | (s6 * ((uint64_t) 1 << 6)); - s[16] = s6 >> 2; - s[17] = s6 >> 10; - s[18] = (s6 >> 18) | (s7 * ((uint64_t) 1 << 3)); - s[19] = s7 >> 5; - s[20] = s7 >> 13; - s[21] = s8 >> 0; - s[22] = s8 >> 8; - s[23] = (s8 >> 16) | (s9 * ((uint64_t) 1 << 5)); - s[24] = s9 >> 3; - s[25] = s9 >> 11; - s[26] = (s9 >> 19) | (s10 * ((uint64_t) 1 << 2)); - s[27] = s10 >> 6; - s[28] = (s10 >> 14) | (s11 * ((uint64_t) 1 << 7)); - s[29] = s11 >> 1; - s[30] = s11 >> 9; - s[31] = s11 >> 17; + s[0] = s0 >> 0; + s[1] = s0 >> 8; + s[2] = (s0 >> 16) | (s1 * ((uint64_t) 1 << 5)); + s[3] = s1 >> 3; + s[4] = s1 >> 11; + s[5] = (s1 >> 19) | (s2 * ((uint64_t) 1 << 2)); + s[6] = s2 >> 6; + s[7] = (s2 >> 14) | (s3 * ((uint64_t) 1 << 7)); + s[8] = s3 >> 1; + s[9] = s3 >> 9; + s[10] = (s3 >> 17) | (s4 * ((uint64_t) 1 << 4)); + s[11] = s4 >> 4; + s[12] = s4 >> 12; + s[13] = (s4 >> 20) | (s5 * ((uint64_t) 1 << 1)); + s[14] = s5 >> 7; + s[15] = (s5 >> 15) | (s6 * ((uint64_t) 1 << 6)); + s[16] = s6 >> 2; + s[17] = s6 >> 10; + s[18] = (s6 >> 18) | (s7 * ((uint64_t) 1 << 3)); + s[19] = s7 >> 5; + s[20] = s7 >> 13; + s[21] = s8 >> 0; + s[22] = s8 >> 8; + s[23] = (s8 >> 16) | (s9 * ((uint64_t) 1 << 5)); + s[24] = s9 >> 3; + s[25] = s9 >> 11; + s[26] = (s9 >> 19) | (s10 * ((uint64_t) 1 << 2)); + s[27] = s10 >> 6; + s[28] = (s10 >> 14) | (s11 * ((uint64_t) 1 << 7)); + s[29] = s11 >> 1; + s[30] = s11 >> 9; + s[31] = s11 >> 17; } /* -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. -*/ + 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; + 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; + s11 += s23 * 666643; + s12 += s23 * 470296; + s13 += s23 * 654183; + s14 -= s23 * 997805; + s15 += s23 * 136657; + s16 -= s23 * 683901; - s10 += s22 * 666643; - s11 += s22 * 470296; - s12 += s22 * 654183; - s13 -= s22 * 997805; - s14 += s22 * 136657; - s15 -= s22 * 683901; + s10 += s22 * 666643; + s11 += s22 * 470296; + s12 += s22 * 654183; + s13 -= s22 * 997805; + s14 += s22 * 136657; + s15 -= s22 * 683901; - s9 += s21 * 666643; - s10 += s21 * 470296; - s11 += s21 * 654183; - s12 -= s21 * 997805; - s13 += s21 * 136657; - s14 -= s21 * 683901; + s9 += s21 * 666643; + s10 += s21 * 470296; + s11 += s21 * 654183; + s12 -= s21 * 997805; + s13 += s21 * 136657; + s14 -= s21 * 683901; - s8 += s20 * 666643; - s9 += s20 * 470296; - s10 += s20 * 654183; - s11 -= s20 * 997805; - s12 += s20 * 136657; - s13 -= s20 * 683901; + s8 += s20 * 666643; + s9 += s20 * 470296; + s10 += s20 * 654183; + s11 -= s20 * 997805; + s12 += s20 * 136657; + s13 -= s20 * 683901; - s7 += s19 * 666643; - s8 += s19 * 470296; - s9 += s19 * 654183; - s10 -= s19 * 997805; - s11 += s19 * 136657; - s12 -= s19 * 683901; + s7 += s19 * 666643; + s8 += s19 * 470296; + s9 += s19 * 654183; + s10 -= s19 * 997805; + s11 += s19 * 136657; + s12 -= s19 * 683901; - s6 += s18 * 666643; - s7 += s18 * 470296; - s8 += s18 * 654183; - s9 -= s18 * 997805; - s10 += s18 * 136657; - s11 -= s18 * 683901; + s6 += s18 * 666643; + s7 += s18 * 470296; + s8 += s18 * 654183; + s9 -= s18 * 997805; + s10 += s18 * 136657; + s11 -= s18 * 683901; carry6 = (s6 + (int64_t) (1L << 20)) >> 21; s7 += carry6; s6 -= carry6 * ((uint64_t) 1L << 21); - carry8 = (s8 + (int64_t) (1L << 20)) >> 21; s9 += carry8; s8 -= carry8 * ((uint64_t) 1L << 21); - carry10 = (s10 + (int64_t) (1L << 20)) >> 21; s11 += carry10; s10 -= carry10 * ((uint64_t) 1L << 21); - carry12 = (s12 + (int64_t) (1L << 20)) >> 21; s13 += carry12; s12 -= carry12 * ((uint64_t) 