/* Public domain by Andrew M. <liquidsun@gmail.com> See: https://github.com/floodyberry/curve25519-donna 32 bit integer curve25519 implementation */ #include "ed25519-donna.h" static const uint32_t reduce_mask_25 = (1 << 25) - 1; static const uint32_t reduce_mask_26 = (1 << 26) - 1; /* out = in */ void curve25519_copy(bignum25519 out, const bignum25519 in) { out[0] = in[0]; out[1] = in[1]; out[2] = in[2]; out[3] = in[3]; out[4] = in[4]; out[5] = in[5]; out[6] = in[6]; out[7] = in[7]; out[8] = in[8]; out[9] = in[9]; } /* out = a + b */ void curve25519_add(bignum25519 out, const bignum25519 a, const bignum25519 b) { out[0] = a[0] + b[0]; out[1] = a[1] + b[1]; out[2] = a[2] + b[2]; out[3] = a[3] + b[3]; out[4] = a[4] + b[4]; out[5] = a[5] + b[5]; out[6] = a[6] + b[6]; out[7] = a[7] + b[7]; out[8] = a[8] + b[8]; out[9] = a[9] + b[9]; } void curve25519_add_after_basic(bignum25519 out, const bignum25519 a, const bignum25519 b) { uint32_t c = 0; out[0] = a[0] + b[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26; out[1] = a[1] + b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25; out[2] = a[2] + b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26; out[3] = a[3] + b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25; out[4] = a[4] + b[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26; out[5] = a[5] + b[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25; out[6] = a[6] + b[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26; out[7] = a[7] + b[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25; out[8] = a[8] + b[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26; out[9] = a[9] + b[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25; out[0] += 19 * c; } void curve25519_add_reduce(bignum25519 out, const bignum25519 a, const bignum25519 b) { uint32_t c = 0; out[0] = a[0] + b[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26; out[1] = a[1] + b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25; out[2] = a[2] + b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26; out[3] = a[3] + b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25; out[4] = a[4] + b[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26; out[5] = a[5] + b[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25; out[6] = a[6] + b[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26; out[7] = a[7] + b[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25; out[8] = a[8] + b[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26; out[9] = a[9] + b[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25; out[0] += 19 * c; } /* multiples of p */ static const uint32_t twoP0 = 0x07ffffda; static const uint32_t twoP13579 = 0x03fffffe; static const uint32_t twoP2468 = 0x07fffffe; static const uint32_t fourP0 = 0x0fffffb4; static const uint32_t fourP13579 = 0x07fffffc; static const uint32_t fourP2468 = 0x0ffffffc; /* out = a - b */ void curve25519_sub(bignum25519 out, const bignum25519 a, const bignum25519 b) { uint32_t c = 0; out[0] = twoP0 + a[0] - b[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26; out[1] = twoP13579 + a[1] - b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25; out[2] = twoP2468 + a[2] - b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26; out[3] = twoP13579 + a[3] - b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25; out[4] = twoP2468 + a[4] - b[4] + c; out[5] = twoP13579 + a[5] - b[5] ; out[6] = twoP2468 + a[6] - b[6] ; out[7] = twoP13579 + a[7] - b[7] ; out[8] = twoP2468 + a[8] - b[8] ; out[9] = twoP13579 + a[9] - b[9] ; } /* out = in * scalar */ void curve25519_scalar_product(bignum25519 out, const bignum25519 in, const uint32_t scalar) { uint64_t a = 0; uint32_t c = 0; a = mul32x32_64(in[0], scalar); out[0] = (uint32_t)a & reduce_mask_26; c = (uint32_t)(a >> 26); a = mul32x32_64(in[1], scalar) + c; out[1] = (uint32_t)a & reduce_mask_25; c = (uint32_t)(a >> 25); a = mul32x32_64(in[2], scalar) + c; out[2] = (uint32_t)a & reduce_mask_26; c = (uint32_t)(a >> 26); a = mul32x32_64(in[3], scalar) + c; out[3] = (uint32_t)a & reduce_mask_25; c = (uint32_t)(a >> 25); a = mul32x32_64(in[4], scalar) + c; out[4] = (uint32_t)a & reduce_mask_26; c = (uint32_t)(a >> 26); a = mul32x32_64(in[5], scalar) + c; out[5] = (uint32_t)a & reduce_mask_25; c = (uint32_t)(a >> 25); a = mul32x32_64(in[6], scalar) + c; out[6] = (uint32_t)a & reduce_mask_26; c = (uint32_t)(a >> 26); a = mul32x32_64(in[7], scalar) + c; out[7] = (uint32_t)a & reduce_mask_25; c = (uint32_t)(a >> 25); a = mul32x32_64(in[8], scalar) + c; out[8] = (uint32_t)a & reduce_mask_26; c = (uint32_t)(a >> 26); a = mul32x32_64(in[9], scalar) + c; out[9] = (uint32_t)a & reduce_mask_25; c = (uint32_t)(a >> 25); out[0] += c * 19; } /* out = a - b, where a is the result of a basic op (add,sub) */ void curve25519_sub_after_basic(bignum25519 out, const bignum25519 a, const bignum25519 b) { uint32_t c = 0; out[0] = fourP0 + a[0] - b[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26; out[1] = fourP13579 + a[1] - b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25; out[2] = fourP2468 + a[2] - b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26; out[3] = fourP13579 + a[3] - b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25; out[4] = fourP2468 + a[4] - b[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26; out[5] = fourP13579 + a[5] - b[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25; out[6] = fourP2468 + a[6] - b[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26; out[7] = fourP13579 + a[7] - b[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25; out[8] = fourP2468 + a[8] - b[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26; out[9] = fourP13579 + a[9] - b[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25; out[0] += 19 * c; } void curve25519_sub_reduce(bignum25519 out, const bignum25519 a, const bignum25519 b) { uint32_t c = 0; out[0] = fourP0 + a[0] - b[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26; out[1] = fourP13579 + a[1] - b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25; out[2] = fourP2468 + a[2] - b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26; out[3] = fourP13579 + a[3] - b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25; out[4] = fourP2468 + a[4] - b[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26; out[5] = fourP13579 + a[5] - b[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25; out[6] = fourP2468 + a[6] - b[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26; out[7] = fourP13579 + a[7] - b[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25; out[8] = fourP2468 + a[8] - b[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26; out[9] = fourP13579 + a[9] - b[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25; out[0] += 19 * c; } /* out = -a */ void curve25519_neg(bignum25519 out, const bignum25519 a) { uint32_t c = 0; out[0] = twoP0 - a[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26; out[1] = twoP13579 - a[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25; out[2] = twoP2468 - a[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26; out[3] = twoP13579 - a[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25; out[4] = twoP2468 - a[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26; out[5] = twoP13579 - a[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25; out[6] = twoP2468 - a[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26; out[7] = twoP13579 - a[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25; out[8] = twoP2468 - a[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26; out[9] = twoP13579 - a[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25; out[0] += 19 * c; } /* out = a * b */ #define curve25519_mul_noinline curve25519_mul void curve25519_mul(bignum25519 out, const bignum25519 a, const bignum25519 b) { uint32_t r0 = 0, r1 = 0, r2 = 0, r3 = 0, r4 = 0, r5 = 0, r6 = 0, r7 = 0, r8 = 0, r9 = 0; uint32_t s0 = 0, s1 = 0, s2 = 0, s3 = 0, s4 = 0, s5 = 0, s6 = 0, s7 = 0, s8 = 0, s9 = 0; uint64_t m0 = 0, m1 = 0, m2 = 0, m3 = 0, m4 = 0, m5 = 0, m6 = 0, m7 = 0, m8 = 0, m9 = 0, c = 0; uint32_t p = 0; r0 = b[0]; r1 = b[1]; r2 = b[2]; r3 = b[3]; r4 = b[4]; r5 = b[5]; r6 = b[6]; r7 = b[7]; r8 = b[8]; r9 = b[9]; s0 = a[0]; s1 = a[1]; s2 = a[2]; s3 = a[3]; s4 = a[4]; s5 = a[5]; s6 = a[6]; s7 = a[7]; s8 = a[8]; s9 = a[9]; m1 = mul32x32_64(r0, s1) + mul32x32_64(r1, s0); m3 = mul32x32_64(r0, s3) + mul32x32_64(r1, s2) + mul32x32_64(r2, s1) + mul32x32_64(r3, s0); m5 = mul32x32_64(r0, s5) + mul32x32_64(r1, s4) + mul32x32_64(r2, s3) + mul32x32_64(r3, s2) + mul32x32_64(r4, s1) + mul32x32_64(r5, s0); m7 = mul32x32_64(r0, s7) + mul32x32_64(r1, s6) + mul32x32_64(r2, s5) + mul32x32_64(r3, s4) + mul32x32_64(r4, s3) + mul32x32_64(r5, s2) + mul32x32_64(r6, s1) + mul32x32_64(r7, s0); m9 = mul32x32_64(r0, s9) + mul32x32_64(r1, s8) + mul32x32_64(r2, s7) + mul32x32_64(r3, s6) + mul32x32_64(r4, s5) + mul32x32_64(r5, s4) + mul32x32_64(r6, s3) + mul32x32_64(r7, s2) + mul32x32_64(r8, s1) + mul32x32_64(r9, s0); r1 *= 2; r3 *= 2; r5 *= 2; r7 *= 2; m0 = mul32x32_64(r0, s0); m2 = mul32x32_64(r0, s2) + mul32x32_64(r1, s1) + mul32x32_64(r2, s0); m4 = mul32x32_64(r0, s4) + mul32x32_64(r1, s3) + mul32x32_64(r2, s2) + mul32x32_64(r3, s1) + mul32x32_64(r4, s0); m6 = mul32x32_64(r0, s6) + mul32x32_64(r1, s5) + mul32x32_64(r2, s4) + mul32x32_64(r3, s3) + mul32x32_64(r4, s2) + mul32x32_64(r5, s1) + mul32x32_64(r6, s0); m8 = mul32x32_64(r0, s8) + mul32x32_64(r1, s7) + mul32x32_64(r2, s6) + mul32x32_64(r3, s5) + mul32x32_64(r4, s4) + mul32x32_64(r5, s3) + mul32x32_64(r6, s2) + mul32x32_64(r7, s1) + mul32x32_64(r8, s0); r1 *= 19; r2 *= 19; r3 = (r3 / 2) * 19; r4 *= 19; r5 = (r5 / 2) * 19; r6 *= 19; r7 = (r7 / 2) * 19; r8 *= 19; r9 *= 19; m1 += (mul32x32_64(r9, s2) + mul32x32_64(r8, s3) + mul32x32_64(r7, s4) + mul32x32_64(r6, s5) + mul32x32_64(r5, s6) + mul32x32_64(r4, s7) + mul32x32_64(r3, s8) + mul32x32_64(r2, s9)); m3 += (mul32x32_64(r9, s4) + mul32x32_64(r8, s5) + mul32x32_64(r7, s6) + mul32x32_64(r6, s7) + mul32x32_64(r5, s8) + mul32x32_64(r4, s9)); m5 += (mul32x32_64(r9, s6) + mul32x32_64(r8, s7) + mul32x32_64(r7, s8) + mul32x32_64(r6, s9)); m7 += (mul32x32_64(r9, s8) + mul32x32_64(r8, s9)); r3 *= 2; r5 *= 2; r7 *= 2; r9 *= 2; m0 += (mul32x32_64(r9, s1) + mul32x32_64(r8, s2) + mul32x32_64(r7, s3) + mul32x32_64(r6, s4) + mul32x32_64(r5, s5) + mul32x32_64(r4, s6) + mul32x32_64(r3, s7) + mul32x32_64(r2, s8) + mul32x32_64(r1, s9)); m2 += (mul32x32_64(r9, s3) + mul32x32_64(r8, s4) + mul32x32_64(r7, s5) + mul32x32_64(r6, s6) + mul32x32_64(r5, s7) + mul32x32_64(r4, s8) + mul32x32_64(r3, s9)); m4 += (mul32x32_64(r9, s5) + mul32x32_64(r8, s6) + mul32x32_64(r7, s7) + mul32x32_64(r6, s8) + mul32x32_64(r5, s9)); m6 += (mul32x32_64(r9, s7) + mul32x32_64(r8, s8) + mul32x32_64(r7, s9)); m8 += (mul32x32_64(r9, s9)); r0 = (uint32_t)m0 & reduce_mask_26; c = (m0 >> 26); m1 += c; r1 = (uint32_t)m1 & reduce_mask_25; c = (m1 >> 25); m2 += c; r2 = (uint32_t)m2 & reduce_mask_26; c = (m2 >> 26); m3 += c; r3 = (uint32_t)m3 & reduce_mask_25; c = (m3 >> 25); m4 += c; r4 = (uint32_t)m4 & reduce_mask_26; c = (m4 >> 26); m5 += c; r5 = (uint32_t)m5 & reduce_mask_25; c = (m5 >> 25); m6 += c; r6 = (uint32_t)m6 & reduce_mask_26; c = (m6 >> 26); m7 += c; r7 = (uint32_t)m7 & reduce_mask_25; c = (m7 >> 25); m8 += c; r8 = (uint32_t)m8 & reduce_mask_26; c = (m8 >> 26); m9 += c; r9 = (uint32_t)m9 & reduce_mask_25; p = (uint32_t)(m9 >> 25); m0 = r0 + mul32x32_64(p,19); r0 = (uint32_t)m0 & reduce_mask_26; p = (uint32_t)(m0 >> 26); r1 += p; out[0] = r0; out[1] = r1; out[2] = r2; out[3] = r3; out[4] = r4; out[5] = r5; out[6] = r6; out[7] = r7; out[8] = r8; out[9] = r9; } /* out = in * in */ void curve25519_square(bignum25519 out, const bignum25519 in) { uint32_t r0 = 0, r1 = 0, r2 = 0, r3 = 0, r4 = 0, r5 = 0, r6 = 0, r7 = 0, r8 = 0, r9 = 0; uint32_t d6 = 0, d7 = 0, d8 = 0, d9 = 0; uint64_t m0 = 0, m1 = 0, m2 = 0, m3 = 0, m4 = 0, m5 = 0, m6 = 0, m7 = 0, m8 = 0, m9 = 0, c = 0; uint32_t p = 0; r0 = in[0]; r1 = in[1]; r2 = in[2]; r3 = in[3]; r4 = in[4]; r5 = in[5]; r6 = in[6]; r7 = in[7]; r8 = in[8]; r9 = in[9]; m0 = mul32x32_64(r0, r0); r0 *= 2; m1 = mul32x32_64(r0, r1); m2 = mul32x32_64(r0, r2) + mul32x32_64(r1, r1 * 2); r1 *= 2; m3 = mul32x32_64(r0, r3) + mul32x32_64(r1, r2 ); m4 = mul32x32_64(r0, r4) + mul32x32_64(r1, r3 * 2) + mul32x32_64(r2, r2); r2 *= 2; m5 = mul32x32_64(r0, r5) + mul32x32_64(r1, r4 ) + mul32x32_64(r2, r3); m6 = mul32x32_64(r0, r6) + mul32x32_64(r1, r5 * 2) + mul32x32_64(r2, r4) + mul32x32_64(r3, r3 * 2); r3 *= 2; m7 = mul32x32_64(r0, r7) + mul32x32_64(r1, r6 ) + mul32x32_64(r2, r5) + mul32x32_64(r3, r4 ); m8 = mul32x32_64(r0, r8) + mul32x32_64(r1, r7 * 2) + mul32x32_64(r2, r6) + mul32x32_64(r3, r5 * 2) + mul32x32_64(r4, r4 ); m9 = mul32x32_64(r0, r9) + mul32x32_64(r1, r8 ) + mul32x32_64(r2, r7) + mul32x32_64(r3, r6 ) + mul32x32_64(r4, r5 * 2); d6 = r6 * 19; d7 = r7 * 2 * 19; d8 = r8 * 19; d9 = r9 * 2 * 19; m0 += (mul32x32_64(d9, r1 ) + mul32x32_64(d8, r2 ) + mul32x32_64(d7, r3 ) + mul32x32_64(d6, r4 * 2) + mul32x32_64(r5, r5 * 2 * 19)); m1 += (mul32x32_64(d9, r2 / 2) + mul32x32_64(d8, r3 ) + mul32x32_64(d7, r4 ) + mul32x32_64(d6, r5 * 2)); m2 += (mul32x32_64(d9, r3 ) + mul32x32_64(d8, r4 * 2) + mul32x32_64(d7, r5 * 2) + mul32x32_64(d6, r6 )); m3 += (mul32x32_64(d9, r4 ) + mul32x32_64(d8, r5 * 2) + mul32x32_64(d7, r6 )); m4 += (mul32x32_64(d9, r5 * 2) + mul32x32_64(d8, r6 * 2) + mul32x32_64(d7, r7 )); m5 += (mul32x32_64(d9, r6 ) + mul32x32_64(d8, r7 * 2)); m6 += (mul32x32_64(d9, r7 * 2) + mul32x32_64(d8, r8 )); m7 += (mul32x32_64(d9, r8 )); m8 += (mul32x32_64(d9, r9 )); r0 = (uint32_t)m0 & reduce_mask_26; c = (m0 >> 26); m1 += c; r1 = (uint32_t)m1 & reduce_mask_25; c = (m1 >> 25); m2 += c; r2 = (uint32_t)m2 & reduce_mask_26; c = (m2 >> 26); m3 += c; r3 = (uint32_t)m3 & reduce_mask_25; c = (m3 >> 25); m4 += c; r4 = (uint32_t)m4 & reduce_mask_26; c = (m4 >> 26); m5 += c; r5 = (uint32_t)m5 & reduce_mask_25; c = (m5 >> 25); m6 += c; r6 = (uint32_t)m6 & reduce_mask_26; c = (m6 >> 26); m7 += c; r7 = (uint32_t)m7 & reduce_mask_25; c = (m7 >> 25); m8 += c; r8 = (uint32_t)m8 & reduce_mask_26; c = (m8 >> 26); m9 += c; r9 = (uint32_t)m9 & reduce_mask_25; p = (uint32_t)(m9 >> 25); m0 = r0 + mul32x32_64(p,19); r0 = (uint32_t)m0 & reduce_mask_26; p = (uint32_t)(m0 >> 26); r1 += p; out[0] = r0; out[1] = r1; out[2] = r2; out[3] = r3; out[4] = r4; out[5] = r5; out[6] = r6; out[7] = r7; out[8] = r8; out[9] = r9; } /* out = in ^ (2 * count) */ void curve25519_square_times(bignum25519 out, const bignum25519 in, int count) { uint32_t r0 = 0, r1 = 0, r2 = 0, r3 = 0, r4 = 0, r5 = 0, r6 = 0, r7 = 0, r8 = 0, r9 = 0; uint32_t d6 = 0, d7 = 0, d8 = 0, d9 = 0; uint64_t m0 = 0, m1 = 0, m2 = 0, m3 = 0, m4 = 0, m5 = 0, m6 = 0, m7 = 0, m8 = 0, m9 = 0, c = 0; uint32_t p = 0; r0 = in[0]; r1 = in[1]; r2 = in[2]; r3 = in[3]; r4 = in[4]; r5 = in[5]; r6 = in[6]; r7 = in[7]; r8 = in[8]; r9 = in[9]; do { m0 = mul32x32_64(r0, r0); r0 *= 2; m1 = mul32x32_64(r0, r1); m2 = mul32x32_64(r0, r2) + mul32x32_64(r1, r1 * 2); r1 *= 2; m3 = mul32x32_64(r0, r3) + mul32x32_64(r1, r2 ); m4 = mul32x32_64(r0, r4) + mul32x32_64(r1, r3 * 2) + mul32x32_64(r2, r2); r2 *= 2; m5 = mul32x32_64(r0, r5) + mul32x32_64(r1, r4 ) + mul32x32_64(r2, r3); m6 = mul32x32_64(r0, r6) + mul32x32_64(r1, r5 * 2) + mul32x32_64(r2, r4) + mul32x32_64(r3, r3 * 2); r3 *= 2; m7 = mul32x32_64(r0, r7) + mul32x32_64(r1, r6 ) + mul32x32_64(r2, r5) + mul32x32_64(r3, r4 ); m8 = mul32x32_64(r0, r8) + mul32x32_64(r1, r7 * 2) + mul32x32_64(r2, r6) + mul32x32_64(r3, r5 * 2) + mul32x32_64(r4, r4 ); m9 = mul32x32_64(r0, r9) + mul32x32_64(r1, r8 ) + mul32x32_64(r2, r7) + mul32x32_64(r3, r6 ) + mul32x32_64(r4, r5 * 2); d6 = r6 * 19; d7 = r7 * 2 * 19; d8 = r8 * 19; d9 = r9 * 2 * 19; m0 += (mul32x32_64(d9, r1 ) + mul32x32_64(d8, r2 ) + mul32x32_64(d7, r3 ) + mul32x32_64(d6, r4 * 2) + mul32x32_64(r5, r5 * 2 * 19)); m1 += (mul32x32_64(d9, r2 / 2) + mul32x32_64(d8, r3 ) + mul32x32_64(d7, r4 ) + mul32x32_64(d6, r5 * 2)); m2 += (mul32x32_64(d9, r3 ) + mul32x32_64(d8, r4 * 2) + mul32x32_64(d7, r5 * 2) + mul32x32_64(d6, r6 )); m3 += (mul32x32_64(d9, r4 ) + mul32x32_64(d8, r5 * 2) + mul32x32_64(d7, r6 )); m4 += (mul32x32_64(d9, r5 * 2) + mul32x32_64(d8, r6 * 2) + mul32x32_64(d7, r7 )); m5 += (mul32x32_64(d9, r6 ) + mul32x32_64(d8, r7 * 2)); m6 += (mul32x32_64(d9, r7 * 2) + mul32x32_64(d8, r8 )); m7 += (mul32x32_64(d9, r8 )); m8 += (mul32x32_64(d9, r9 )); r0 = (uint32_t)m0 & reduce_mask_26; c = (m0 >> 26); m1 += c; r1 = (uint32_t)m1 & reduce_mask_25; c = (m1 >> 25); m2 += c; r2 = (uint32_t)m2 & reduce_mask_26; c = (m2 >> 26); m3 += c; r3 = (uint32_t)m3 & reduce_mask_25; c = (m3 >> 25); m4 += c; r4 = (uint32_t)m4 & reduce_mask_26; c = (m4 >> 26); m5 += c; r5 = (uint32_t)m5 & reduce_mask_25; c = (m5 >> 25); m6 += c; r6 = (uint32_t)m6 & reduce_mask_26; c = (m6 >> 26); m7 += c; r7 = (uint32_t)m7 & reduce_mask_25; c = (m7 >> 25); m8 += c; r8 = (uint32_t)m8 & reduce_mask_26; c = (m8 >> 26); m9 += c; r9 = (uint32_t)m9 & reduce_mask_25; p = (uint32_t)(m9 >> 25); m0 = r0 + mul32x32_64(p,19); r0 = (uint32_t)m0 & reduce_mask_26; p = (uint32_t)(m0 >> 26); r1 += p; } while (--count); out[0] = r0; out[1] = r1; out[2] = r2; out[3] = r3; out[4] = r4; out[5] = r5; out[6] = r6; out[7] = r7; out[8] = r8; out[9] = r9; } /* Take a little-endian, 32-byte number and expand it into polynomial form */ void curve25519_expand(bignum25519 out, const unsigned char in[32]) { uint32_t x0 = 0, x1 = 0, x2 = 0, x3 = 0, x4 = 0, x5 = 0, x6 = 0, x7 = 0; #define F(s) \ ((((uint32_t)in[s + 0]) ) | \ (((uint32_t)in[s + 1]) << 8) | \ (((uint32_t)in[s + 2]) << 16) | \ (((uint32_t)in[s + 3]) << 24)) x0 = F(0); x1 = F(4); x2 = F(8); x3 = F(12); x4 = F(16); x5 = F(20); x6 = F(24); x7 = F(28); #undef F out[0] = ( x0 ) & reduce_mask_26; out[1] = ((((uint64_t)x1 << 32) | x0) >> 26) & reduce_mask_25; out[2] = ((((uint64_t)x2 << 32) | x1) >> 19) & reduce_mask_26; out[3] = ((((uint64_t)x3 << 32) | x2) >> 13) & reduce_mask_25; out[4] = (( x3) >> 6) & reduce_mask_26; out[5] = ( x4 ) & reduce_mask_25; out[6] = ((((uint64_t)x5 << 32) | x4) >> 25) & reduce_mask_26; out[7] = ((((uint64_t)x6 << 32) | x5) >> 19) & reduce_mask_25; out[8] = ((((uint64_t)x7 << 32) | x6) >> 12) & reduce_mask_26; out[9] = (( x7) >> 6) & reduce_mask_25; /* ignore the top bit */ } /* Take a fully reduced polynomial form number and contract it into a * little-endian, 32-byte array */ void curve25519_contract(unsigned char out[32], const bignum25519 in) { bignum25519 f = {0}; curve25519_copy(f, in); #define carry_pass() \ f[1] += f[0] >> 26; f[0] &= reduce_mask_26; \ f[2] += f[1] >> 25; f[1] &= reduce_mask_25; \ f[3] += f[2] >> 26; f[2] &= reduce_mask_26; \ f[4] += f[3] >> 25; f[3] &= reduce_mask_25; \ f[5] += f[4] >> 26; f[4] &= reduce_mask_26; \ f[6] += f[5] >> 25; f[5] &= reduce_mask_25; \ f[7] += f[6] >> 26; f[6] &= reduce_mask_26; \ f[8] += f[7] >> 25; f[7] &= reduce_mask_25; \ f[9] += f[8] >> 26; f[8] &= reduce_mask_26; #define