mirror of
https://github.com/trezor/trezor-firmware.git
synced 2024-11-23 16:08:17 +00:00
563 lines
22 KiB
C
563 lines
22 KiB
C
/*
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Public domain by Andrew M. <liquidsun@gmail.com>
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See: https://github.com/floodyberry/curve25519-donna
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32 bit integer curve25519 implementation
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*/
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typedef uint32_t bignum25519[10];
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static const uint32_t reduce_mask_25 = (1 << 25) - 1;
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static const uint32_t reduce_mask_26 = (1 << 26) - 1;
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/* out = in */
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DONNA_INLINE static void
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curve25519_copy(bignum25519 out, const bignum25519 in) {
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out[0] = in[0];
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out[1] = in[1];
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out[2] = in[2];
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out[3] = in[3];
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out[4] = in[4];
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out[5] = in[5];
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out[6] = in[6];
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out[7] = in[7];
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out[8] = in[8];
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out[9] = in[9];
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}
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/* out = a + b */
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DONNA_INLINE static void
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curve25519_add(bignum25519 out, const bignum25519 a, const bignum25519 b) {
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out[0] = a[0] + b[0];
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out[1] = a[1] + b[1];
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out[2] = a[2] + b[2];
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out[3] = a[3] + b[3];
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out[4] = a[4] + b[4];
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out[5] = a[5] + b[5];
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out[6] = a[6] + b[6];
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out[7] = a[7] + b[7];
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out[8] = a[8] + b[8];
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out[9] = a[9] + b[9];
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}
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DONNA_INLINE static void
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curve25519_add_after_basic(bignum25519 out, const bignum25519 a, const bignum25519 b) {
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uint32_t c;
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out[0] = a[0] + b[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
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out[1] = a[1] + b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
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out[2] = a[2] + b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
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out[3] = a[3] + b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
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out[4] = a[4] + b[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
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out[5] = a[5] + b[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
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out[6] = a[6] + b[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
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out[7] = a[7] + b[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
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out[8] = a[8] + b[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
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out[9] = a[9] + b[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
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out[0] += 19 * c;
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}
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DONNA_INLINE static void
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curve25519_add_reduce(bignum25519 out, const bignum25519 a, const bignum25519 b) {
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uint32_t c;
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out[0] = a[0] + b[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
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out[1] = a[1] + b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
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out[2] = a[2] + b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
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out[3] = a[3] + b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
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out[4] = a[4] + b[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
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out[5] = a[5] + b[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
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out[6] = a[6] + b[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
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out[7] = a[7] + b[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
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out[8] = a[8] + b[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
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out[9] = a[9] + b[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
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out[0] += 19 * c;
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}
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/* multiples of p */
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static const uint32_t twoP0 = 0x07ffffda;
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static const uint32_t twoP13579 = 0x03fffffe;
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static const uint32_t twoP2468 = 0x07fffffe;
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static const uint32_t fourP0 = 0x0fffffb4;
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static const uint32_t fourP13579 = 0x07fffffc;
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static const uint32_t fourP2468 = 0x0ffffffc;
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/* out = a - b */
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DONNA_INLINE static void
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curve25519_sub(bignum25519 out, const bignum25519 a, const bignum25519 b) {
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uint32_t c;
