#include "fixedint.h" #include "fe.h" #ifndef ED25519_LOAD_BYTES #define ED25519_LOAD_BYTES /* helper functions */ static uint64_t load_3(const unsigned char *in) { uint64_t result; result = (uint64_t) in[0]; result |= ((uint64_t) in[1]) << 8; result |= ((uint64_t) in[2]) << 16; return result; } static uint64_t load_4(const unsigned char *in) { uint64_t result; result = (uint64_t) in[0]; result |= ((uint64_t) in[1]) << 8; result |= ((uint64_t) in[2]) << 16; result |= ((uint64_t) in[3]) << 24; return result; } #endif /* h = 0 */ void fe_0(fe h) { h[0] = 0; h[1] = 0; h[2] = 0; h[3] = 0; h[4] = 0; h[5] = 0; h[6] = 0; h[7] = 0; h[8] = 0; h[9] = 0; } /* h = 1 */ void fe_1(fe h) { h[0] = 1; h[1] = 0; h[2] = 0; h[3] = 0; h[4] = 0; h[5] = 0; h[6] = 0; h[7] = 0; h[8] = 0; h[9] = 0; } /* h = f + g Can overlap h with f or g. Preconditions: |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. Postconditions: |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ void fe_add(fe h, const fe f, const fe g) { int32_t f0 = f[0]; int32_t f1 = f[1]; int32_t f2 = f[2]; int32_t f3 = f[3]; int32_t f4 = f[4]; int32_t f5 = f[5]; int32_t f6 = f[6]; int32_t f7 = f[7]; int32_t f8 = f[8]; int32_t f9 = f[9]; int32_t g0 = g[0]; int32_t g1 = g[1]; int32_t g2 = g[2]; int32_t g3 = g[3]; int32_t g4 = g[4]; int32_t g5 = g[5]; int32_t g6 = g[6]; int32_t g7 = g[7]; int32_t g8 = g[8]; int32_t g9 = g[9]; int32_t h0 = f0 + g0; int32_t h1 = f1 + g1; int32_t h2 = f2 + g2; int32_t h3 = f3 + g3; int32_t h4 = f4 + g4; int32_t h5 = f5 + g5; int32_t h6 = f6 + g6; int32_t h7 = f7 + g7; int32_t h8 = f8 + g8; int32_t h9 = f9 + g9; h[0] = h0; h[1] = h1; h[2] = h2; h[3] = h3; h[4] = h4; h[5] = h5; h[6] = h6; h[7] = h7; h[8] = h8; h[9] = h9; } /* Replace (f,g) with (g,g) if b == 1; replace (f,g) with (f,g) if b == 0. Preconditions: b in {0,1}. */ void fe_cmov(fe f, const fe g, unsigned int b) { int32_t f0 = f[0]; int32_t f1 = f[1]; int32_t f2 = f[2]; int32_t f3 = f[3]; int32_t f4 = f[4]; int32_t f5 = f[5]; int32_t f6 = f[6]; int32_t f7 = f[7]; int32_t f8 = f[8]; int32_t f9 = f[9]; int32_t g0 = g[0]; int32_t g1 = g[1]; int32_t g2 = g[2]; int32_t g3 = g[3]; int32_t g4 = g[4]; int32_t g5 = g[5]; int32_t g6 = g[6]; int32_t g7 = g[7]; int32_t g8 = g[8]; int32_t g9 = g[9]; int32_t x0 = f0 ^ g0; int32_t x1 = f1 ^ g1; int32_t x2 = f2 ^ g2; int32_t x3 = f3 ^ g3; int32_t x4 = f4 ^ g4; int32_t x5 = f5 ^ g5; int32_t x6 = f6 ^ g6; int32_t x7 = f7 ^ g7; int32_t x8 = f8 ^ g8; int32_t x9 = f9 ^ g9; b = (unsigned int) (- (int) b); /* silence warning */ x0 &= b; x1 &= b; x2 &= b; x3 &= b; x4 &= b; x5 &= b; x6 &= b; x7 &= b; x8 &= b; x9 &= b; f[0] = f0 ^ x0; f[1] = f1 ^ x1; f[2] = f2 ^ x2; f[3] = f3 ^ x3; f[4] = f4 ^ x4; f[5] = f5 ^ x5; f[6] = f6 ^ x6; f[7] = f7 ^ x7; f[8] = f8 ^ x8; f[9] = f9 ^ x9; } /* Replace (f,g) with (g,f) if b == 1; replace (f,g) with (f,g) if b == 0. Preconditions: b in {0,1}. */ void fe_cswap(fe f,fe g,unsigned int b) { int32_t f0 = f[0]; int32_t f1 = f[1]; int32_t f2 = f[2]; int32_t f3 = f[3]; int32_t f4 = f[4]; int32_t f5 = f[5]; int32_t f6 = f[6]; int32_t f7 = f[7]; int32_t f8 = f[8]; int32_t f9 = f[9]; int32_t g0 = g[0]; int32_t g1 = g[1]; int32_t g2 = g[2]; int32_t g3 = g[3]; int32_t g4 = g[4]; int32_t g5 = g[5]; int32_t g6 = g[6]; int32_t g7 = g[7]; int32_t g8 = g[8]; int32_t g9 = g[9]; int32_t x0 = f0 ^ g0; int32_t x1 = f1 ^ g1; int32_t x2 = f2 ^ g2; int32_t x3 = f3 ^ g3; int32_t x4 = f4 ^ g4; int32_t x5 = f5 ^ g5; int32_t x6 = f6 ^ g6; int32_t x7 = f7 ^ g7; int32_t x8 = f8 ^ g8; int32_t x9 = f9 ^ g9; b = -b; x0 &= b; x1 &= b; x2 &= b; x3 &= b; x4 &= b; x5 &= b; x6 &= b; x7 &= b; x8 &= b; x9 &= b; f[0] = f0 ^ x0; f[1] = f1 ^ x1; f[2] = f2 ^ x2; f[3] = f3 ^ x3; f[4] = f4 ^ x4; f[5] = f5 ^ x5; f[6] = f6 ^ x6; f[7] = f7 ^ x7; f[8] = f8 ^ x8; f[9] = f9 ^ x9; g[0] = g0 ^ x0; g[1] = g1 ^ x1; g[2] = g2 ^ x2; g[3] = g3 ^ x3; g[4] = g4 ^ x4; g[5] = g5 ^ x5; g[6] = g6 ^ x6; g[7] = g7 ^ x7; g[8] = g8 ^ x8; g[9] = g9 ^ x9; } /* h = f */ void fe_copy(fe h, const fe f) { int32_t f0 = f[0]; int32_t f1 = f[1]; int32_t f2 = f[2]; int32_t f3 = f[3]; int32_t f4 = f[4]; int32_t