carry_pass_full() \ carry_pass() \ f[0] += 19 * (f[9] >> 25); f[9] &= reduce_mask_25; #define carry_pass_final() \ carry_pass() \ f[9] &= reduce_mask_25; carry_pass_full() carry_pass_full() /* now t is between 0 and 2^255-1, properly carried. */ /* case 1: between 0 and 2^255-20. case 2: between 2^255-19 and 2^255-1. */ f[0] += 19; carry_pass_full() /* now between 19 and 2^255-1 in both cases, and offset by 19. */ f[0] += (reduce_mask_26 + 1) - 19; f[1] += (reduce_mask_25 + 1) - 1; f[2] += (reduce_mask_26 + 1) - 1; f[3] += (reduce_mask_25 + 1) - 1; f[4] += (reduce_mask_26 + 1) - 1; f[5] += (reduce_mask_25 + 1) - 1; f[6] += (reduce_mask_26 + 1) - 1; f[7] += (reduce_mask_25 + 1) - 1; f[8] += (reduce_mask_26 + 1) - 1; f[9] += (reduce_mask_25 + 1) - 1; /* now between 2^255 and 2^256-20, and offset by 2^255. */ carry_pass_final() #undef carry_pass #undef carry_full #undef carry_final f[1] <<= 2; f[2] <<= 3; f[3] <<= 5; f[4] <<= 6; f[6] <<= 1; f[7] <<= 3; f[8] <<= 4; f[9] <<= 6; #define F(i, s) \ out[s+0] |= (unsigned char )(f[i] & 0xff); \ out[s+1] = (unsigned char )((f[i] >> 8) & 0xff); \ out[s+2] = (unsigned char )((f[i] >> 16) & 0xff); \ out[s+3] = (unsigned char )((f[i] >> 24) & 0xff); out[0] = 0; out[16] = 0; F(0,0); F(1,3); F(2,6); F(3,9); F(4,12); F(5,16); F(6,19); F(7,22); F(8,25); F(9,28); #undef F } /* if (iswap) swap(a, b) */ void curve25519_swap_conditional(bignum25519 a, bignum25519 b, uint32_t iswap) { const uint32_t swap = (uint32_t)(-(int32_t)iswap); uint32_t x0 = 0, x1 = 0, x2 = 0, x3 = 0, x4 = 0, x5 = 0, x6 = 0, x7 = 0, x8 = 0, x9 = 0; x0 = swap & (a[0] ^ b[0]); a[0] ^= x0; b[0] ^= x0; x1 = swap & (a[1] ^ b[1]); a[1] ^= x1; b[1] ^= x1; x2 = swap & (a[2] ^ b[2]); a[2] ^= x2; b[2] ^= x2; x3 = swap & (a[3] ^ b[3]); a[3] ^= x3; b[3] ^= x3; x4 = swap & (a[4] ^ b[4]); a[4] ^= x4; b[4] ^= x4; x5 = swap & (a[5] ^ b[5]); a[5] ^= x5; b[5] ^= x5; x6 = swap & (a[6] ^ b[6]); a[6] ^= x6; b[6] ^= x6; x7 = swap & (a[7] ^ b[7]); a[7] ^= x7; b[7] ^= x7; x8 = swap & (a[8] ^ b[8]); a[8] ^= x8; b[8] ^= x8; x9 = swap & (a[9] ^ b[9]); a[9] ^= x9; b[9] ^= x9; } void curve25519_set(bignum25519 r, uint32_t x){ r[0] = x & reduce_mask_26; x >>= 26; r[1] = x & reduce_mask_25; r[2] = 0; r[3] = 0; r[4] = 0; r[5] = 0; r[6] = 0; r[7] = 0; r[8] = 0; r[9] = 0; } void curve25519_set_d(bignum25519 r){ curve25519_copy(r, ge25519_ecd); } void curve25519_set_2d(bignum25519 r){ curve25519_copy(r, ge25519_ec2d); } void curve25519_set_sqrtneg1(bignum25519 r){ curve25519_copy(r, ge25519_sqrtneg1); } int curve25519_isnegative(const bignum25519 f) { unsigned char s[32] = {0}; curve25519_contract(s, f); return s[0] & 1; } int curve25519_isnonzero(const bignum25519 f) { unsigned char s[32] = {0}; curve25519_contract(s, f); return ((((int) (s[0] | s[1] | s[2] | s[3] | s[4] | s[5] | s[6] | s[7] | s[8] | s[9] | s[10] | s[11] | s[12] | s[13] | s[14] | s[15] | s[16] | s[17] | s[18] | s[19] | s[20] | s[21] | s[22] | s[23] | s[24] | s[25] | s[26] | s[27] | s[28] | s[29] | s[30] | s[31]) - 1) >> 8) + 1) & 0x1; } void curve25519_reduce(bignum25519 out, const bignum25519 in) { uint32_t c = 