#include #include #include #include "crypto_verify_32.h" #include "private/curve25519_ref10.h" static inline uint64_t load_3(const unsigned char *in) { uint64_t result; result = (uint64_t) in[0]; result |= ((uint64_t) in[1]) << 8; result |= ((uint64_t) in[2]) << 16; return result; } static inline uint64_t load_4(const unsigned char *in) { uint64_t result; result = (uint64_t) in[0]; result |= ((uint64_t) in[1]) << 8; result |= ((uint64_t) in[2]) << 16; result |= ((uint64_t) in[3]) << 24; return result; } /* h = 0 */ void fe_0(fe h) { memset(&h[0], 0, 10 * sizeof h[0]); } /* h = 1 */ void fe_1(fe h) { 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. */ void fe_add(fe h, const fe f, const fe g) { int32_t f0 = f[0]; int32_t f1 = f[1]; int32_t f2 = f[2]; int32_t f3 = f[3]; int32_t f4 = f[4]; int32_t f5 = f[5]; int32_t f6 = f[6]; int32_t f7 = f[7]; int32_t f8 = f[8]; int32_t f9 = f[9]; int32_t g0 = g[0]; int32_t g1 = g[1]; int32_t g2 = g[2]; int32_t g3 = g[3]; int32_t g4 = g[4]; int32_t g5 = g[5]; int32_t g6 = g[6]; int32_t g7 = g[7]; int32_t g8 = g[8]; int32_t g9 = g[9]; int32_t h0 = f0 + g0; int32_t h1 = f1 + g1; int32_t h2 = f2 + g2; int32_t h3 = f3 + g3; int32_t h4 = f4 + g4; int32_t h5 = f5 + g5; int32_t h6 = f6 + g6; int32_t h7 = f7 + g7; int32_t h8 = f8 + g8; int32_t h9 = f9 + g9; h[0] = h0; h[1] = h1; h[2] = h2; h[3] = h3; h[4] = h4; h[5] = h5; h[6] = h6; h[7] = h7; h[8] = h8; h[9] = h9; } /* Replace (f,g) with (g,g) if b == 1; replace (f,g) with (f,g) if b == 0. * Preconditions: b in {0,1}. */ void fe_cmov(fe f, const fe g, unsigned int b) { int32_t f0 = f[0]; int32_t f1 = f[1]; int32_t f2 = f[2]; int32_t f3 = f[3]; int32_t f4 = f[4]; int32_t f5 = f[5]; int32_t f6 = f[6]; int32_t f7 = f[7]; int32_t f8 = f[8]; int32_t f9 = f[9]; int32_t g0 = g[0]; int32_t g1 = g[1]; int32_t g2 = g[2]; int32_t g3 = g[3]; int32_t g4 = g[4]; int32_t g5 = g[5]; int32_t g6 = g[6]; int32_t g7 = g[7]; int32_t g8 = g[8]; int32_t g9 = g[9]; int32_t x0 = f0 ^ g0; int32_t x1 = f1 ^ g1; int32_t x2 = f2 ^ g2; int32_t x3 = f3 ^ g3; int32_t x4 = f4 ^ g4; int32_t x5 = f5 ^ g5; int32_t x6 = f6 ^ g6; int32_t x7 = f7 ^ g7; int32_t x8 = f8 ^ g8; int32_t x9 = f9 ^ g9; b = (unsigned int) (-(int) b); 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 */ void fe_copy(fe h, const fe f) { int32_t f0 = f[0]; int32_t f1 = f[1]; int32_t f2 = f[2]; int32_t f3 = f[3]; int32_t f4 = f[4]; int32_t f5 = f[5]; int32_t f6 = f[6]; int32_t f7 = f[7]; int32_t f8 = f[8]; int32_t f9 = f[9]; h[0] = f0; h[1] = f1; h[2] = f2; h[3] = f3; h[4] = f4; h[5] = f5; h[6] = f6; h[7] = f7; h[8] = f8; h[9] = f9; } /* Ignores top bit of h. */ void fe_frombytes(fe h, const unsigned char *s) { int64_t h0 = load_4(s); int64_t h1 = load_3(s + 4) << 6; int64_t h2 = load_3(s + 7) << 5; int64_t h3 = load_3(s + 10) << 3; int64_t h4 = load_3(s + 13) << 2; int64_t h5 = load_4(s + 16); int64_t h6 = load_3(s + 20) << 7; int64_t h7 = load_3(s + 23) << 5; int64_t h8 = load_3(s + 26) << 4; int64_t h9 = (load_3(s + 29) & 8388607) << 2; int64_t carry0; int64_t carry1; int64_t carry2; int64_t carry3; int64_t carry4; int64_t carry5; int64_t carry6; int64_t carry7; int64_t carry8; int64_t carry9; carry9 = (h9 + (int64_t)(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); 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; /* 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 */ /* 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; } /* return 1 if f is in {1,3,5,...,q-2} return 0 if f is in {0,2,4,...,q-1} * Preconditions: |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ int fe_isnegative(const fe f) { unsigned char s[32]; fe_tobytes(s, f); return s[0] & 1; } /* return 1 if f == 0 return 0 if f != 0 * Preconditions: |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ 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); } /* h = f * g Can overlap h with f or g. * Preconditions: |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. * Postconditions: |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. */ /* Notes on implementation strategy: * Using schoolbook multiplication. Karatsuba would save a little in some cost models. * Most multiplications by 2 and 19 are 32-bit precomputations; cheaper than 64-bit postcomputations. * There is one remaining multiplication by 19 in the carry chain; one *19 precomputation can be merged into this, but the resulting data flow is considerably less clean. * There are 12 carries below. 