f5 = f[5]; int32_t f6 = f[6]; int32_t f7 = f[7]; int32_t f8 = f[8]; int32_t f9 = f[9]; h[0] = f0; h[1] = f1; h[2] = f2; h[3] = f3; h[4] = f4; h[5] = f5; h[6] = f6; h[7] = f7; h[8] = f8; h[9] = f9; } /* Ignores top bit of h. */ void fe_frombytes(fe h, const unsigned char *s) { int64_t h0 = load_4(s); int64_t h1 = load_3(s + 4) << 6; int64_t h2 = load_3(s + 7) << 5; int64_t h3 = load_3(s + 10) << 3; int64_t h4 = load_3(s + 13) << 2; int64_t h5 = load_4(s + 16); int64_t h6 = load_3(s + 20) << 7; int64_t h7 = load_3(s + 23) << 5; int64_t h8 = load_3(s + 26) << 4; int64_t h9 = (load_3(s + 29) & 8388607) << 2; int64_t carry0; int64_t carry1; int64_t carry2; int64_t carry3; int64_t carry4; int64_t carry5; int64_t carry6; int64_t carry7; int64_t carry8; int64_t carry9; carry9 = (h9 + (int64_t) (1 << 24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25; carry1 = (h1 + (int64_t) (1 << 24)) >> 25; h2 += carry1; h1 -= carry1 << 25; carry3 = (h3 + (int64_t) (1 << 24)) >> 25; h4 += carry3; h3 -= carry3 << 25; carry5 = (h5 + (int64_t) (1 << 24)) >> 25; h6 += carry5; h5 -= carry5 << 25; carry7 = (h7 + (int64_t) (1 << 24)) >> 25; h8 += carry7; h7 -= carry7 << 25; carry0 = (h0 + (int64_t) (1 << 25)) >> 26; h1 += carry0; h0 -= carry0 << 26; carry2 = (h2 + (int64_t) (1 << 25)) >> 26; h3 += carry2; h2 -= carry2 << 26; carry4 = (h4 + (int64_t) (1 << 25)) >> 26; h5 += carry4; h4 -= carry4 << 26; carry6 = (h6 + (int64_t) (1 << 25)) >> 26; h7 += carry6; h6 -= carry6 << 26; carry8 = (h8 + (int64_t) (1 << 25)) >> 26; h9 += carry8; h8 -= carry8 << 26; h[0] = (int32_t) h0; h[1] = (int32_t) h1; h[2] = (int32_t) h2; h[3] = (int32_t) h3; h[4] = (int32_t) h4; h[5] = (int32_t) h5; h[6] = (int32_t) h6; h[7] = (int32_t) h7; h[8] = (int32_t) h8; h[9] = (int32_t) h9; } void fe_invert(fe out, const fe z) { fe t0; fe t1; fe t2; fe t3; int i; fe_sq(t0, z); for (i = 1; i < 1; ++i) { fe_sq(t0, t0); } fe_sq(t1, t0); for (i = 1; i < 2; ++i) { fe_sq(t1, t1); } fe_mul(t1, z, t1); fe_mul(t0, t0, t1); fe_sq(t2, t0); for (i = 1; i < 1; ++i) { fe_sq(t2, t2); } fe_mul(t1, t1, t2); fe_sq(t2, t1); for (i = 1; i < 5; ++i) { fe_sq(t2, t2); } fe_mul(t1, t2, t1); fe_sq(t2, t1); for (i = 1; i < 10; ++i) { fe_sq(t2, t2); } fe_mul(t2, t2, t1); fe_sq(t3, t2); for (i = 1; i < 20; ++i) { fe_sq(t3, t3); } fe_mul(t2, t3, t2); fe_sq(t2, t2); for (i = 1; i < 10; ++i) { fe_sq(t2, t2); } fe_mul(t1, t2, t1); fe_sq(t2, t1); for (i = 1; i < 50; ++i) { fe_sq(t2, t2); } fe_mul(t2, t2, t1); fe_sq(t3, t2); for (i = 1; i < 100; ++i) { fe_sq(t3, t3); } fe_mul(t2, t3, t2); fe_sq(t2, t2); for (i = 1; i < 50; ++i) { fe_sq(t2, t2); } fe_mul(t1, t2, t1); fe_sq(t1, t1); for (i = 1; i < 5; ++i) { fe_sq(t1, t1); } fe_mul(out, t1, t0); } /* return 1 if f is in {1,3,5,...,q-2} return 0 if f is in {0,2,4,...,q-1} Preconditions: |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ int fe_isnegative(const fe f) { unsigned char s[32]; fe_tobytes(s, f); return s[0] & 1; } /* return 1 if f == 0 return 0 if f != 0 Preconditions: |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ int fe_isnonzero(const fe f) { unsigned char s[32]; unsigned char r; fe_tobytes(s, f); r = s[0]; #define F(i) r |= s[i] F(1); F(2); F(3); F(4); F(5); F(6); F(7); F(8); F(9); F(10); F(11); F(12); F(13); F(14); F(15); F(16); F(17); F(18); F(19); F(20); F(21); F(22); F(23); F(24); F(25); F(26); F(27); F(28); F(29); F(30); F(31); #undef F return r != 0; } /* h = f * g Can overlap h with f or g. Preconditions: |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. Postconditions: |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. */ /* Notes on implementation strategy: Using schoolbook multiplication. Karatsuba would save a little in some cost models. Most multiplications by 2 and 19 are 32-bit precomputations; cheaper than 64-bit postcomputations. There is one remaining multiplication by 19 in the carry chain; one *19 precomputation can be merged into this, but the resulting data flow is considerably less clean. There are 12 carries below. 