0; out[0] = in[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26; out[1] = in[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25; out[2] = in[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26; out[3] = in[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25; out[4] = in[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26; out[5] = in[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25; out[6] = in[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26; out[7] = in[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25; out[8] = in[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26; out[9] = in[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25; out[0] += 19 * c; } void curve25519_divpowm1(bignum25519 r, const bignum25519 u, const bignum25519 v) { bignum25519 v3={0}, uv7={0}, t0={0}, t1={0}, t2={0}; int i = 0; curve25519_square(v3, v); curve25519_mul(v3, v3, v); /* v3 = v^3 */ curve25519_square(uv7, v3); curve25519_mul(uv7, uv7, v); curve25519_mul(uv7, uv7, u); /* uv7 = uv^7 */ /*fe_pow22523(uv7, uv7);*/ /* From fe_pow22523.c */ curve25519_square(t0, uv7); curve25519_square(t1, t0); curve25519_square(t1, t1); curve25519_mul(t1, uv7, t1); curve25519_mul(t0, t0, t1); curve25519_square(t0, t0); curve25519_mul(t0, t1, t0); curve25519_square(t1, t0); for (i = 0; i < 4; ++i) { curve25519_square(t1, t1); } curve25519_mul(t0, t1, t0); curve25519_square(t1, t0); for (i = 0; i < 9; ++i) { curve25519_square(t1, t1); } curve25519_mul(t1, t1, t0); curve25519_square(t2, t1); for (i = 0; i < 19; ++i) { curve25519_square(t2, t2); } curve25519_mul(t1, t2, t1); for (i = 0; i < 10; ++i) { curve25519_square(t1, t1); } curve25519_mul(t0, t1, t0); curve25519_square(t1, t0); for (i = 0; i < 49; ++i) { curve25519_square(t1, t1); } curve25519_mul(t1, t1, t0); curve25519_square(t2, t1); for (i = 0; i < 99; ++i) { curve25519_square(t2, t2); } curve25519_mul(t1, t2, t1); for (i = 0; i < 50; ++i) { curve25519_square(t1, t1); } curve25519_mul(t0, t1, t0); curve25519_square(t0, t0); curve25519_square(t0, t0); curve25519_mul(t0, t0, uv7); /* End fe_pow22523.c */ /* t0 = (uv^7)^((q-5)/8) */ curve25519_mul(t0, t0, v3); curve25519_mul(r, t0, u); /* u^(m+1)v^(-(m+1)) */ } void curve25519_expand_reduce(bignum25519 out, const unsigned char in[32]) { uint32_t x0 = 0, x1 = 0, x2 = 0, x3 = 0, x4 = 0, x5 = 0, x6 = 0, x7 = 0; #define F(s) \ ((((uint32_t)in[s + 0]) ) | \ (((uint32_t)in[s + 1]) << 8) | \ (((uint32_t)in[s + 2]) << 16) | \ (((uint32_t)in[s + 3]) << 24)) x0 = F(0); x1 = F(4); x2 = F(8); x3 = F(12); x4 = F(16); x5 = F(20); x6 = F(24); x7 = F(28); #undef F out[0] = ( x0 ) & reduce_mask_26; out[1] = ((((uint64_t)x1 << 32) | x0) >> 26) & reduce_mask_25; out[2] = ((((uint64_t)x2 << 32) | x1) >> 19) & reduce_mask_26; out[3] = ((((uint64_t)x3 << 32) | x2) >> 13) & reduce_mask_25; out[4] = (( x3) >> 6) & reduce_mask_26; out[5] = ( x4 ) & reduce_mask_25; out[6] = ((((uint64_t)x5 << 32) | x4) >> 25) & reduce_mask_26; out[7] = ((((uint64_t)x6 << 32) | x5) >> 19) & reduce_mask_25; out[8] = ((((uint64_t)x7 << 32) | x6) >> 12) & reduce_mask_26; out[9] = (( x7) >> 6); // & reduce_mask_25; /* ignore the top bit */ out[0] += 19 * (out[9] >> 25); out[9] &= reduce_mask_25; }