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out[0] = twoP0 + a[0] - b[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
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out[1] = twoP13579 + a[1] - b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
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out[2] = twoP2468 + a[2] - b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
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out[3] = twoP13579 + a[3] - b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
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out[4] = twoP2468 + a[4] - b[4] + c;
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out[5] = twoP13579 + a[5] - b[5] ;
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out[6] = twoP2468 + a[6] - b[6] ;
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out[7] = twoP13579 + a[7] - b[7] ;
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out[8] = twoP2468 + a[8] - b[8] ;
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out[9] = twoP13579 + a[9] - b[9] ;
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}
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DONNA_INLINE DONNA_UNUSED static void
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curve25519_scalar_product(bignum25519 out, const bignum25519 in, const uint32_t scalar);
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/* out = in * scalar */
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void curve25519_scalar_product(bignum25519 out, const bignum25519 in, const uint32_t scalar) {
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uint64_t a;
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uint32_t c;
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a = mul32x32_64(in[0], scalar); out[0] = (uint32_t)a & reduce_mask_26; c = (uint32_t)(a >> 26);
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a = mul32x32_64(in[1], scalar) + c; out[1] = (uint32_t)a & reduce_mask_25; c = (uint32_t)(a >> 25);
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a = mul32x32_64(in[2], scalar) + c; out[2] = (uint32_t)a & reduce_mask_26; c = (uint32_t)(a >> 26);
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a = mul32x32_64(in[3], scalar) + c; out[3] = (uint32_t)a & reduce_mask_25; c = (uint32_t)(a >> 25);
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a = mul32x32_64(in[4], scalar) + c; out[4] = (uint32_t)a & reduce_mask_26; c = (uint32_t)(a >> 26);
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a = mul32x32_64(in[5], scalar) + c; out[5] = (uint32_t)a & reduce_mask_25; c = (uint32_t)(a >> 25);
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a = mul32x32_64(in[6], scalar) + c; out[6] = (uint32_t)a & reduce_mask_26; c = (uint32_t)(a >> 26);
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a = mul32x32_64(in[7], scalar) + c; out[7] = (uint32_t)a & reduce_mask_25; c = (uint32_t)(a >> 25);
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a = mul32x32_64(in[8], scalar) + c; out[8] = (uint32_t)a & reduce_mask_26; c = (uint32_t)(a >> 26);
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a = mul32x32_64(in[9], scalar) + c; out[9] = (uint32_t)a & reduce_mask_25; c = (uint32_t)(a >> 25);
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out[0] += c * 19;
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}
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/* out = a - b, where a is the result of a basic op (add,sub) */
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DONNA_INLINE static void
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curve25519_sub_after_basic(bignum25519 out, const bignum25519 a, const bignum25519 b) {
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uint32_t c;
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out[0] = fourP0 + a[0] - b[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
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out[1] = fourP13579 + a[1] - b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
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out[2] = fourP2468 + a[2] - b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
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out[3] = fourP13579 + a[3] - b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
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out[4] = fourP2468 + a[4] - b[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
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out[5] = fourP13579 + a[5] - b[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
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out[6] = fourP2468 + a[6] - b[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
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out[7] = fourP13579 + a[7] - b[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
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out[8] = fourP2468 + a[8] - b[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
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out[9] = fourP13579 + a[9] - b[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
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out[0] += 19 * c;
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}
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DONNA_INLINE static void
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curve25519_sub_reduce(bignum25519 out, const bignum25519 a, const bignum25519 b) {
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uint32_t c;
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out[0] = fourP0 + a[0] - b[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
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out[1] = fourP13579 + a[1] - b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
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out[2] = fourP2468 + a[2] - b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
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out[3] = fourP13579 + a[3] - b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
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out[4] = fourP2468 + a[4] - b[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
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out[5] = fourP13579 + a[5] - b[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
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out[6] = fourP2468 + a[6] - b[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
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out[7] = fourP13579 + a[7] - b[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
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out[8] = fourP2468 + a[8] - b[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
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out[9] = fourP13579 + a[9] - b[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
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out[0] += 19 * c;
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}
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/* out = -a */
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DONNA_INLINE static void