10 of them are 2-way parallelizable and vectorizable. Can get away with 11 carries, but then data flow is much deeper. With tighter constraints on inputs can squeeze carries into int32. */ void fe_mul(fe h, const fe f, const fe g) { int32_t f0 = f[0]; int32_t f1 = f[1]; int32_t f2 = f[2]; int32_t f3 = f[3]; int32_t f4 = f[4]; int32_t f5 = f[5]; int32_t f6 = f[6]; int32_t f7 = f[7]; int32_t f8 = f[8]; int32_t f9 = f[9]; int32_t g0 = g[0]; int32_t g1 = g[1]; int32_t g2 = g[2]; int32_t g3 = g[3]; int32_t g4 = g[4]; int32_t g5 = g[5]; int32_t g6 = g[6]; int32_t g7 = g[7]; int32_t g8 = g[8]; int32_t g9 = g[9]; int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */ int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */ int32_t g3_19 = 19 * g3; int32_t g4_19 = 19 * g4; int32_t g5_19 = 19 * g5; int32_t g6_19 = 19 * g6; int32_t g7_19 = 19 * g7; int32_t g8_19 = 19 * g8; int32_t g9_19 = 19 * g9; int32_t f1_2 = 2 * f1; int32_t f3_2 = 2 * f3; int32_t f5_2 = 2 * f5; int32_t f7_2 = 2 * f7; int32_t f9_2 = 2 * f9; int64_t f0g0 = f0 * (int64_t) g0; int64_t f0g1 = f0 * (int64_t) g1; int64_t f0g2 = f0 * (int64_t) g2; int64_t f0g3 = f0 * (int64_t) g3; int64_t f0g4 = f0 * (int64_t) g4; int64_t f0g5 = f0 * (int64_t) g5; int64_t f0g6 = f0 * (int64_t) g6; int64_t f0g7 = f0 * (int64_t) g7; int64_t f0g8 = f0 * (int64_t) g8; int64_t f0g9 = f0 * (int64_t) g9; int64_t f1g0 = f1 * (int64_t) g0; int64_t f1g1_2 = f1_2 * (int64_t) g1; int64_t f1g2 = f1 * (int64_t) g2; int64_t f1g3_2 = f1_2 * (int64_t) g3; int64_t f1g4 = f1 * (int64_t) g4; int64_t f1g5_2 = f1_2 * (int64_t) g5; int64_t f1g6 = f1 * (int64_t) g6; int64_t f1g7_2 = f1_2 * (int64_t) g7; int64_t f1g8 = f1 * (int64_t) g8; int64_t f1g9_38 = f1_2 * (int64_t) g9_19; int64_t f2g0 = f2 * (int64_t) g0; int64_t f2g1 = f2 * (int64_t) g1; int64_t f2g2 = f2 * (int64_t) g2; int64_t f2g3 = f2 * (int64_t) g3; int64_t f2g4 = f2 * (int64_t) g4; int64_t f2g5 = f2 * (int64_t) g5; int64_t f2g6 = f2 * (int64_t) g6; int64_t f2g7 = f2 * (int64_t) g7; int64_t f2g8_19 = f2 * (int64_t) g8_19; int64_t f2g9_19 = f2 * (int64_t) g9_19; int64_t f3g0 = f3 * (int64_t) g0; int64_t f3g1_2 = f3_2 * (int64_t) g1; int64_t f3g2 = f3 * (int64_t) g2; int64_t f3g3_2 = f3_2 * (int64_t) g3; int64_t f3g4 = f3 * (int64_t) g4; int64_t f3g5_2 = f3_2 * (int64_t) g5; int64_t f3g6 = f3 * (int64_t) g6; int64_t f3g7_38 = f3_2 * (int64_t) g7_19; int64_t f3g8_19 = f3 * (int64_t) g8_19; int64_t f3g9_38 = f3_2 * (int64_t) g9_19; int64_t f4g0 = f4 * (int64_t) g0; int64_t f4g1 = f4 * (int64_t) g1; int64_t f4g2 = f4 * (int64_t) g2; int64_t f4g3 = f4 * (int64_t) g3; int64_t f4g4 = f4 * (int64_t) g4; int64_t f4g5 = f4 * (int64_t) g5; int64_t f4g6_19 = f4 * (int64_t) g6_19; int64_t f4g7_19 = f4 * (int64_t) g7_19; int64_t f4g8_19 = f4 * (int64_t) g8_19; int64_t f4g9_19 = f4 * (int64_t) g9_19; int64_t f5g0 = f5 * (int64_t) g0; int64_t f5g1_2 = f5_2 * (int64_t) g1; int64_t f5g2 = f5 * (int64_t) g2; int64_t f5g3_2 = f5_2 * (int64_t) g3; int64_t f5g4 = f5 * (int64_t) g4; int64_t f5g5_38 = f5_2 * (int64_t) g5_19; int64_t f5g6_19 = f5 * (int64_t) g6_19; int64_t f5g7_38 = f5_2 * (int64_t) g7_19; int64_t f5g8_19 = f5 * (int64_t) g8_19; int64_t f5g9_38 = f5_2 * (int64_t) g9_19; int64_t f6g0 = f6 * (int64_t) g0; int64_t f6g1 = f6 * (int64_t) g1; int64_t f6g2 = f6 * (int64_t) g2; int64_t f6g3 = f6 * (int64_t) g3; int64_t f6g4_19 = f6 * (int64_t) g4_19; int64_t f6g5_19 = f6 * (int64_t) g5_19; int64_t f6g6_19 = f6 * (int64_t) g6_19; int64_t f6g7_19 = f6 * (int64_t) g7_19; int64_t f6g8_19 = f6 * (int64_t) g8_19; int64_t f6g9_19 = f6 * (int64_t) g9_19; int64_t f7g0 = f7 * (int64_t) g0; int64_t f7g1_2 = f7_2 * (int64_t) g1; int64_t f7g2 = f7 * (int64_t) g2; int64_t f7g3_38 = f7_2 * (int64_t) g3_19; int64_t f7g4_19 = f7 * (int64_t) g4_19; int64_t f7g5_38 = f7_2 * (int64_t) g5_19; int64_t f7g6_19 = f7 * (int64_t) g6_19; int64_t f7g7_38 = f7_2 * (int64_t) g7_19; int64_t f7g8_19 = f7 * (int64_t) g8_19; int64_t f7g9_38 = f7_2 * (int64_t) g9_19; int64_t f8g0 = f8 * (int64_t) g0; int64_t f8g1 = f8 * (int64_t) g1; int64_t f8g2_19 = f8 * (int64_t) g2_19; int64_t f8g3_19 = f8 * (int64_t) g3_19; int64_t f8g4_19 = f8 * (int64_t) g4_19; int64_t