10 of them are 2-way parallelizable and vectorizable. Can get away with 11 carries, but then data flow is much deeper. * With tighter constraints on inputs can squeeze carries into int32. */ void fe_mul(fe h, const fe f, const fe g) { int32_t f0 = f[0]; int32_t f1 = f[1]; int32_t f2 = f[2]; int32_t f3 = f[3]; int32_t f4 = f[4]; int32_t f5 = f[5]; int32_t f6 = f[6]; int32_t f7 = f[7]; int32_t f8 = f[8]; int32_t f9 = f[9]; int32_t g0 = g[0]; int32_t g1 = g[1]; int32_t g2 = g[2]; int32_t g3 = g[3]; int32_t g4 = g[4]; int32_t g5 = g[5]; int32_t g6 = g[6]; int32_t g7 = g[7]; int32_t g8 = g[8]; int32_t g9 = g[9]; int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */ int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */ int32_t g3_19 = 19 * g3; int32_t g4_19 = 19 * g4; int32_t g5_19 = 19 * g5; int32_t g6_19 = 19 * g6; int32_t g7_19 = 19 * g7; int32_t g8_19 = 19 * g8; int32_t g9_19 = 19 * g9; int32_t f1_2 = 2 * f1; int32_t f3_2 = 2 * f3; int32_t f5_2 = 2 * f5; int32_t f7_2 = 2 * f7; int32_t f9_2 = 2 * f9; int64_t f0g0 = f0 * (int64_t) g0; int64_t f0g1 = f0 * (int64_t) g1; int64_t f0g2 = f0 * (int64_t) g2; int64_t f0g3 = f0 * (int64_t) g3; int64_t f0g4 = f0 * (int64_t) g4; int64_t f0g5 = f0 * (int64_t) g5; int64_t f0g6 = f0 * (int64_t) g6; int64_t f0g7 = f0 * (int64_t) g7; int64_t f0g8 = f0 * (int64_t) g8; int64_t f0g9 = f0 * (int64_t) g9; int64_t f1g0 = f1 * (int64_t) g0; int64_t f1g1_2 = f1_2 * (int64_t) g1; int64_t f1g2 = f1 * (int64_t) g2; int64_t f1g3_2 = f1_2 * (int64_t) g3; int64_t f1g4 = f1 * (int64_t) g4; int64_t f1g5_2 = f1_2 * (int64_t) g5; int64_t f1g6 = f1 * (int64_t) g6; int64_t f1g7_2 = f1_2 * (int64_t) g7; int64_t f1g8 = f1 * (int64_t) g8; int64_t f1g9_38 = f1_2 * (int64_t) g9_19; int64_t f2g0 = f2 * (int64_t) g0; int64_t f2g1 = f2 * (int64_t) g1; int64_t f2g2 = f2 * (int64_t) g2; int64_t f2g3 = f2 * (int64_t) g3; int64_t f2g4 = f2 * (int64_t) g4; int64_t f2g5 = f2 * (int64_t) g5; int64_t f2g6 = f2 * (int64_t) g6; int64_t f2g7 = f2 * (int64_t) g7; int64_t f2g8_19 = f2 * (int64_t) g8_19; int64_t f2g9_19 = f2 * (int64_t) g9_19; int64_t f3g0 = f3 * (int64_t) g0; int64_t f3g1_2 = f3_2 * (int64_t) g1; int64_t f3g2 = f3 * (int64_t) g2; int64_t f3g3_2 = f3_2 * (int64_t) g3; int64_t f3g4 = f3 * (int64_t) g4; int64_t f3g5_2 = f3_2 * (int64_t) g5; int64_t f3g6 = f3 * (int64_t) g6; int64_t f3g7_38 = f3_2 * (int64_t) g7_19; int64_t f3g8_19 = f3 * (int64_t) g8_19; int64_t f3g9_38 = f3_2 * (int64_t) g9_19; int64_t f4g0 = f4 * (int64_t) g0; int64_t f4g1 = f4 * (int64_t) g1; int64_t f4g2 = f4 * (int64_t) g2; int64_t f4g3 = f4 * (int64_t) g3; int64_t f4g4 = f4 * (int64_t) g4; int64_t f4g5 = f4 * (int64_t) g5; int64_t f4g6_19 = f4 * (int64_t) g6_19; int64_t f4g7_19 = f4 * (int64_t) g7_19; int64_t f4g8_19 = f4 * (int64_t) g8_19; int64_t f4g9_19 = f4 * (int64_t) g9_19; int64_t f5g0 = f5 * (int64_t) g0; int64_t f5g1_2 = f5_2 * (int64_t) g1; int64_t f5g2 = f5 * (int64_t) g2; int64_t f5g3_2 = f5_2 * (int64_t) g3; int64_t f5g4 = f5 * (int64_t) g4; int64_t f5g5_38 = f5_2 * (int64_t) g5_19; int64_t f5g6_19 = f5 * (int64_t) g6_19; int64_t f5g7_38 = f5_2 * (int64_t) g7_19; int64_t f5g8_19 = f5 * (int64_t) g8_19; int64_t f5g9_38 = f5_2 * (int64_t) g9_19; int64_t f6g0 = f6 * (int64_t) g0; int64_t f6g1 = f6 * (int64_t) g1; int64_t f6g2 = f6 * (int64_t) g2; int64_t f6g3 = f6 * (int64_t) g3; int64_t f6g4_19 = f6 * (int64_t) g4_19; int64_t f6g5_19 = f6 * (int64_t) g5_19; int64_t f6g6_19 = f6 * (int64_t) g6_19; int64_t f6g7_19 = f6 * (int64_t) g7_19; int64_t f6g8_19 = f6 * (int64_t) g8_19; int64_t f6g9_19 = f6 * (int64_t) g9_19; int64_t f7g0 = f7 * (int64_t) g0; int64_t f7g1_2 = f7_2 * (int64_t) g1; int64_t f7g2 = f7 * (int64_t) g2; int64_t f7g3_38 = f7_2 * (int64_t) g3_19; int64_t f7g4_19 = f7 * (int64_t) g4_19; int64_t f7g5_38 = f7_2 * (int64_t) g5_19; int64_t f7g6_19 = f7 * (int64_t) g6_19; int64_t f7g7_38 = f7_2 * (int64_t) g7_19; int64_t f7g8_19 = f7 * (int64_t) g8_19; int64_t f7g9_38 = f7_2 * (int64_t) g9_19; int64_t f8g0 = f8 * (int64_t) g0; int64_t f8g1 = f8 * (int64_t) g1; int64_t f8g2_19 = f8 * (int64_t) g2_19; int64_t