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curve25519_neg(bignum25519 out, const bignum25519 a) {
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uint32_t c;
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out[0] = twoP0 - a[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
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out[1] = twoP13579 - a[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
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out[2] = twoP2468 - a[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
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out[3] = twoP13579 - a[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
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out[4] = twoP2468 - a[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
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out[5] = twoP13579 - a[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
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out[6] = twoP2468 - a[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
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out[7] = twoP13579 - a[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
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out[8] = twoP2468 - a[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
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out[9] = twoP13579 - a[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
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out[0] += 19 * c;
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}
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/* out = a * b */
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#define curve25519_mul_noinline curve25519_mul
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DONNA_INLINE static void
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curve25519_mul(bignum25519 out, const bignum25519 a, const bignum25519 b) {
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uint32_t r0,r1,r2,r3,r4,r5,r6,r7,r8,r9;
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uint32_t s0,s1,s2,s3,s4,s5,s6,s7,s8,s9;
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uint64_t m0,m1,m2,m3,m4,m5,m6,m7,m8,m9,c;
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uint32_t p;
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r0 = b[0];
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r1 = b[1];
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r2 = b[2];
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r3 = b[3];
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r4 = b[4];
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r5 = b[5];
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r6 = b[6];
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r7 = b[7];
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r8 = b[8];
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r9 = b[9];
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s0 = a[0];
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s1 = a[1];
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s2 = a[2];
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s3 = a[3];
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s4 = a[4];
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s5 = a[5];
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s6 = a[6];
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s7 = a[7];
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s8 = a[8];
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s9 = a[9];
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m1 = mul32x32_64(r0, s1) + mul32x32_64(r1, s0);
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m3 = mul32x32_64(r0, s3) + mul32x32_64(r1, s2) + mul32x32_64(r2, s1) + mul32x32_64(r3, s0);
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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);
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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);
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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);
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r1 *= 2;
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r3 *= 2;
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r5 *= 2;
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r7 *= 2;
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m0 = mul32x32_64(r0, s0);
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m2 = mul32x32_64(r0, s2) + mul32x32_64(r1, s1) + mul32x32_64(r2, s0);
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m4 = mul32x32_64(r0, s4) + mul32x32_64(r1, s3) + mul32x32_64(r2, s2) + mul32x32_64(r3, s1) + mul32x32_64(r4, s0);
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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);
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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);
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r1 *= 19;
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r2 *= 19;
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r3 = (r3 / 2) * 19;
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r4 *= 19;
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r5 = (r5 / 2) * 19;
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r6 *= 19;
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r7 = (r7 / 2) * 19;
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r8 *= 19;
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r9 *= 19;
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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));
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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));
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m5 += (mul32x32_64(r9, s6) + mul32x32_64(r8, s7) + mul32x32_64(r7, s8) + mul32x32_64(r6, s9));
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m7 += (mul32x32_64(r9, s8) + mul32x32_64(r8, s9));
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r3 *= 2;
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r5 *= 2;
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r7 *= 2;
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r9 *= 2;
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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));
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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));
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m4 += (mul32x32_64(r9, s5) + mul32x32_64(r8, s6) + mul32x32_64(r7, s7) + mul32x32_64(r6, s8) + mul32x32_64(r5, s9));
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m6 += (mul32x32_64(r9, s7) + mul32x32_64(r8, s8) + mul32x32_64(r7, s9));
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m8 += (mul32x32_64(r9, s9));
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r0 = (uint32_t)m0 & reduce_mask_26; c = (m0 >> 26);
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m1 += c; r1 = (uint32_t)m1 & reduce_mask_25; c = (m1 >> 25);