f8g5_19 = f8 * (int64_t) g5_19; int64_t f8g6_19 = f8 * (int64_t) g6_19; int64_t f8g7_19 = f8 * (int64_t) g7_19; int64_t f8g8_19 = f8 * (int64_t) g8_19; int64_t f8g9_19 = f8 * (int64_t) g9_19; int64_t f9g0 = f9 * (int64_t) g0; int64_t f9g1_38 = f9_2 * (int64_t) g1_19; int64_t f9g2_19 = f9 * (int64_t) g2_19; int64_t f9g3_38 = f9_2 * (int64_t) g3_19; int64_t f9g4_19 = f9 * (int64_t) g4_19; int64_t f9g5_38 = f9_2 * (int64_t) g5_19; int64_t f9g6_19 = f9 * (int64_t) g6_19; int64_t f9g7_38 = f9_2 * (int64_t) g7_19; int64_t f9g8_19 = f9 * (int64_t) g8_19; int64_t f9g9_38 = f9_2 * (int64_t) g9_19; int64_t h0 = f0g0 + f1g9_38 + f2g8_19 + f3g7_38 + f4g6_19 + f5g5_38 + f6g4_19 + f7g3_38 + f8g2_19 + f9g1_38; int64_t h1 = f0g1 + f1g0 + f2g9_19 + f3g8_19 + f4g7_19 + f5g6_19 + f6g5_19 + f7g4_19 + f8g3_19 + f9g2_19; int64_t h2 = f0g2 + f1g1_2 + f2g0 + f3g9_38 + f4g8_19 + f5g7_38 + f6g6_19 + f7g5_38 + f8g4_19 + f9g3_38; int64_t h3 = f0g3 + f1g2 + f2g1 + f3g0 + f4g9_19 + f5g8_19 + f6g7_19 + f7g6_19 + f8g5_19 + f9g4_19; int64_t h4 = f0g4 + f1g3_2 + f2g2 + f3g1_2 + f4g0 + f5g9_38 + f6g8_19 + f7g7_38 + f8g6_19 + f9g5_38; int64_t h5 = f0g5 + f1g4 + f2g3 + f3g2 + f4g1 + f5g0 + f6g9_19 + f7g8_19 + f8g7_19 + f9g6_19; int64_t h6 = f0g6 + f1g5_2 + f2g4 + f3g3_2 + f4g2 + f5g1_2 + f6g0 + f7g9_38 + f8g8_19 + f9g7_38; int64_t h7 = f0g7 + f1g6 + f2g5 + f3g4 + f4g3 + f5g2 + f6g1 + f7g0 + f8g9_19 + f9g8_19; int64_t h8 = f0g8 + f1g7_2 + f2g6 + f3g5_2 + f4g4 + f5g3_2 + f6g2 + f7g1_2 + f8g0 + f9g9_38; int64_t h9 = f0g9 + f1g8 + f2g7 + f3g6 + f4g5 + f5g4 + f6g3 + f7g2 + f8g1 + f9g0 ; int64_t carry0; int64_t carry1; int64_t carry2; int64_t carry3; int64_t carry4; int64_t carry5; int64_t carry6; int64_t carry7; int64_t carry8; int64_t carry9; carry0 = (h0 + (int64_t) (1 << 25)) >> 26; h1 += carry0; h0 -= carry0 << 26; carry4 = (h4 + (int64_t) (1 << 25)) >> 26; h5 += carry4; h4 -= carry4 << 26; carry1 = (h1 + (int64_t) (1 << 24)) >> 25; h2 += carry1; h1 -= carry1 << 25; carry5 = (h5 + (int64_t) (1 << 24)) >> 25; h6 += carry5; h5 -= carry5 << 25; carry2 = (h2 + (int64_t) (1 << 25)) >> 26; h3 += carry2; h2 -= carry2 << 26; carry6 = (h6 + (int64_t) (1 << 25)) >> 26; h7 += carry6; h6 -= carry6 << 26; carry3 = (h3 + (int64_t) (1 << 24)) >> 25; h4 += carry3; h3 -= carry3 << 25; carry7 = (h7 + (int64_t) (1 << 24)) >> 25; h8 += carry7; h7 -= carry7 << 25; carry4 = (h4 + (int64_t) (1 << 25)) >> 26; h5 += carry4; h4 -= carry4 << 26; carry8 = (h8 + (int64_t) (1 << 25)) >> 26; h9 += carry8; h8 -= carry8 << 26; carry9 = (h9 + (int64_t) (1 << 24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25; carry0 = (h0 + (int64_t) (1 << 25)) >> 26; h1 += carry0; h0 -= carry0 << 26; h[0] = (int32_t) h0; h[1] = (int32_t) h1; h[2] = (int32_t) h2; h[3] = (int32_t) h3; h[4] = (int32_t) h4; h[5] = (int32_t) h5; h[6] = (int32_t) h6; h[7] = (int32_t) h7; h[8] = (int32_t) h8; h[9] = (int32_t) h9; } /* h = f * 121666 Can overlap h with f. Preconditions: |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. Postconditions: |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. */ void fe_mul121666(fe h, fe f) { int32_t f0 = f[0]; int32_t f1 = f[1]; int32_t f2 = f[2]; int32_t f3 = f[3]; int32_t f4 = f[4]; int32_t f5 = f[5]; int32_t f6 = f[6]; int32_t f7 = f[7]; int32_t f8 = f[8]; int32_t f9 = f[9]; int64_t h0 = f0 * (int64_t) 121666; int64_t h1 = f1 * (int64_t) 121666; int64_t h2 = f2 * (int64_t) 121666; int64_t h3 = f3 * (int64_t) 121666; int64_t h4 = f4 * (int64_t) 121666; int64_t h5 = f5 * (int64_t) 121666; int64_t h6 = f6 * (int64_t) 121666; int64_t h7 = f7 * (int64_t) 121666; int64_t h8 = f8 * (int64_t) 121666; int64_t h9 = f9 * (int64_t) 121666; int64_t carry0; int64_t carry1; int64_t carry2; int64_t carry3; int64_t carry4; int64_t carry5; int64_t carry6; int64_t carry7; int64_t carry8; int64_t carry9; carry9 = (h9 