f8g3_19 = f8 * (int64_t) g3_19; int64_t f8g4_19 = f8 * (int64_t) g4_19; int64_t f8g5_19 = f8 * (int64_t) g5_19; int64_t f8g6_19 = f8 * (int64_t) g6_19; int64_t f8g7_19 = f8 * (int64_t) g7_19; int64_t f8g8_19 = f8 * (int64_t) g8_19; int64_t f8g9_19 = f8 * (int64_t) g9_19; int64_t f9g0 = f9 * (int64_t) g0; int64_t f9g1_38 = f9_2 * (int64_t) g1_19; int64_t f9g2_19 = f9 * (int64_t) g2_19; int64_t f9g3_38 = f9_2 * (int64_t) g3_19; int64_t f9g4_19 = f9 * (int64_t) g4_19; int64_t f9g5_38 = f9_2 * (int64_t) g5_19; int64_t f9g6_19 = f9 * (int64_t) g6_19; int64_t f9g7_38 = f9_2 * (int64_t) g7_19; int64_t f9g8_19 = f9 * (int64_t) g8_19; int64_t f9g9_38 = f9_2 * (int64_t) g9_19; int64_t h0 = f0g0 + f1g9_38 + f2g8_19 + f3g7_38 + f4g6_19 + f5g5_38 + f6g4_19 + f7g3_38 + f8g2_19 + f9g1_38; int64_t h1 = f0g1 + f1g0 + f2g9_19 + f3g8_19 + f4g7_19 + f5g6_19 + f6g5_19 + f7g4_19 + f8g3_19 + f9g2_19; int64_t h2 = f0g2 + f1g1_2 + f2g0 + f3g9_38 + f4g8_19 + f5g7_38 + f6g6_19 + f7g5_38 + f8g4_19 + f9g3_38; int64_t h3 = f0g3 + f1g2 + f2g1 + f3g0 + f4g9_19 + f5g8_19 + f6g7_19 + f7g6_19 + f8g5_19 + f9g4_19; int64_t h4 = f0g4 + f1g3_2 + f2g2 + f3g1_2 + f4g0 + f5g9_38 + f6g8_19 + f7g7_38 + f8g6_19 + f9g5_38; int64_t h5 = f0g5 + f1g4 + f2g3 + f3g2 + f4g1 + f5g0 + f6g9_19 + f7g8_19 + f8g7_19 + f9g6_19; int64_t h6 = f0g6 + f1g5_2 + f2g4 + f3g3_2 + f4g2 + f5g1_2 + f6g0 + f7g9_38 + f8g8_19 + f9g7_38; int64_t h7 = f0g7 + f1g6 + f2g5 + f3g4 + f4g3 + f5g2 + f6g1 + f7g0 + f8g9_19 + f9g8_19; int64_t h8 = f0g8 + f1g7_2 + f2g6 + f3g5_2 + f4g4 + f5g3_2 + f6g2 + f7g1_2 + f8g0 + f9g9_38; int64_t h9 = f0g9 + f1g8 + f2g7 + f3g6 + f4g5 + f5g4 + f6g3 + f7g2 + f8g1 + f9g0; int64_t carry0; int64_t carry1; int64_t carry2; int64_t carry3; int64_t carry4; int64_t carry5; int64_t carry6; int64_t carry7; int64_t carry8; int64_t carry9; /* |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 */ 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 */ 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 */ 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 */ 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. */ 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; } /* h = f * f Can overlap h with f. * Preconditions: |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. * Postconditions: |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. */ /* See fe_mul.c for discussion of implementation strategy. */ void fe_sq(fe h, const fe f) { int32_t f0 = f[0]; int32_t f1 = f[1]; int32_t f2 = f[2]; int32_t f3 = f[3]; int32_t f4 = f[4]; int32_t f5 = f[5]; int32_t f6 = f[6]; int32_t f7 = f[7]; int32_t f8 = f[8]; int32_t f9 = f[9]; int32_t f0_2 = 2 * f0; int32_t f1_2 = 2 * f1; int32_t f2_2 = 2 * f2; int32_t f3_2 = 2 * f3; int32_t f4_2 = 2 * f4; int32_t f5_2 = 2 * f5; int32_t f6_2 = 2 * f6; int32_t f7_2 = 2 * f7; int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */ int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */ int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */ int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */ int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */ int64_t f0f0 = f0 * (int64_t) f0; int64_t f0f1_2 = f0_2 * (int64_t) f1; int64_t f0f2_2 = f0_2 * (int64_t) f2; int64_t f0f3_2 = f0_2 * (int64_t) f3; int64_t f0f4_2 = f0_2 * (int64_t) f4; int64_t f0f5_2 = f0_2 * (int64_t) f5; int64_t f0f6_2 = f0_2 * (int64_t) f6; int64_t f0f7_2 = f0_2 * (int64_t) f7; int64_t f0f8_2 = f0_2 * (int64_t) f8; int64_t f0f9_2 = f0_2 * (int64_t) f9; int64_t f1f1_2 = f1_2 * (int64_t) f1; int64_t f1f2_2 = f1_2 * (int64_t) f2; int64_t f1f3_4 = f1_2 * (int64_t) f3_2; int64_t f1f4_2 = f1_2 * (int64_t) f4; int64_t f1f5_4 = f1_2 * (int64_t) f5_2; int64_t f1f6_2 = f1_2 * (int64_t) f6; int64_t f1f7_4 = f1_2 * (int64_t) f7_2; int64_t f1f8_2 = f1_2 * (int64_t) f8; int64_t f1f9_76 = f1_2 * (int64_t) f9_38; int64_t f2f2 = f2 * (int64_t) f2; int64_t f2f3_2 = f2_2 * (int64_t) f3; int64_t f2f4_2 = f2_2 * (int64_t) f4; int64_t f2f5_2 = f2_2 * (int64_t) f5; int64_t f2f6_2 = f2_2 * (int64_t) f6; int64_t f2f7_2 = f2_2 * (int64_t) f7; int64_t f2f8_38 = f2_2 * (int64_t) f8_19; int64_t f2f9_38 = f2 * (int64_t) f9_38; int64_t f3f3_2 = f3_2 * (int64_t) f3; int64_t f3f4_2 = f3_2 * (int64_t) f4; int64_t f3f5_4 = f3_2 * (int64_t) f5_2; int64_t