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m2 += c; r2 = (uint32_t)m2 & reduce_mask_26; c = (m2 >> 26);
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m3 += c; r3 = (uint32_t)m3 & reduce_mask_25; c = (m3 >> 25);
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m4 += c; r4 = (uint32_t)m4 & reduce_mask_26; c = (m4 >> 26);
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m5 += c; r5 = (uint32_t)m5 & reduce_mask_25; c = (m5 >> 25);
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m6 += c; r6 = (uint32_t)m6 & reduce_mask_26; c = (m6 >> 26);
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m7 += c; r7 = (uint32_t)m7 & reduce_mask_25; c = (m7 >> 25);
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m8 += c; r8 = (uint32_t)m8 & reduce_mask_26; c = (m8 >> 26);
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m9 += c; r9 = (uint32_t)m9 & reduce_mask_25; p = (uint32_t)(m9 >> 25);
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m0 = r0 + mul32x32_64(p,19); r0 = (uint32_t)m0 & reduce_mask_26; p = (uint32_t)(m0 >> 26);
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r1 += p;
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out[0] = r0;
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out[1] = r1;
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out[2] = r2;
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out[3] = r3;
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out[4] = r4;
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out[5] = r5;
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out[6] = r6;
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out[7] = r7;
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out[8] = r8;
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out[9] = r9;
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}
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/* out = in * in */
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DONNA_INLINE static void
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curve25519_square(bignum25519 out, const bignum25519 in) {
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uint32_t r0,r1,r2,r3,r4,r5,r6,r7,r8,r9;
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uint32_t d6,d7,d8,d9;
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uint64_t m0,m1,m2,m3,m4,m5,m6,m7,m8,m9,c;
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uint32_t p;
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r0 = in[0];
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r1 = in[1];
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r2 = in[2];
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r3 = in[3];
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r4 = in[4];
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r5 = in[5];
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r6 = in[6];
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r7 = in[7];
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r8 = in[8];
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r9 = in[9];
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m0 = mul32x32_64(r0, r0);
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r0 *= 2;
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m1 = mul32x32_64(r0, r1);
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m2 = mul32x32_64(r0, r2) + mul32x32_64(r1, r1 * 2);
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r1 *= 2;
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m3 = mul32x32_64(r0, r3) + mul32x32_64(r1, r2 );
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m4 = mul32x32_64(r0, r4) + mul32x32_64(r1, r3 * 2) + mul32x32_64(r2, r2);
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r2 *= 2;
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m5 = mul32x32_64(r0, r5) + mul32x32_64(r1, r4 ) + mul32x32_64(r2, r3);
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m6 = mul32x32_64(r0, r6) + mul32x32_64(r1, r5 * 2) + mul32x32_64(r2, r4) + mul32x32_64(r3, r3 * 2);
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r3 *= 2;
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m7 = mul32x32_64(r0, r7) + mul32x32_64(r1, r6 ) + mul32x32_64(r2, r5) + mul32x32_64(r3, r4 );
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m8 = mul32x32_64(r0, r8) + mul32x32_64(r1, r7 * 2) + mul32x32_64(r2, r6) + mul32x32_64(r3, r5 * 2) + mul32x32_64(r4, r4 );
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m9 = mul32x32_64(r0, r9) + mul32x32_64(r1, r8 ) + mul32x32_64(r2, r7) + mul32x32_64(r3, r6 ) + mul32x32_64(r4, r5 * 2);
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d6 = r6 * 19;
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d7 = r7 * 2 * 19;
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d8 = r8 * 19;
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d9 = r9 * 2 * 19;
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m0 += (mul32x32_64(d9, r1 ) + mul32x32_64(d8, r2 ) + mul32x32_64(d7, r3 ) + mul32x32_64(d6, r4 * 2) + mul32x32_64(r5, r5 * 2 * 19));
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m1 += (mul32x32_64(d9, r2 / 2) + mul32x32_64(d8, r3 ) + mul32x32_64(d7, r4 ) + mul32x32_64(d6, r5 * 2));
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m2 += (mul32x32_64(d9, r3 ) + mul32x32_64(d8, r4 * 2) + mul32x32_64(d7, r5 * 2) + mul32x32_64(d6, r6 ));
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m3 += (mul32x32_64(d9, r4 ) + mul32x32_64(d8, r5 * 2) + mul32x32_64(d7, r6 ));
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m4 += (mul32x32_64(d9, r5 * 2) + mul32x32_64(d8, r6 * 2) + mul32x32_64(d7, r7 ));
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m5 += (mul32x32_64(d9, r6 ) + mul32x32_64(d8, r7 * 2));
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m6 += (mul32x32_64(d9, r7 * 2) + mul32x32_64(d8, r8 ));
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m7 += (mul32x32_64(d9, r8 ));
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m8 += (mul32x32_64(d9, r9 ));
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r0 = (uint32_t)m0 & reduce_mask_26; c = (m0 >> 26);
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m1 += c; r1 = (uint32_t)m1 & reduce_mask_25; c = (m1 >> 25);
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m2 += c; r2 = (uint32_t)m2 & reduce_mask_26; c = (m2 >> 26);
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m3 += c; r3 = (uint32_t)m3 & reduce_mask_25; c = (m3 >> 25);
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m4 += c; r4 = (uint32_t)m4 & reduce_mask_26; c = (m4 >> 26);
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m5 += c; r5 = (uint32_t)m5 & reduce_mask_25; c = (m5 >> 25);
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m6 += c; r6 = (uint32_t)m6 & reduce_mask_26; c = (m6 >> 26);
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m7 += c; r7 = (uint32_t)m7 & reduce_mask_25; c = (m7 >> 25);
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m8 += c; r8 = (uint32_t)m8 & reduce_mask_26; c = (m8 >> 26);
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m9 += c; r9 = (uint32_t)m9 & reduce_mask_25; p = (uint32_t)(m9 >> 25);