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25; carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25; carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25; carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25; carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25; carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26; carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26; carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26; h[0] = h0; h[1] = h1; h[2] = h2; h[3] = h3; h[4] = h4; h[5] = h5; h[6] = h6; h[7] = h7; h[8] = h8; h[9] = h9; } /* h = -f Preconditions: |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. Postconditions: |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. */ void fe_neg(fe h, const fe f) { int32_t f0 = f[0]; int32_t f1 = f[1]; int32_t f2 = f[2]; int32_t f3 = f[3]; int32_t f4 = f[4]; int32_t f5 = f[5]; int32_t f6 = f[6]; int32_t f7 = f[7]; int32_t f8 = f[8]; int32_t f9 = f[9]; int32_t h0 = -f0; int32_t h1 = -f1; int32_t h2 = -f2; int32_t h3 = -f3; int32_t h4 = -f4; int32_t h5 = -f5; int32_t h6 = -f6; int32_t h7 = -f7; int32_t h8 = -f8; int32_t h9 = -f9; h[0] = h0; h[1] = h1; h[2] = h2; h[3] = h3; h[4] = h4; h[5] = h5; h[6] = h6; h[7] = h7; h[8] = h8; h[9] = h9; } void fe_pow22523(fe out, const fe z) { fe t0; fe t1; fe t2; int i; fe_sq(t0, z); for (i = 1; i < 1; ++i) { fe_sq(t0, t0); } fe_sq(t1, t0); for (i = 1; i < 2; ++i) { fe_sq(t1, t1); } fe_mul(t1, z, t1); fe_mul(t0, t0, t1); fe_sq(t0, t0); for (i = 1; i < 1; ++i) { fe_sq(t0, t0); } fe_mul(t0, t1, t0); fe_sq(t1, t0); for (i = 1; i < 5; ++i) { fe_sq(t1, t1); } fe_mul(t0, t1, t0); fe_sq(t1, t0); for (i = 1; i < 10; ++i) { fe_sq(t1, t1); } fe_mul(t1, t1, t0); fe_sq(t2, t1); for (i = 1; i < 20; ++i) { fe_sq(t2, t2); } fe_mul(t1, t2, t1); fe_sq(t1, t1); for (i = 1; i < 10; ++i) { fe_sq(t1, t1); } fe_mul(t0, t1, t0); fe_sq(t1, t0); for (i = 1; i < 50; ++i) { fe_sq(t1, t1); } fe_mul(t1, t1, t0); fe_sq(t2, t1); for (i = 1; i < 100; ++i) { fe_sq(t2, t2); } fe_mul(t1, t2, t1); fe_sq(t1, t1); for (i = 1; i < 50; ++i) { fe_sq(t1, t1); } fe_mul(t0, t1, t0); fe_sq(t0, t0); for (i = 1; i < 2; ++i) { fe_sq(t0, t0); } fe_mul(out, t0, z); return; } /* h = f * f Can overlap h with f. Preconditions: |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. Postconditions: |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. */ /* See fe_mul.c for discussion of implementation strategy. */ void fe_sq(fe h, const fe f) { int32_t f0 = f[0]; int32_t f1 = f[1]; int32_t f2 = f[2]; int32_t f3 = f[3]; int32_t f4 = f[4]; int32_t f5 = f[5]; int32_t f6 = f[6]; int32_t f7 = f[7]; int32_t f8 = f[8]; int32_t f9 = f[9]; int32_t f0_2 = 2 * f0; int32_t f1_2 = 2 * f1; int32_t f2_2 = 2 * f2; int32_t f3_2 = 2 * f3; int32_t f4_2 = 2 * f4; int32_t f5_2 = 2 * f5; int32_t f6_2 = 2 * f6; int32_t f7_2 = 2 * f7; int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */ int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */ int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */ int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */ int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */ int64_t f0f0 = f0 * (int64_t) f0; int64_t f0f1_2 = f0_2 * (int64_t) f1; int64_t f0f2_2 = f0_2 * (int64_t) f2; int64_t f0f3_2 = f0_2 * (int64_t) f3; int64_t f0f4_2 = f0_2 * (int64_t) f4; int64_t f0f5_2 = f0_2 * (int64_t) f5; int64_t f0f6_2 = f0_2 * (int64_t) f6; int64_t f0f7_2 = f0_2 * (int64_t) f7; int64_t f0f8_2 = f0_2 * (int64_t) f8; int64_t f0f9_2 = f0_2 * (int64_t) f9; int64_t f1f1_2 = f1_2 * (int64_t) f1; int64_t f1f2_2 = f1_2 * (int64_t) f2; int64_t f1f3_4 = f1_2 * (int64_t) f3_2; int64_t f1f4_2 = f1_2 * (int64_t) f4; int64_t f1f5_4 = f1_2 * (int64_t) f5_2; int64_t f1f6_2 = f1_2 * (int64_t) f6; int64_t f1f7_4 = f1_2 * (int64_t) f7_2; int64_t f1f8_2 = f1_2 * (int64_t) f8; int64_t f1f9_76 = f1_2 * (int64_t) f9_38; int64_t f2f2 = f2 * (int64_t) f2; int64_t f2f3_2 = f2_2 * (int64_t) f3; int64_t f2f4_2 = f2_2 * (int64_t) f4; int64_t f2f5_2 = f2_2 * (int64_t) f5; int64_t f2f6_2 = f2_2 * (int64_t) f6; int64_t f2f7_2 = f2_2 * (int64_t) f7; int64_t f2f8_38 = f2_2 * (int64_t) f8_19; int64_t f2f9_38 = f2 * (int64_t) f9_38; int64_t f3f3_2 = f3_2 * (int64_t) f3; int64_t f3f4_2 = f3_2 * (int64_t) f4; int64_t f3f5_4 = f3_2 * (int64_t) f5_2; int64_t f3f6_2 = f3_2 * (int64_t) f6; int64_t f3f7_76 = f3_2 * (int64_t) f7_38; int64_t f3f8_38 = f3_2 * (int64_t) f8_19; int64_t f3f9_76 = f3_2 * (int64_t) f9_38; int64_t f4f4 = f4 * (int64_t) f4; int64_t f4f5_2 = f4_2 * (int64_t) f5; int64_t f4f6_38 = f4_2 * (int64_t) f6_19; int64_t f4f7_38 = f4 * (int64_t) f7_38; int64_t f4f8_38 = f4_2 * (int64_t) f8_19; int64_t f4f9_38 = f4 * (int64_t) f9_38; int64_t f5f5_38 = f5 * (int64_t) f5_38; int64_t f5f6_38 = f5_2 * (int64_t) f6_19; int64_t f5f7_76 = f5_2 * (int64_t) f7_38; int64_t f5f8_38 = f5_2 * (int64_t) f8_19; int64_t f5f9_76 = f5_2 * (int64_t) f9_38; int64_t f6f6_19 = f6 * (int64_t) f6_19; int64_t f6f7_38 = f6 * (int64_t) f7_38; int64_t f6f8_38 = f6_2 * (int64_t) f8_19; int64_t f6f9_38 = f6 * (int64_t) f9_38; int64_t f7f7_38 = f7 * (int64_t) f7_38; int64_t f7f8_38 = f7_2 * (int64_t) f8_19; int64_t f7f9_76 = f7_2 * (int64_t) f9_38; int64_t f8f8_19 = f8 * (int64_t) f8_19; int64_t f8f9_38 = f8 * (int64_t) f9_38; int64_t f9f9_38 = f9 * (int64_t) f9_38; int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38; int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38; int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19; int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38; int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38; int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38; int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19; int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38; int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38; int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2; int64_t carry0; int64_t carry1; int64_t carry2; int64_t carry3; int64_t carry4; int64_t carry5; int64_t carry6; int64_t carry7; int64_t carry8; int64_t carry9; carry0 = (h0 + (int64_t) (1 << 25)) >> 26; h1 += carry0; h0 -= carry0 << 26; carry4 = (h4 + (int64_t) (1 << 25)) >> 26; h5 += carry4; h4 -= carry4 << 26; carry1 = (h1 + (int64_t) (1 << 24)) >> 25; h2 += carry1; h1 -= carry1 << 25; carry5 = (h5 + (int64_t) (1 << 24)) >> 25; h6 += carry5; h5 -= carry5 << 25; carry2 = (h2 + (int64_t) (1 << 25)) >> 26; h3 += carry2; h2 -= carry2 << 26; carry6 = (h6 + (int64_t) (1 << 25)) >> 26; h7 += carry6; h6 -= carry6 << 26; carry3 = (h3 + (int64_t) (1 << 24)) >> 25; h4 += carry3; h3 -= carry3 << 25; carry7 = (h7 + (int64_t) (1 << 24)) >> 25; h8 += carry7; h7 -= carry7 << 25; carry4 = (h4 + (int64_t) (1 << 25)) >> 26; h5 += carry4; h4 -= carry4 << 26; carry8 = (h8 + (int64_t) (1 << 25)) >> 26; h9 += carry8; h8 -= carry8 << 26; carry9 = (h9 + (int64_t) (1 << 24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25; carry0 = (h0 + (int64_t) (1 << 25)) >> 26; h1 += carry0; h0 -= carry0 << 26; h[0] = (int32_t) h0; h[1] = (int32_t) h1; h[2] = (int32_t) h2; h[3] = (int32_t) h3; h[4] = (int32_t) h4; h[5] = (int32_t) h5; h[6] = (int32_t) h6; h[7] = (int32_t) h7; h[8] = (int32_t) h8; h[9] = (int32_t) h9; } /* h = 2 * f * f Can overlap h with f. Preconditions: |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. Postconditions: |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. */ /* See fe_mul.c for discussion of implementation strategy. */ void fe_sq2(fe h, const fe f) { int32_t f0 = f[0]; int32_t f1 = f[1]; int32_t f2 = f[2]; int32_t f3 = f[3]; int32_t f4 = f[4]; int32_t f5 = f[5]; int32_t f6 = f[6]; int32_t f7 = f[7]; int32_t f8 = f[8]; int32_t f9 = f[9]; int32_t f0_2 = 2 * f0; int32_t f1_2 = 2 * f1; int32_t f2_2 = 2 * f2; int32_t f3_2 = 2 * f3; int32_t f4_2 = 2 * f4; int32_t f5_2 = 2 * f5; int32_t f6_2 = 2 * f6; int32_t f7_2 = 2 * f7; int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */ int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */ int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */ int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */ int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */ int64_t f0f0 = f0 * (int64_t) f0; int64_t f0f1_2 = f0_2 * (int64_t) f1; int64_t f0f2_2 = f0_2 * (int64_t) f2; int64_t f0f3_2 = f0_2 * (int64_t) f3; int64_t f0f4_2 = f0_2 * (int64_t) f4; int64_t f0f5_2 = f0_2 * (int64_t) f5; int64_t f0f6_2 = f0_2 * (int64_t) f6; int64_t f0f7_2 = f0_2 * (int64_t) f7; int64_t f0f8_2 = f0_2 * (int64_t) f8; int64_t f0f9_2 = f0_2 * (int64_t) f9; int64_t f1f1_2 = f1_2 * (int64_t) f1; int64_t f1f2_2 = f1_2 * (int64_t) f2; int64_t f1f3_4 = f1_2 * (int64_t) f3_2; int64_t f1f4_2 = f1_2 * (int64_t) f4; int64_t f1f5_4 = f1_2 * (int64_t) f5_2; int64_t f1f6_2 = f1_2 * (int64_t) f6; int64_t f1f7_4 = f1_2 * (int64_t) f7_2; int64_t f1f8_2 = f1_2 * (int64_t) f8; int64_t f1f9_76 = f1_2 * (int64_t) f9_38; int64_t f2f2 = f2 * (int64_t) f2; int64_t f2f3_2 = f2_2 * (int64_t) f3; int64_t f2f4_2 = f2_2 * (int64_t) f4; int64_t f2f5_2 = f2_2 * (int64_t) f5; int64_t f2f6_2 = f2_2 * (int64_t) f6; int64_t f2f7_2 = f2_2 * (int64_t) f7; int64_t f2f8_38 = f2_2 * (int64_t) f8_19; int64_t f2f9_38 = f2 * (int64_t) f9_38; int64_t f3f3_2 = f3_2 * (int64_t) f3; int64_t f3f4_2 = f3_2 * (int64_t) f4; int64_t f3f5_4 = f3_2 * (int64_t) f5_2; int64_t f3f6_2 = f3_2 * (int64_t) f6; int64_t f3f7_76 = f3_2 * (int64_t) f7_38; int64_t f3f8_38 = f3_2 * (int64_t) f8_19; int64_t f3f9_76 = f3_2 * (int64_t) f9_38; int64_t f4f4 = f4 * (int64_t) f4; int64_t f4f5_2 = f4_2 * (int64_t) f5; int64_t f4f6_38 = f4_2 * (int64_t) f6_19; int64_t f4f7_38 = f4 * (int64_t) f7_38; int64_t f4f8_38 = f4_2 * (int64_t) f8_19; int64_t f4f9_38 = f4 * (int64_t) f9_38; int64_t f5f5_38 = f5 * (int64_t) f5_38; int64_t f5f6_38 = f5_2 * (int64_t) f6_19; int64_t f5f7_76 = f5_2 * (int64_t) f7_38; int64_t f5f8_38 = f5_2 * (int64_t) f8_19; int64_t f5f9_76 = f5_2 * (int64_t) f9_38; int64_t f6f6_19 = f6 * (int64_t) f6_19; int64_t f6f7_38 = f6 * (int64_t) f7_38; int64_t f6f8_38 = f6_2 * (int64_t) f8_19; int64_t f6f9_38 = f6 * (int64_t) f9_38; int64_t f7f7_38 = f7 * (int64_t) f7_38; int64_t f7f8_38 = f7_2 * (int64_t) f8_19; int64_t f7f9_76 = f7_2 * (int64_t) f9_38; int64_t f8f8_19 = f8 * (int64_t) f8_19; int64_t f8f9_38 = f8 * (int64_t) f9_38; int64_t f9f9_38 = f9 * (int64_t) f9_38; int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38; int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38; int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19; int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38; int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38; int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38; int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19; int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38; int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38; int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2; int64_t carry0; int64_t carry1; int64_t carry2; int64_t carry3; int64_t carry4; int64_t carry5; int64_t carry6; int64_t carry7; int64_t carry8; int64_t carry9; h0 += h0; h1 += h1; h2 += h2; h3 += h3; h4 += h4; h5 += h5; h6 += h6; h7 += h7; h8 += h8; h9 += h9; carry0 = (h0 + (int64_t) (1 << 25)) >> 26; h1 += carry0; h0 -= carry0 << 26; carry4 = (h4 + (int64_t) (1 << 25)) >> 26; h5 += carry4; h4 -= carry4 << 26; carry1 = (h1 + (int64_t) (1 << 24)) >> 25; h2 += carry1; h1 -= carry1 << 25; carry5 = (h5 + (int64_t) (1 << 24)) >> 25; h6 += carry5; h5 -= carry5 << 25; carry2 = (h2 + (int64_t) (1 << 25)) >> 26; h3 += carry2; h2 -= carry2 << 26; carry6 = (h6 + (int64_t) (1 << 25)) >> 26; h7 += carry6; h6 -= carry6 << 26; carry3 = (h3 + (int64_t) (1 << 24)) >> 25; h4 += carry3; h3 -= carry3 << 25; carry7 = (h7 + (int64_t) (1 << 24)) >> 25; h8 += carry7; h7 -= carry7 << 25; carry4 = (h4 + (int64_t) (1 << 25)) >> 26; h5 += carry4; h4 -= carry4 << 26; carry8 = (h8 + (int64_t) (1 << 25)) >> 26; h9 += carry8; h8 -= carry8 << 26; carry9 = (h9 + (int64_t) (1 << 24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25; carry0 = (h0 + (int64_t) (1 << 25)) >> 26; h1 += carry0; h0 -= carry0 << 26; h[0] = (int32_t) h0; h[1] = (int32_t) h1; h[2] = (int32_t) h2; h[3] = (int32_t) h3; h[4] = (int32_t) h4; h[5] = (int32_t) h5; h[6] = (int32_t) h6; h[7] = (int32_t) h7; h[8] = (int32_t) h8; h[9] = (int32_t) h9; } /* h = f - g Can overlap h with f or g. Preconditions: |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. Postconditions: |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ void fe_sub(fe h, const fe f, const