f3f6_2 = f3_2 * (int64_t) f6; int64_t f3f7_76 = f3_2 * (int64_t) f7_38; int64_t f3f8_38 = f3_2 * (int64_t) f8_19; int64_t f3f9_76 = f3_2 * (int64_t) f9_38; int64_t f4f4 = f4 * (int64_t) f4; int64_t f4f5_2 = f4_2 * (int64_t) f5; int64_t f4f6_38 = f4_2 * (int64_t) f6_19; int64_t f4f7_38 = f4 * (int64_t) f7_38; int64_t f4f8_38 = f4_2 * (int64_t) f8_19; int64_t f4f9_38 = f4 * (int64_t) f9_38; int64_t f5f5_38 = f5 * (int64_t) f5_38; int64_t f5f6_38 = f5_2 * (int64_t) f6_19; int64_t f5f7_76 = f5_2 * (int64_t) f7_38; int64_t f5f8_38 = f5_2 * (int64_t) f8_19; int64_t f5f9_76 = f5_2 * (int64_t) f9_38; int64_t f6f6_19 = f6 * (int64_t) f6_19; int64_t f6f7_38 = f6 * (int64_t) f7_38; int64_t f6f8_38 = f6_2 * (int64_t) f8_19; int64_t f6f9_38 = f6 * (int64_t) f9_38; int64_t f7f7_38 = f7 * (int64_t) f7_38; int64_t f7f8_38 = f7_2 * (int64_t) f8_19; int64_t f7f9_76 = f7_2 * (int64_t) f9_38; int64_t f8f8_19 = f8 * (int64_t) f8_19; int64_t f8f9_38 = f8 * (int64_t) f9_38; int64_t f9f9_38 = f9 * (int64_t) f9_38; int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38; int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38; int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19; int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38; int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38; int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38; int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19; int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38; int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38; int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2; int64_t carry0; int64_t carry1; int64_t carry2; int64_t carry3; int64_t carry4; int64_t carry5; int64_t carry6; int64_t carry7; int64_t carry8; int64_t carry9; carry0 = (h0 + (int64_t)(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); 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); 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); 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 = 2 * f * f Can overlap h with f. * Preconditions: |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. * Postconditions: |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. */ /* See fe_mul.c for discussion of implementation strategy. */ void fe_sq2(fe h, const fe f) { int32_t f0 = f[0]; int32_t f1 = f[1]; int32_t f2 = f[2]; int32_t f3 = f[3]; int32_t f4 = f[4]; int32_t f5 = f[5]; int32_t f6 = f[6]; int32_t f7 = f[7]; int32_t f8 = f[8]; int32_t f9 = f[9]; int32_t f0_2 = 2 * f0; int32_t f1_2 = 2 * f1; int32_t f2_2 = 2 * f2; int32_t f3_2 = 2 * f3; int32_t f4_2 = 2 * f4; int32_t f5_2 = 2 * f5; int32_t f6_2 = 2 * f6; int32_t f7_2 = 2 * f7; int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */ int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */ int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */ int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */ int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */ int64_t f0f0 = f0 * (int64_t) f0; int64_t f0f1_2 = f0_2 * (int64_t) f1; int64_t f0f2_2 = f0_2 * (int64_t) f2; int64_t f0f3_2 = f0_2 * (int64_t) f3; int64_t f0f4_2 = f0_2 * (int64_t) f4; int64_t f0f5_2 = f0_2 * (int64_t) f5; int64_t f0f6_2 = f0_2 * (int64_t) f6; int64_t f0f7_2 = f0_2 * (int64_t) f7; int64_t f0f8_2 = f0_2 * (int64_t) f8; int64_t f0f9_2 = f0_2 * (int64_t) f9; int64_t f1f1_2 = f1_2 * (int64_t) f1; int64_t f1f2_2 = f1_2 * (int64_t) f2; int64_t f1f3_4 = f1_2 * (int64_t) f3_2; int64_t f1f4_2 = f1_2 * (int64_t) f4; int64_t f1f5_4 = f1_2 * (int64_t) f5_2; int64_t f1f6_2 = f1_2 * (int64_t) f6; int64_t f1f7_4 = f1_2 * (int64_t) f7_2; int64_t f1f8_2 = f1_2 * (int64_t) f8; int64_t f1f9_76 = f1_2 * (int64_t) f9_38; int64_t f2f2 = f2 * (int64_t) f2; int64_t f2f3_2 = f2_2 * (int64_t) f3; int64_t f2f4_2 = f2_2 * (int64_t) f4; int64_t f2f5_2 = f2_2 * (int64_t) f5; int64_t f2f6_2 = f2_2 * (int64_t) f6; int64_t f2f7_2 = f2_2 * (int64_t) f7; int64_t f2f8_38 = f2_2 * (int64_t) f8_19; int64_t f2f9_38 = f2 * (int64_t) f9_38; int64_t f3f3_2 = f3_2 * (int64_t) f3; int64_t f3f4_2 = f3_2 * (int64_t) f4; int64_t f3f5_4 = f3_2 * (int64_t) f5_2; int64_t f3f6_2 = f3_2 * (int64_t) f6; int64_t f3f7_76 = f3_2 * (int64_t) f7_38; int64_t f3f8_38 = f3_2 * (int64_t) f8_19; int64_t f3f9_76 = f3_2 * (int64_t) f9_38; int64_t