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m0 = r0 + mul32x32_64(p,19); r0 = (uint32_t)m0 & reduce_mask_26; p = (uint32_t)(m0 >> 26);
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r1 += p;
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out[0] = r0;
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out[1] = r1;
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out[2] = r2;
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out[3] = r3;
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out[4] = r4;
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out[5] = r5;
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out[6] = r6;
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out[7] = r7;
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out[8] = r8;
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out[9] = r9;
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}
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/* out = in ^ (2 * count) */
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static void
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curve25519_square_times(bignum25519 out, const bignum25519 in, int count) {
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uint32_t r0,r1,r2,r3,r4,r5,r6,r7,r8,r9;
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uint32_t d6,d7,d8,d9;
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uint64_t m0,m1,m2,m3,m4,m5,m6,m7,m8,m9,c;
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uint32_t p;
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r0 = in[0];
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r1 = in[1];
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r2 = in[2];
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r3 = in[3];
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r4 = in[4];
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r5 = in[5];
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r6 = in[6];
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r7 = in[7];
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r8 = in[8];
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r9 = in[9];
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do {
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m0 = mul32x32_64(r0, r0);
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r0 *= 2;
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m1 = mul32x32_64(r0, r1);
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m2 = mul32x32_64(r0, r2) + mul32x32_64(r1, r1 * 2);
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r1 *= 2;
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m3 = mul32x32_64(r0, r3) + mul32x32_64(r1, r2 );
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m4 = mul32x32_64(r0, r4) + mul32x32_64(r1, r3 * 2) + mul32x32_64(r2, r2);
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r2 *= 2;
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m5 = mul32x32_64(r0, r5) + mul32x32_64(r1, r4 ) + mul32x32_64(r2, r3);
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m6 = mul32x32_64(r0, r6) + mul32x32_64(r1, r5 * 2) + mul32x32_64(r2, r4) + mul32x32_64(r3, r3 * 2);
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r3 *= 2;
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m7 = mul32x32_64(r0, r7) + mul32x32_64(r1, r6 ) + mul32x32_64(r2, r5) + mul32x32_64(r3, r4 );
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m8 = mul32x32_64(r0, r8) + mul32x32_64(r1, r7 * 2) + mul32x32_64(r2, r6) + mul32x32_64(r3, r5 * 2) + mul32x32_64(r4, r4 );
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m9 = mul32x32_64(r0, r9) + mul32x32_64(r1, r8 ) + mul32x32_64(r2, r7) + mul32x32_64(r3, r6 ) + mul32x32_64(r4, r5 * 2);
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d6 = r6 * 19;
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d7 = r7 * 2 * 19;
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d8 = r8 * 19;
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d9 = r9 * 2 * 19;
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m0 += (mul32x32_64(d9, r1 ) + mul32x32_64(d8, r2 ) + mul32x32_64(d7, r3 ) + mul32x32_64(d6, r4 * 2) + mul32x32_64(r5, r5 * 2 * 19));
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m1 += (mul32x32_64(d9, r2 / 2) + mul32x32_64(d8, r3 ) + mul32x32_64(d7, r4 ) + mul32x32_64(d6, r5 * 2));
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m2 += (mul32x32_64(d9, r3 ) + mul32x32_64(d8, r4 * 2) + mul32x32_64(d7, r5 * 2) + mul32x32_64(d6, r6 ));
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m3 += (mul32x32_64(d9, r4 ) + mul32x32_64(d8, r5 * 2) + mul32x32_64(d7, r6 ));
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m4 += (mul32x32_64(d9, r5 * 2) + mul32x32_64(d8, r6 * 2) + mul32x32_64(d7, r7 ));
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m5 += (mul32x32_64(d9, r6 ) + mul32x32_64(d8, r7 * 2));
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m6 += (mul32x32_64(d9, r7 * 2) + mul32x32_64(d8, r8 ));
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m7 += (mul32x32_64(d9, r8 ));
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m8 += (mul32x32_64(d9, r9 ));
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r0 = (uint32_t)m0 & reduce_mask_26; c = (m0 >> 26);
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m1 += c; r1 = (uint32_t)m1 & reduce_mask_25; c = (m1 >> 25);
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m2 += c; r2 = (uint32_t)m2 & reduce_mask_26; c = (m2 >> 26);
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m3 += c; r3 = (uint32_t)m3 & reduce_mask_25; c = (m3 >> 25);
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m4 += c; r4 = (uint32_t)m4 & reduce_mask_26; c = (m4 >> 26);
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m5 += c; r5 = (uint32_t)m5 & reduce_mask_25; c = (m5 >> 25);
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m6 += c; r6 = (uint32_t)m6 & reduce_mask_26; c = (m6 >> 26);
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m7 += c; r7 = (uint32_t)m7 & reduce_mask_25; c = (m7 >> 25);
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m8 += c; r8 = (uint32_t)m8 & reduce_mask_26; c = (m8 >> 26);
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m9 += c; r9 = (uint32_t)m9 & reduce_mask_25; p = (uint32_t)(m9 >> 25);
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m0 = r0 + mul32x32_64(p,19); r0 = (uint32_t)m0 & reduce_mask_26; p = (uint32_t)(m0 >> 26);
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r1 += p;
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} while (--count);
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out[0] = r0;
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out[1] = r1;
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out[2] = r2;
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out[3] = r3;
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out[4] = r4;
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out[5] = r5;
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out[6] = r6;
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out[7] = r7;