1L << 21); - carry14 = (s14 + (int64_t) (1L << 20)) >> 21; s15 += carry14; s14 -= carry14 * ((uint64_t) 1L << 21); - carry16 = (s16 + (int64_t) (1L << 20)) >> 21; s17 += carry16; s16 -= carry16 * ((uint64_t) 1L << 21); + carry8 = (s8 + (int64_t) (1L << 20)) >> 21; s9 += carry8; s8 -= carry8 * ((uint64_t) 1L << 21); + carry10 = (s10 + (int64_t) (1L << 20)) >> 21; s11 += carry10; s10 -= carry10 * ((uint64_t) 1L << 21); + carry12 = (s12 + (int64_t) (1L << 20)) >> 21; s13 += carry12; s12 -= carry12 * ((uint64_t) 1L << 21); + carry14 = (s14 + (int64_t) (1L << 20)) >> 21; s15 += carry14; s14 -= carry14 * ((uint64_t) 1L << 21); + carry16 = (s16 + (int64_t) (1L << 20)) >> 21; s17 += carry16; s16 -= carry16 * ((uint64_t) 1L << 21); - carry7 = (s7 + (int64_t) (1L << 20)) >> 21; s8 += carry7; s7 -= carry7 * ((uint64_t) 1L << 21); - carry9 = (s9 + (int64_t) (1L << 20)) >> 21; s10 += carry9; s9 -= carry9 * ((uint64_t) 1L << 21); - carry11 = (s11 + (int64_t) (1L << 20)) >> 21; s12 += carry11; s11 -= carry11 * ((uint64_t) 1L << 21); - carry13 = (s13 + (int64_t) (1L << 20)) >> 21; s14 += carry13; s13 -= carry13 * ((uint64_t) 1L << 21); - carry15 = (s15 + (int64_t) (1L << 20)) >> 21; s16 += carry15; s15 -= carry15 * ((uint64_t) 1L << 21); + carry7 = (s7 + (int64_t) (1L << 20)) >> 21; s8 += carry7; s7 -= carry7 * ((uint64_t) 1L << 21); + carry9 = (s9 + (int64_t) (1L << 20)) >> 21; s10 += carry9; s9 -= carry9 * ((uint64_t) 1L << 21); + carry11 = (s11 + (int64_t) (1L << 20)) >> 21; s12 += carry11; s11 -= carry11 * ((uint64_t) 1L << 21); + carry13 = (s13 + (int64_t) (1L << 20)) >> 21; s14 += carry13; s13 -= carry13 * ((uint64_t) 1L << 21); + carry15 = (s15 + (int64_t) (1L << 20)) >> 21; s16 += carry15; s15 -= carry15 * ((uint64_t) 1L << 21); - s5 += s17 * 666643; - s6 += s17 * 470296; - s7 += s17 * 654183; - s8 -= s17 * 997805; - s9 += s17 * 136657; - s10 -= s17 * 683901; + s5 += s17 * 666643; + s6 += s17 * 470296; + s7 += s17 * 654183; + s8 -= s17 * 997805; + s9 += s17 * 136657; + s10 -= s17 * 683901; - s4 += s16 * 666643; - s5 += s16 * 470296; - s6 += s16 * 654183; - s7 -= s16 * 997805; - s8 += s16 * 136657; - s9 -= s16 * 683901; + s4 += s16 * 666643; + s5 += s16 * 470296; + s6 += s16 * 654183; + s7 -= s16 * 997805; + s8 += s16 * 136657; + s9 -= s16 * 683901; - s3 += s15 * 666643; - s4 += s15 * 470296; - s5 += s15 * 654183; - s6 -= s15 * 997805; - s7 += s15 * 136657; - s8 -= s15 * 683901; + s3 += s15 * 666643; + s4 += s15 * 470296; + s5 += s15 * 654183; + s6 -= s15 * 997805; + s7 += s15 * 136657; + s8 -= s15 * 683901; - s2 += s14 * 666643; - s3 += s14 * 470296; - s4 += s14 * 654183; - s5 -= s14 * 997805; - s6 += s14 * 136657; - s7 -= s14 * 683901; + s2 += s14 * 666643; + s3 += s14 * 470296; + s4 += s14 * 654183; + s5 -= s14 * 997805; + s6 += s14 * 136657; + s7 -= s14 * 683901; - s1 += s13 * 666643; - s2 += s13 * 470296; - s3 += s13 * 654183; - s4 -= s13 * 997805; - s5 += s13 * 136657; - s6 -= s13 * 683901; + s1 += s13 * 666643; + s2 += s13 * 470296; + s3 += s13 * 654183; + s4 -= s13 * 997805; + s5 += s13 * 136657; + s6 -= s13 * 683901; - s0 += s12 * 666643; - s1 += s12 * 470296; - s2 += s12 * 654183; - s3 -= s12 * 997805; - s4 += s12 * 136657; - s5 -= s12 * 683901; - s12 = 0; + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + s12 = 0; - carry0 = (s0 + (int64_t) (1L << 20)) >> 21; s1 += carry0; s0 -= carry0 * ((uint64_t) 1L << 21); - carry2 = (s2 + (int64_t) (1L << 20)) >> 21; s3 += carry2; s2 -= carry2 * ((uint64_t) 1L << 21); - carry4 = (s4 + (int64_t) (1L << 20)) >> 21; s5 += carry4; s4 -= carry4 * ((uint64_t) 1L << 21); - carry6 = (s6 + (int64_t) (1L << 20)) >> 21; s7 += carry6; s6 -= carry6 * ((uint64_t) 1L << 21); - carry8 = (s8 + (int64_t) (1L << 20)) >> 21; s9 += carry8; s8 -= carry8 * ((uint64_t) 1L << 21); - carry10 = (s10 + (int64_t) (1L << 20)) >> 21; s11 += carry10; s10 -= carry10 * ((uint64_t) 1L << 21); + carry0 = (s0 + (int64_t) (1L << 20)) >> 21; s1 += carry0; s0 -= carry0 * ((uint64_t) 1L << 21); + carry2 = (s2 + (int64_t) (1L << 20)) >> 21; s3 += carry2; s2 -= carry2 * ((uint64_t) 1L << 21); + carry4 = (s4 + (int64_t) (1L << 20)) >> 21; s5 += carry4; s4 -= carry4 * ((uint64_t) 1L << 21); + carry6 = (s6 + (int64_t) (1L << 20)) >> 21; s7 += carry6; s6 -= carry6 * ((uint64_t) 1L << 21); + carry8 = (s8 + (int64_t) (1L << 20)) >> 21; s9 += carry8; s8 -= carry8 * ((uint64_t) 1L << 21); + carry10 = (s10 + (int64_t) (1L << 20)) >> 21; s11 += carry10; s10 -= carry10 * ((uint64_t) 1L << 21); - carry1 = (s1 + (int64_t) (1L << 20)) >> 21; s2 += carry1; s1 -= carry1 * ((uint64_t) 1L << 21); - carry3 = (s3 + (int64_t) (1L << 20)) >> 21; s4 += carry3; s3 -= carry3 * ((uint64_t) 1L << 21); - carry5 = (s5 + (int64_t) (1L << 20)) >> 21; s6 += carry5; s5 -= carry5 * ((uint64_t) 1L << 21); - carry7 = (s7 + (int64_t) (1L << 20)) >> 21; s8 += carry7; s7 -= carry7 * ((uint64_t) 1L << 21); - carry9 = (s9 + (int64_t) (1L << 20)) >> 21; s10 += carry9; s9 -= carry9 * ((uint64_t) 1L << 21); - carry11 = (s11 + (int64_t) (1L << 20)) >> 21; s12 += carry11; s11 -= carry11 * ((uint64_t) 1L << 21); + carry1 = (s1 + (int64_t) (1L << 20)) >> 21; s2 += carry1; s1 -= carry1 * ((uint64_t) 1L << 21); + carry3 = (s3 + (int64_t) (1L << 20)) >> 21; s4 += carry3; s3 -= carry3 * ((uint64_t) 1L << 21); + carry5 = (s5 + (int64_t) (1L << 20)) >> 21; s6 += carry5; s5 -= carry5 * ((uint64_t) 1L << 21); + carry7 = (s7 + (int64_t) (1L << 20)) >> 21; s8 += carry7; s7 -= carry7 * ((uint64_t) 1L << 21); + carry9 = (s9 + (int64_t) (1L << 20)) >> 21; s10 += carry9; s9 -= carry9 * ((uint64_t) 1L << 21); + carry11 = (s11 + (int64_t) (1L << 20)) >> 21; s12 += carry11; s11 -= carry11 * ((uint64_t) 1L << 21); - s0 += s12 * 666643; - s1 += s12 * 470296; - s2 += s12 * 654183; - s3 -= s12 * 997805; - s4 += s12 * 136657; - s5 -= s12 * 683901; - s12 = 0; + 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 * ((uint64_t) 1L << 21); - carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 * ((uint64_t) 1L << 21); - carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 * ((uint64_t) 1L << 21); - carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 * ((uint64_t) 1L << 21); - carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 * ((uint64_t) 1L << 21); - carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 * ((uint64_t) 1L << 21); - carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 * ((uint64_t) 1L << 21); - carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 * ((uint64_t) 1L << 21); - carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 * ((uint64_t) 1L << 21); - carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 * ((uint64_t) 1L << 21); - carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 * ((uint64_t) 1L << 21); - carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 * ((uint64_t) 1L << 21); + carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 * ((uint64_t) 1L << 21); + carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 * ((uint64_t) 1L << 21); + carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 * ((uint64_t) 1L << 21); + carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 * ((uint64_t) 1L << 21); + carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 * ((uint64_t) 1L << 21); + carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 * ((uint64_t) 1L << 21); + carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 * ((uint64_t) 1L << 21); + carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 * ((uint64_t) 1L << 21); + carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 * ((uint64_t) 1L << 21); + carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 * ((uint64_t) 1L << 21); + carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 * ((uint64_t) 1L << 21); + carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 * ((uint64_t) 1L << 21); - s0 += s12 * 666643; - s1 += s12 * 470296; - s2 += s12 * 654183; - s3 -= s12 * 997805; - s4 += s12 * 136657; - s5 -= s12 * 683901; + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; - carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 * ((uint64_t) 1L << 21); - carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 * ((uint64_t) 1L << 21); - carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 * ((uint64_t) 1L << 21); - carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 * ((uint64_t) 1L << 21); - carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 * ((uint64_t) 1L << 21); - carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 * ((uint64_t) 1L << 21); - carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 * ((uint64_t) 1L << 21); - carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 * ((uint64_t) 1L << 21); - carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 * ((uint64_t) 1L << 21); - carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 * ((uint64_t) 1L << 21); - carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 * ((uint64_t) 1L << 21); + carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 * ((uint64_t) 1L << 21); + carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 * ((uint64_t) 1L << 21); + carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 * ((uint64_t) 1L << 21); + carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 * ((uint64_t) 1L << 21); + carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 * ((uint64_t) 1L << 21); + carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 * ((uint64_t) 1L << 21); + carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 * ((uint64_t) 1L << 21); + carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 * ((uint64_t) 1L << 21); + carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 * ((uint64_t) 1L << 21); + carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 * ((uint64_t) 1L << 21); + carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 * ((uint64_t) 1L << 21); - s[0] = s0 >> 0; - s[1] = s0 >> 8; - s[2] = (s0 >> 16) | (s1 * ((uint64_t) 1 << 5)); - s[3] = s1 >> 3; - s[4] = s1 >> 11; - s[5] = (s1 >> 19) | (s2 * ((uint64_t) 1 << 2)); - s[6] = s2 >> 6; - s[7] = (s2 >> 14) | (s3 * ((uint64_t) 1 << 7)); - s[8] = s3 >> 1; - s[9] = s3 >> 9; - s[10] = (s3 >> 17) | (s4 * ((uint64_t) 1 << 4)); - s[11] = s4 >> 4; - s[12] = s4 >> 12; - s[13] = (s4 >> 20) | (s5 * ((uint64_t) 1 << 1)); - s[14] = s5 >> 7; - s[15] = (s5 >> 15) | (s6 * ((uint64_t) 1 << 6)); - s[16] = s6 >> 2; - s[17] = s6 >> 10; - s[18] = (s6 >> 18) | (s7 * ((uint64_t) 1 << 3)); - s[19] = s7 >> 5; - s[20] = s7 >> 13; - s[21] = s8 >> 0; - s[22] = s8 >> 8; - s[23] = (s8 >> 16) | (s9 * ((uint64_t) 1 << 5)); - s[24] = s9 >> 3; - s[25] = s9 >> 11; - s[26] = (s9 >> 19) | (s10 * ((uint64_t) 1 << 2)); - s[27] = s10 >> 6; - s[28] = (s10 >> 14) | (s11 * ((uint64_t) 1 << 7)); - s[29] = s11 >> 1; - s[30] = s11 >> 9; - s[31] = s11 >> 17; + s[0] = s0 >> 0; + s[1] = s0 >> 8; + s[2] = (s0 >> 16) | (s1 * ((uint64_t) 1 << 5)); + s[3] = s1 >> 3; + s[4] = s1 >> 11; + s[5] = (s1 >> 19) | (s2 * ((uint64_t) 1 << 2)); + s[6] = s2 >> 6; + s[7] = (s2 >> 14) | (s3 * ((uint64_t) 1 << 7)); + s[8] = s3 >> 1; + s[9] = s3 >> 9; + s[10] = (s3 >> 17) | (s4 * ((uint64_t) 1 << 4)); + s[11] = s4 >> 4; + s[12] = s4 >> 12; + s[13] = (s4 >> 20) | (s5 * ((uint64_t) 1 << 1)); + s[14] = s5 >> 7; + s[15] = (s5 >> 15) | (s6 * ((uint64_t) 1 << 6)); + s[16] = s6 >> 2; + s[17] = s6 >> 10; + s[18] = (s6 >> 18) | (s7 * ((uint64_t) 1 << 3)); + s[19] = s7 >> 5; + s[20] = s7 >> 13; + s[21] = s8 >> 0; + s[22] = s8 >> 8; + s[23] = (s8 >> 16) | (s9 * ((uint64_t) 1 << 5)); + s[24] = s9 >> 3; + s[25] = s9 >> 11; + s[26] = (s9 >> 19) | (s10 * ((uint64_t) 1 << 2)); + s[27] = s10 >> 6; + s[28] = (s10 >> 14) | (s11 * ((uint64_t) 1 << 7)); + s[29] = s11 >> 1; + s[30] = s11 >> 9; + s[31] = s11 >> 17; } diff --git a/src/libsodium/crypto_core/curve25519/ref10/curve25519_ref10.h b/src/libsodium/crypto_core/curve25519/ref10/curve25519_ref10.h index af0744e4..4fdf23ec 100644 --- a/src/libsodium/crypto_core/curve25519/ref10/curve25519_ref10.h +++ b/src/libsodium/crypto_core/curve25519/ref10/curve25519_ref10.h @@ -8,12 +8,12 @@ typedef int32_t fe[10]; /* -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. -*/ + 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. + */ #define fe_frombytes crypto_core_curve25519_ref10_fe_frombytes #define fe_tobytes crypto_core_curve25519_ref10_fe_tobytes @@ -51,55 +51,55 @@ extern void fe_invert(fe,const fe); extern void fe_pow22523(fe,const fe); /* -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) -*/ + 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) + */ #define ge_p2 crypto_core_curve25519_ref10_ge_p2 typedef struct { - fe X; - fe Y; - fe Z; + fe X; + fe Y; + fe Z; } ge_p2; #define ge_p3 crypto_core_curve25519_ref10_ge_p3 typedef struct { - fe X; - fe Y; - fe Z; - fe T; + fe X; + fe Y; + fe Z; + fe T; } ge_p3; #define ge_p1p1 crypto_core_curve25519_ref10_ge_p1p1 typedef struct { - fe X; - fe Y; - fe Z; - fe T; + fe X; + fe Y; + fe Z; + fe T; } ge_p1p1; #define ge_precomp crypto_core_curve25519_ref10_ge_precomp typedef struct { - fe yplusx; - fe yminusx; - fe xy2d; + fe yplusx; + fe yminusx; + fe xy2d; } ge_precomp; #define ge_cached crypto_core_curve25519_ref10_ge_cached typedef struct { - fe YplusX; - fe YminusX; - fe Z; - fe T2d; + fe YplusX; + fe YminusX; + fe Z; + fe T2d; } ge_cached; #define ge_frombytes_negate_vartime crypto_core_curve25519_ref10_ge_frombytes_negate_vartime @@ -147,9 +147,9 @@ extern void ge_double_scalarmult_vartime(ge_p2 *,const unsigned char *,const ge_ extern void ge_scalarmult_vartime(ge_p3 *,const unsigned char *,const ge_p3 *); /* -The set of scalars is \Z/l -where l = 2^252 + 27742317777372353535851937790883648493. -*/ + The set of scalars is \Z/l + where l = 2^252 + 27742317777372353535851937790883648493. + */ #define sc_reduce crypto_core_curve25519_ref10_sc_reduce #define sc_muladd crypto_core_curve25519_ref10_sc_muladd