f4f4 = f4 * (int64_t) f4; int64_t f4f5_2 = f4_2 * (int64_t) f5; int64_t f4f6_38 = f4_2 * (int64_t) f6_19; int64_t f4f7_38 = f4 * (int64_t) f7_38; int64_t f4f8_38 = f4_2 * (int64_t) f8_19; int64_t f4f9_38 = f4 * (int64_t) f9_38; int64_t f5f5_38 = f5 * (int64_t) f5_38; int64_t f5f6_38 = f5_2 * (int64_t) f6_19; int64_t f5f7_76 = f5_2 * (int64_t) f7_38; int64_t f5f8_38 = f5_2 * (int64_t) f8_19; int64_t f5f9_76 = f5_2 * (int64_t) f9_38; int64_t f6f6_19 = f6 * (int64_t) f6_19; int64_t f6f7_38 = f6 * (int64_t) f7_38; int64_t f6f8_38 = f6_2 * (int64_t) f8_19; int64_t f6f9_38 = f6 * (int64_t) f9_38; int64_t f7f7_38 = f7 * (int64_t) f7_38; int64_t f7f8_38 = f7_2 * (int64_t) f8_19; int64_t f7f9_76 = f7_2 * (int64_t) f9_38; int64_t f8f8_19 = f8 * (int64_t) f8_19; int64_t f8f9_38 = f8 * (int64_t) f9_38; int64_t f9f9_38 = f9 * (int64_t) f9_38; int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38; int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38; int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19; int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38; int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38; int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38; int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19; int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38; int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38; int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2; int64_t carry0; int64_t carry1; int64_t carry2; int64_t carry3; int64_t carry4; int64_t carry5; int64_t carry6; int64_t carry7; int64_t carry8; int64_t carry9; h0 += h0; h1 += h1; h2 += h2; h3 += h3; h4 += h4; h5 += h5; h6 += h6; h7 += h7; h8 += h8; h9 += h9; carry0 = (h0 + (int64_t)(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); 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); 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); 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; } void fe_invert(fe out, const fe z) { fe t0; fe t1; fe t2; fe t3; int i; fe_sq(t0, z); fe_sq(t1, t0); fe_sq(t1, t1); fe_mul(t1, z, t1); fe_mul(t0, t0, t1); fe_sq(t2, t0); fe_mul(t1, t1, t2); fe_sq(t2, t1); for (i = 1; i < 5; ++i) { fe_sq(t2, t2); } fe_mul(t1, t2, t1); fe_sq(t2, t1); for (i = 1; i < 10; ++i) { fe_sq(t2, t2); } fe_mul(t2, t2, t1); fe_sq(t3, t2); for (i = 1; i < 20; ++i) { fe_sq(t3, t3); } fe_mul(t2, t3, t2); fe_sq(t2, t2); for (i = 1; i < 10; ++i) { fe_sq(t2, t2); } fe_mul(t1, t2, t1); fe_sq(t2, t1); for (i = 1; i < 50; ++i) { fe_sq(t2, t2); } fe_mul(t2, t2, t1); fe_sq(t3, t2); for (i = 1; i < 100; ++i) { fe_sq(t3, t3); } fe_mul(t2, t3, t2); fe_sq(t2, t2); for (i = 1; i < 50; ++i) { fe_sq(t2, t2); } fe_mul(t1, t2, t1); fe_sq(t1, t1); for (i = 1; i < 5; ++i) { fe_sq(t1, t1); } fe_mul(out, t1, t0); } void fe_pow22523(fe out, const fe z) { fe t0; fe t1; fe t2; int i; fe_sq(t0, z); fe_sq(t1, t0); fe_sq(t1, t1); fe_mul(t1, z, t1); fe_mul(t0, t0, t1); fe_sq(t0, t0); fe_mul(t0, t1, t0); fe_sq(t1, t0); for (i = 1; i < 5; ++i) { fe_sq(t1, t1); } fe_mul(t0, t1, t0); fe_sq(t1, t0); for (i = 1; i < 10; ++i) { fe_sq(t1, t1); } fe_mul(t1, t1, t0); fe_sq(t2, t1); for (i = 1; i < 20; ++i) { fe_sq(t2, t2); } fe_mul(t1, t2, t1); fe_sq(t1, t1); for (i = 1; i < 10; ++i) { fe_sq(t1, t1); } fe_mul(t0, t1, t0); fe_sq(t1, t0); for (i = 1; i < 50; ++i) { fe_sq(t1, t1); } fe_mul(t1, t1, t0); fe_sq(t2, t1); for (i = 1; i < 100; ++i) { fe_sq(t2, t2); } fe_mul(t1, t2, t1); fe_sq(t1, t1); for (i = 1; i < 50; ++i) { fe_sq(t1, t1); } fe_mul(t0, t1, t0); fe_sq(t0, t0); fe_sq(t0, t0); fe_mul(out, t0, 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. */ 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; } /* r = p + q */ void ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) { fe t0; fe_add(r->X, p->Y, p->X); fe_sub(r->Y, p->Y, p->X); fe_mul(r->Z, r->X, q->YplusX); fe_mul(r->Y, r->Y, q->YminusX); fe_mul(r->T, q->T2d, p->T); fe_mul(r->X, p->Z, q->Z); fe_add(t0, r->X, r->X); fe_sub(r->X, r->Z, r->Y); fe_add(r->Y, r->Z, r->Y); fe_add(r->Z, t0, r->T); fe_sub(r->T, t0, r->T); } static void slide(signed char *r, const unsigned char *a) { int i; int b; int k; int ribs; int cmp; 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]) { ribs = r[i + b] << b; cmp = r[i] + ribs; if (cmp <= 15) { r[i] = cmp; r[i + b] = 0; } else { cmp = r[i] - ribs; if (cmp >= -15) { r[i] = cmp; for (k = i + b; k < 256; ++k) { if (!r[k]) { r[k] = 1; break; } r[k] = 0; } } else { break; } } } } } } } static const ge_precomp Bi[8] = { #include "base2.h" }; /* 37095705934669439343138083508754565189542113879843219016388785533085940283555 */ static const fe d = { -10913610, 13857413, -15372611, 6949391, 114729, -8787816, -6275908, -3247719, -18696448, -12055116 }; /* sqrt(-1) */ static const fe sqrtm1 = { -32595792, -7943725, 9377950, 3500415, 12389472, -272473, -25146209, -2005654, 326686, 11406482 }; int ge_frombytes_negate_vartime(ge_p3 *h, const unsigned char *s) { fe u; fe v; fe v3; fe vxx; fe check; fe_frombytes(h->Y, s); fe_1(h->Z); fe_sq(u, h->Y); fe_mul(v, u, d); fe_sub(u, u, h->Z); /* u = y^2-1 */ fe_add(v, v, h->Z); /* v = dy^2+1 */ fe_sq(v3, v); fe_mul(v3, v3, v); /* v3 = v^3 */ fe_sq(h->X, v3); fe_mul(h->X, h->X, v); fe_mul(h->X, h->X, u); /* x = uv^7 */ fe_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */ fe_mul(h->X, h->X, v3); fe_mul(h->X, h->X, u); /* x = uv^3(uv^7)^((q-5)/8) */ fe_sq(vxx, h->X); fe_mul(vxx, vxx, v); fe_sub(check, vxx, u); /* vx^2-u */ if (fe_isnonzero(check)) { fe_add(check, vxx, u); /* vx^2+u */ if (fe_isnonzero(check)) { return -1; } fe_mul(h->X, h->X, sqrtm1); } if (fe_isnegative(h->X) == (s[31] >> 7)) { fe_neg(h->X, h->X); } fe_mul(h->T, h->X, h->Y); return 0; } /* r = p + q */ void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) { fe t0; fe_add(r->X, p->Y, p->X); fe_sub(r->Y, p->Y, p->X); fe_mul(r->Z, r->X, q->yplusx); fe_mul(r->Y, r->Y, q->yminusx); fe_mul(r->T, q->xy2d, p->T); fe_add(t0, p->Z, p->Z); fe_sub(r->X, r->Z, r->Y); fe_add(r->Y, r->Z, r->Y); fe_add(r->Z, t0, r->T); fe_sub(r->T, t0, r->T); } /* r = p - q */ void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) { fe t0; fe_add(r->X, p->Y, p->X); fe_sub(r->Y, p->Y, p->X); fe_mul(r->Z, r->X, q->yminusx); fe_mul(r->Y, r->Y, q->yplusx); fe_mul(r->T, q->xy2d, p->T); fe_add(t0, p->Z, p->Z); fe_sub(r->X, r->Z, r->Y); fe_add(r->Y, r->Z, r->Y); fe_sub(r->Z, t0, r->T); fe_add(r->T, t0, r->T); } /* r = p */ 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); } /* 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); } void ge_p2_0(ge_p2 *h) { fe_0(h->X); fe_1(h->Y); fe_1(h->Z); } /* r = 2 * p */ void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p) { fe t0; fe_sq(r->X, p->X); fe_sq(r->Z, p->Y); fe_sq2(r->T, p->Z); fe_add(r->Y, p->X, p->Y); fe_sq(t0, r->Y); fe_add(r->Y, r->Z, r->X); fe_sub(r->Z, r->Z, r->X); fe_sub(r->X, t0, r->Y); fe_sub(r->T, r->T, r->Z); } void ge_p3_0(ge_p3 *h) { fe_0(h->X); fe_1(h->Y); fe_1(h->Z); fe_0(h->T); } /* r = p */ /* 2 * d = * 16295367250680780974490674513165176452449235426866156013048779062215315747161 */ static const fe d2 = { -21827239, -5839606, -30745221, 13898782, 229458, 15978800, -12551817, -6495438, 29715968, 9444199 }; 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); } /* 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); } void ge_p3_tobytes(unsigned char *s, const ge_p3 *h) { fe recip; fe x; fe y; fe_invert(recip, h->Z); fe_mul(x, h->X, recip); fe_mul(y, h->Y, recip); fe_tobytes(s, y); s[31] ^= fe_isnegative(x) << 7; } /* 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); } void ge_precomp_0(ge_precomp *h) { 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; } 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; } 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); } /* base[i][j] = (j+1)*256^i*B */ static const ge_precomp base[32][8] = { #include "base.h" }; 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_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 */ void ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) { fe t0; fe_add(r->X, p->Y, p->X); fe_sub(r->Y, p->Y, p->X); fe_mul(r->Z, r->X, q->YminusX); fe_mul(r->Y, r->Y, q->YplusX); fe_mul(r->T, q->T2d, p->T); fe_mul(r->X, p->Z, q->Z); fe_add(t0, r->X, r->X); fe_sub(r->X, r->Z, r->Y); fe_add(r->Y, r->Z, r->Y); fe_sub(r->Z, t0, r->T); fe_add(r->T, t0, r->T); } void ge_tobytes(unsigned char *s, const ge_p2 *h) { fe recip; fe x; fe y; fe_invert(recip, h->Z); fe_mul(x, h->X, recip); fe_mul(y, h->Y, recip); fe_tobytes(s, y); s[31] ^= fe_isnegative(x) << 