fe g) { int32_t f0 = f[0]; int32_t f1 = f[1]; int32_t f2 = f[2]; int32_t f3 = f[3]; int32_t f4 = f[4]; int32_t f5 = f[5]; int32_t f6 = f[6]; int32_t f7 = f[7]; int32_t f8 = f[8]; int32_t f9 = f[9]; int32_t g0 = g[0]; int32_t g1 = g[1]; int32_t g2 = g[2]; int32_t g3 = g[3]; int32_t g4 = g[4]; int32_t g5 = g[5]; int32_t g6 = g[6]; int32_t g7 = g[7]; int32_t g8 = g[8]; int32_t g9 = g[9]; int32_t h0 = f0 - g0; int32_t h1 = f1 - g1; int32_t h2 = f2 - g2; int32_t h3 = f3 - g3; int32_t h4 = f4 - g4; int32_t h5 = f5 - g5; int32_t h6 = f6 - g6; int32_t h7 = f7 - g7; int32_t h8 = f8 - g8; int32_t h9 = f9 - g9; h[0] = h0; h[1] = h1; h[2] = h2; h[3] = h3; h[4] = h4; h[5] = h5; h[6] = h6; h[7] = h7; h[8] = h8; h[9] = h9; } /* Preconditions: |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. Write p=2^255-19; q=floor(h/p). Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))). Proof: Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4. Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4. Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9). Then 0<y<1. Write r=h-pq. Have 0<=r<=p-1=2^255-20. Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1. Write x=r+19(2^-255)r+y. Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q. Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1)) so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q. */ void fe_tobytes(unsigned char *s, const fe h) { int32_t h0 = h[0]; int32_t h1 = h[1]; int32_t h2 = h[2]; int32_t h3 = h[3]; int32_t h4 = h[4]; int32_t h5 = h[5]; int32_t h6 = h[6]; int32_t h7 = h[7]; int32_t h8 = h[8]; int32_t h9 = h[9]; int32_t q; int32_t carry0; int32_t carry1; int32_t carry2; int32_t carry3; int32_t carry4; int32_t carry5; int32_t carry6; int32_t carry7; int32_t carry8; int32_t carry9; q = (19 * h9 + (((int32_t) 1) << 24)) >> 25; q = (h0 + q) >> 26; q = (h1 + q) >> 25; q = (h2 + q) >> 26; q = (h3 + q) >> 25; q = (h4 + q) >> 26; q = (h5 + q) >> 25; q = (h6 + q) >> 26; q = (h7 + q) >> 25; q = (h8 + q) >> 26; q = (h9 + q) >> 25; /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */ h0 += 19 * q; /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */ carry0 = h0 >> 26; h1 += carry0; h0 -= carry0 << 26; carry1 = h1 >> 25; h2 += carry1; h1 -= carry1 << 25; carry2 = h2 >> 26; h3 += carry2; h2 -= carry2 << 26; carry3 = h3 >> 25; h4 += carry3; h3 -= carry3 << 25; carry4 = h4 >> 26; h5 += carry4; h4 -= carry4 << 26; carry5 = h5 >> 25; h6 += carry5; h5 -= carry5 << 25; carry6 = h6 >> 26; h7 += carry6; h6 -= carry6 << 26; carry7 = h7 >> 25; h8 += carry7; h7 -= carry7 << 25; carry8 = h8 >> 26; h9 += carry8; h8 -= carry8 << 26; carry9 = h9 >> 25; h9 -= carry9 << 25; /* h10 = carry9 */ /* Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20. Have h0+...+2^230 h9 between 0 and 2^255-1; evidently 2^255 h10-2^255 q = 0. Goal: Output h0+...+2^230 h9. */ s[0] = (unsigned char) (h0 >> 0); s[1] = (unsigned char) (h0 >> 8); s[2] = (unsigned char) (h0 >> 16); s[3] = (unsigned char) ((h0 >> 24) | (h1 << 2)); s[4] = (unsigned char) (h1 >> 6); s[5] = (unsigned char) (h1 >> 14); s[6] = (unsigned char) ((h1 >> 22) | (h2 << 3)); s[7] = (unsigned char) (h2 >> 5); s[8] = (unsigned char) (h2 >> 13); s[9] = (unsigned char) ((h2 >> 21) | (h3 << 5)); s[10] = (unsigned char) (h3 >> 3); s[11] = (unsigned char) (h3 >> 11); s[12] = (unsigned char) ((h3 >> 19) | (h4 << 6)); s[13] = (unsigned char) (h4 >> 2); s[14] = (unsigned char) (h4 >> 10); s[15] = (unsigned char) (h4 >> 18); s[16] = (unsigned char) (h5 >> 0); s[17] = (unsigned char) (h5 >> 8); s[18] = (unsigned char) (h5 >> 16); s[19] = (unsigned char) ((h5 >> 24) | (h6 << 1)); s[20] = (unsigned char) (h6 >> 7); s[21] = (unsigned char) (h6 >> 15); s[22] = (unsigned char) ((h6 >> 23) | (h7 << 3)); s[23] = (unsigned char) (h7 >> 5); s[24] = (unsigned char) (h7 >> 13); s[25] = (unsigned char) ((h7 >> 21) | (h8 << 4)); s[26] = (unsigned char) (h8 >> 4); s[27] = (unsigned char) (h8 >> 12); s[28] = (unsigned char) ((h8 >> 20) | (h9 << 6)); s[29] = (unsigned char) (h9 >> 2); s[30] = (unsigned char) (h9 >> 10); s[31] = (unsigned char) (h9 >> 18); }