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out[8] = r8;
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out[9] = r9;
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}
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/* Take a little-endian, 32-byte number and expand it into polynomial form */
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static void
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curve25519_expand(bignum25519 out, const unsigned char in[32]) {
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static const union { uint8_t b[2]; uint16_t s; } endian_check = {{1,0}};
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uint32_t x0,x1,x2,x3,x4,x5,x6,x7;
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if (endian_check.s == 1) {
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/* Take care, this only works when in is aligned */
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x0 = *(uint32_t *)(in + 0);
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x1 = *(uint32_t *)(in + 4);
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x2 = *(uint32_t *)(in + 8);
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x3 = *(uint32_t *)(in + 12);
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x4 = *(uint32_t *)(in + 16);
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x5 = *(uint32_t *)(in + 20);
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x6 = *(uint32_t *)(in + 24);
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x7 = *(uint32_t *)(in + 28);
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} else {
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#define F(s) \
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((((uint32_t)in[s + 0]) ) | \
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(((uint32_t)in[s + 1]) << 8) | \
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(((uint32_t)in[s + 2]) << 16) | \
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(((uint32_t)in[s + 3]) << 24))
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x0 = F(0);
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x1 = F(4);
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x2 = F(8);
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x3 = F(12);
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x4 = F(16);
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x5 = F(20);
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x6 = F(24);
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x7 = F(28);
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#undef F
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}
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out[0] = ( x0 ) & reduce_mask_26;
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out[1] = ((((uint64_t)x1 << 32) | x0) >> 26) & reduce_mask_25;
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out[2] = ((((uint64_t)x2 << 32) | x1) >> 19) & reduce_mask_26;
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out[3] = ((((uint64_t)x3 << 32) | x2) >> 13) & reduce_mask_25;
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out[4] = (( x3) >> 6) & reduce_mask_26;
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out[5] = ( x4 ) & reduce_mask_25;
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out[6] = ((((uint64_t)x5 << 32) | x4) >> 25) & reduce_mask_26;
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out[7] = ((((uint64_t)x6 << 32) | x5) >> 19) & reduce_mask_25;
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out[8] = ((((uint64_t)x7 << 32) | x6) >> 12) & reduce_mask_26;
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out[9] = (( x7) >> 6) & reduce_mask_25; /* ignore the top bit */
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}
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|
|
/* Take a fully reduced polynomial form number and contract it into a
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* little-endian, 32-byte array
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*/
|
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static void
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curve25519_contract(unsigned char out[32], const bignum25519 in) {
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bignum25519 f;
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curve25519_copy(f, in);
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|
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#define carry_pass() \
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f[1] += f[0] >> 26; f[0] &= reduce_mask_26; \
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f[2] += f[1] >> 25; f[1] &= reduce_mask_25; \
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f[3] += f[2] >> 26; f[2] &= reduce_mask_26; \
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f[4] += f[3] >> 25; f[3] &= reduce_mask_25; \
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f[5] += f[4] >> 26; f[4] &= reduce_mask_26; \
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f[6] += f[5] >> 25; f[5] &= reduce_mask_25; \
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f[7] += f[6] >> 26; f[6] &= reduce_mask_26; \
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f[8] += f[7] >> 25; f[7] &= reduce_mask_25; \
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f[9] += f[8] >> 26; f[8] &= reduce_mask_26;
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|
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#define carry_pass_full() \
|
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carry_pass() \
|
|
f[0] += 19 * (f[9] >> 25); f[9] &= reduce_mask_25;
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|
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#define carry_pass_final() \
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carry_pass() \
|
|
f[9] &= reduce_mask_25;
|
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|
|
carry_pass_full()
|
|
carry_pass_full()
|
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|
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/* 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;
|
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carry_pass_full()
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|
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/* now between 19 and 2^255-1 in both cases, and offset by 19. */
|
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f[0] += (reduce_mask_26 + 1) - 19;
|
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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;
|
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f[8] += (reduce_mask_26 + 1) - 1;
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f[9] += (reduce_mask_25 + 1) - 1;
|
|
|
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/* 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) */
|
|
DONNA_INLINE static void
|
|
curve25519_swap_conditional(bignum25519 a, bignum25519 b, uint32_t iswap) {
|
|
const uint32_t swap = (uint32_t)(-(int32_t)iswap);
|
|
uint32_t x0,x1,x2,x3,x4,x5,x6,x7,x8,x9;
|
|
|
|
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;
|
|
}
|