7; } /* 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. */ void ge_double_scalarmult_vartime(ge_p2 *r, const unsigned char *a, const ge_p3 *A, const unsigned char *b) { signed char aslide[256]; signed char bslide[256]; ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */ ge_p1p1 t; ge_p3 u; ge_p3 A2; int i; slide(aslide, a); slide(bslide, b); ge_p3_to_cached(&Ai[0], A); ge_p3_dbl(&t, A); ge_p1p1_to_p3(&A2, &t); ge_add(&t, &A2, &Ai[0]); ge_p1p1_to_p3(&u, &t); ge_p3_to_cached(&Ai[1], &u); ge_add(&t, &A2, &Ai[1]); ge_p1p1_to_p3(&u, &t); ge_p3_to_cached(&Ai[2], &u); ge_add(&t, &A2, &Ai[2]); ge_p1p1_to_p3(&u, &t); ge_p3_to_cached(&Ai[3], &u); ge_add(&t, &A2, &Ai[3]); ge_p1p1_to_p3(&u, &t); ge_p3_to_cached(&Ai[4], &u); ge_add(&t, &A2, &Ai[4]); ge_p1p1_to_p3(&u, &t); ge_p3_to_cached(&Ai[5], &u); ge_add(&t, &A2, &Ai[5]); ge_p1p1_to_p3(&u, &t); ge_p3_to_cached(&Ai[6], &u); ge_add(&t, &A2, &Ai[6]); ge_p1p1_to_p3(&u, &t); ge_p3_to_cached(&Ai[7], &u); ge_p2_0(r); for (i = 255; i >= 0; --i) { if (aslide[i] || bslide[i]) break; } for (; i >= 0; --i) { ge_p2_dbl(&t, r); if (aslide[i] > 0) { ge_p1p1_to_p3(&u, &t); ge_add(&t, &u, &Ai[aslide[i] / 2]); } else if (aslide[i] < 0) { ge_p1p1_to_p3(&u, &t); ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]); } if (bslide[i] > 0) { ge_p1p1_to_p3(&u, &t); ge_madd(&t, &u, &Bi[bslide[i] / 2]); } else if (bslide[i] < 0) { ge_p1p1_to_p3(&u, &t); ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]); } ge_p1p1_to_p2(r, &t); } } 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; 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_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]); } 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; 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 */ 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); 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. */ void sc_muladd(unsigned char *s, const unsigned char *a, const unsigned char *b, const unsigned char *c) { int64_t a0 = 2097151 & load_3(a); int64_t a1 = 2097151 & (load_4(a + 2) >> 5); int64_t a2 = 2097151 & (load_3(a + 5) >> 2); int64_t a3 = 2097151 & (load_4(a + 7) >> 7); int64_t a4 = 2097151 & (load_4(a + 10) >> 4); int64_t a5 = 2097151 & (load_3(a + 13) >> 1); int64_t a6 = 2097151 & (load_4(a + 15) >> 6); int64_t a7 = 2097151 & (load_3(a + 18) >> 3); int64_t a8 = 2097151 & load_3(a + 21); int64_t a9 = 2097151 & (load_4(a + 23) >> 5); int64_t a10 = 2097151 & (load_3(a + 26) >> 2); int64_t a11 = (load_4(a + 28) >> 7); int64_t b0 = 2097151 & load_3(b); int64_t b1 = 2097151 & (load_4(b + 2) >> 5); int64_t b2 = 2097151 & (load_3(b + 5) >> 2); int64_t b3 = 2097151 & (load_4(b + 7) >> 7); int64_t b4 = 2097151 & (load_4(b + 10) >> 4); int64_t b5 = 2097151 & (load_3(b + 13) >> 1); int64_t b6 = 2097151 & (load_4(b + 15) >> 6); int64_t b7 = 2097151 & (load_3(b + 18) >> 3); int64_t b8 = 2097151 & load_3(b + 21); int64_t b9 = 2097151 & (load_4(b + 23) >> 5); int64_t b10 = 2097151 & (load_3(b + 26) >> 2); int64_t b11 = (load_4(b + 28) >> 7); int64_t c0 = 2097151 & load_3(c); int64_t c1 = 2097151 & (load_4(c + 2) >> 5); int64_t c2 = 2097151 & (load_3(c + 5) >> 2); int64_t c3 = 2097151 & (load_4(c + 7) >> 7); int64_t c4 = 2097151 & (load_4(c + 10) >> 4); int64_t c5 = 2097151 & (load_3(c + 13) >> 1); int64_t c6 = 2097151 & (load_4(c + 15) >> 6); int64_t c7 = 2097151 & (load_3(c + 18) >> 3); int64_t c8 = 2097151 & load_3(c + 21); int64_t c9 = 2097151 & (load_4(c + 23) >> 5); int64_t c10 = 2097151 & (load_3(c + 26) >> 2); int64_t c11 = (load_4(c + 28) >> 7); int64_t s0; int64_t s1; int64_t s2; int64_t s3; int64_t s4; int64_t s5; int64_t s6; int64_t s7; int64_t s8; int64_t s9; int64_t s10; int64_t s11; int64_t s12; int64_t s13; int64_t s14; int64_t s15; int64_t s16; int64_t s17; int64_t s18; int64_t s19; int64_t s20; int64_t s21; int64_t s22; int64_t s23; int64_t carry0; int64_t carry1; int64_t carry2; int64_t carry3; int64_t carry4; int64_t carry5; int64_t carry6; int64_t carry7; int64_t carry8; int64_t carry9; int64_t carry10; int64_t carry11; int64_t carry12; int64_t carry13; int64_t carry14; int64_t carry15; int64_t carry16; int64_t carry17; int64_t carry18; int64_t carry19; int64_t carry20; int64_t carry21; int64_t carry22; s0 = c0 + a0 * b0; s1 = c1 + a0 * b1 + a1 * b0; s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0; s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0; s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0; s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0; s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0; s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 + a6 * b1 + a7 * b0; s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 + a6 * b2 + a7 * b1 + a8 * b0; s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 + a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0; s10 = c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 + a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0; s11 = c11 + a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 + a6 * b5 + a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0; s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 + a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1; s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 + a9 * b4 + a10 * b3 + a11 * b2; s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 + a10 * b4 + a11 * b3; s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 + a11 * b4; s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5; s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6; s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7; s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8; s20 = a9 * b11 + a10 * b10 + a11 * b9; s21 = a10 * b11 + a11 * b10; s22 = a11 * b11; s23 = 0; carry0 = (s0 + (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); 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; 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; 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; 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); 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; 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; 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; 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); 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); 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); 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. */ void sc_reduce(unsigned char *s) { int64_t s0 = 2097151 & load_3(s); int64_t s1 = 2097151 & (load_4(s + 2) >> 5); int64_t s2 = 2097151 & (load_3(s + 5) >> 2); int64_t s3 = 2097151 & (load_4(s + 7) >> 7); int64_t s4 = 2097151 & (load_4(s + 10) >> 4); int64_t s5 = 2097151 & (load_3(s + 13) >> 1); int64_t s6 = 2097151 & (load_4(s + 15) >> 6); int64_t s7 = 2097151 & (load_3(s + 18) >> 3); int64_t s8 = 2097151 & load_3(s + 21); int64_t s9 = 2097151 & (load_4(s + 23) >> 5); int64_t s10 = 2097151 & (load_3(s + 26) >> 2); int64_t s11 = 2097151 & (load_4(s + 28) >> 7); int64_t s12 = 2097151 & (load_4(s + 31) >> 4); int64_t s13 = 2097151 & (load_3(s + 34) >> 1); int64_t s14 = 2097151 & (load_4(s + 36) >> 6); int64_t s15 = 2097151 & (load_3(s + 39) >> 3); int64_t s16 = 2097151 & load_3(s + 42); int64_t s17 = 2097151 & (load_4(s + 44) >> 5); int64_t s18 = 2097151 & (load_3(s + 47) >> 2); int64_t s19 = 2097151 & (load_4(s + 49) >> 7); int64_t s20 = 2097151 & (load_4(s + 52) >> 4); int64_t s21 = 2097151 & (load_3(s + 55) >> 1); int64_t s22 = 2097151 & (load_4(s + 57) >> 6); int64_t s23 = (load_4(s + 60) >> 3); int64_t carry0; int64_t carry1; int64_t carry2; int64_t carry3; int64_t carry4; int64_t carry5; int64_t carry6; int64_t carry7; int64_t carry8; int64_t carry9; int64_t carry10; int64_t carry11; int64_t carry12; int64_t carry13; int64_t carry14; int64_t carry15; int64_t carry16; s11 += s23 * 666643; s12 += s23 * 470296; s13 += s23 * 654183; s14 -= s23 * 997805; s15 += s23 * 136657; s16 -= s23 * 683901; 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; 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; 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); 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; 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; 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; 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); 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; 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; 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; }