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413 lines
14 KiB
413 lines
14 KiB
/*
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Public domain by Adam Langley <agl@imperialviolet.org> &
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Andrew M. <liquidsun@gmail.com>
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See: https://github.com/floodyberry/curve25519-donna
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64bit integer curve25519 implementation
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*/
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typedef uint64_t bignum25519[5];
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static const uint64_t reduce_mask_40 = ((uint64_t)1 << 40) - 1;
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static const uint64_t reduce_mask_51 = ((uint64_t)1 << 51) - 1;
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static const uint64_t reduce_mask_56 = ((uint64_t)1 << 56) - 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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}
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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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}
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/* out = a + b, where a and/or b are the result of a basic op (add,sub) */
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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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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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}
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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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uint64_t c;
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out[0] = a[0] + b[0] ; c = (out[0] >> 51); out[0] &= reduce_mask_51;
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out[1] = a[1] + b[1] + c; c = (out[1] >> 51); out[1] &= reduce_mask_51;
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out[2] = a[2] + b[2] + c; c = (out[2] >> 51); out[2] &= reduce_mask_51;
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out[3] = a[3] + b[3] + c; c = (out[3] >> 51); out[3] &= reduce_mask_51;
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out[4] = a[4] + b[4] + c; c = (out[4] >> 51); out[4] &= reduce_mask_51;
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out[0] += c * 19;
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}
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/* multiples of p */
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static const uint64_t twoP0 = 0x0fffffffffffda;
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static const uint64_t twoP1234 = 0x0ffffffffffffe;
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static const uint64_t fourP0 = 0x1fffffffffffb4;
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static const uint64_t fourP1234 = 0x1ffffffffffffc;
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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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out[0] = a[0] + twoP0 - b[0];
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out[1] = a[1] + twoP1234 - b[1];
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out[2] = a[2] + twoP1234 - b[2];
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out[3] = a[3] + twoP1234 - b[3];
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out[4] = a[4] + twoP1234 - b[4];
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}
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/* out = a - b, where a and/or b are 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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out[0] = a[0] + fourP0 - b[0];
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out[1] = a[1] + fourP1234 - b[1];
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out[2] = a[2] + fourP1234 - b[2];
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out[3] = a[3] + fourP1234 - b[3];
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out[4] = a[4] + fourP1234 - b[4];
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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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uint64_t c;
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out[0] = a[0] + fourP0 - b[0] ; c = (out[0] >> 51); out[0] &= reduce_mask_51;
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out[1] = a[1] + fourP1234 - b[1] + c; c = (out[1] >> 51); out[1] &= reduce_mask_51;
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out[2] = a[2] + fourP1234 - b[2] + c; c = (out[2] >> 51); out[2] &= reduce_mask_51;
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out[3] = a[3] + fourP1234 - b[3] + c; c = (out[3] >> 51); out[3] &= reduce_mask_51;
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out[4] = a[4] + fourP1234 - b[4] + c; c = (out[4] >> 51); out[4] &= reduce_mask_51;
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out[0] += c * 19;
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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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uint64_t c;
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out[0] = twoP0 - a[0] ; c = (out[0] >> 51); out[0] &= reduce_mask_51;
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out[1] = twoP1234 - a[1] + c; c = (out[1] >> 51); out[1] &= reduce_mask_51;
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out[2] = twoP1234 - a[2] + c; c = (out[2] >> 51); out[2] &= reduce_mask_51;
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out[3] = twoP1234 - a[3] + c; c = (out[3] >> 51); out[3] &= reduce_mask_51;
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out[4] = twoP1234 - a[4] + c; c = (out[4] >> 51); out[4] &= reduce_mask_51;
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out[0] += c * 19;
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}
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/* out = a * b */
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DONNA_INLINE static void
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curve25519_mul(bignum25519 out, const bignum25519 in2, const bignum25519 in) {
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#if !defined(HAVE_NATIVE_UINT128)
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uint128_t mul;
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#endif
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uint128_t t[5];
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uint64_t r0,r1,r2,r3,r4,s0,s1,s2,s3,s4,c;
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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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s0 = in2[0];
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s1 = in2[1];
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s2 = in2[2];
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s3 = in2[3];
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s4 = in2[4];
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#if defined(HAVE_NATIVE_UINT128)
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t[0] = ((uint128_t) r0) * s0;
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t[1] = ((uint128_t) r0) * s1 + ((uint128_t) r1) * s0;
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t[2] = ((uint128_t) r0) * s2 + ((uint128_t) r2) * s0 + ((uint128_t) r1) * s1;
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t[3] = ((uint128_t) r0) * s3 + ((uint128_t) r3) * s0 + ((uint128_t) r1) * s2 + ((uint128_t) r2) * s1;
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t[4] = ((uint128_t) r0) * s4 + ((uint128_t) r4) * s0 + ((uint128_t) r3) * s1 + ((uint128_t) r1) * s3 + ((uint128_t) r2) * s2;
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#else
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mul64x64_128(t[0], r0, s0)
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mul64x64_128(t[1], r0, s1) mul64x64_128(mul, r1, s0) add128(t[1], mul)
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mul64x64_128(t[2], r0, s2) mul64x64_128(mul, r2, s0) add128(t[2], mul) mul64x64_128(mul, r1, s1) add128(t[2], mul)
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mul64x64_128(t[3], r0, s3) mul64x64_128(mul, r3, s0) add128(t[3], mul) mul64x64_128(mul, r1, s2) add128(t[3], mul) mul64x64_128(mul, r2, s1) add128(t[3], mul)
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mul64x64_128(t[4], r0, s4) mul64x64_128(mul, r4, s0) add128(t[4], mul) mul64x64_128(mul, r3, s1) add128(t[4], mul) mul64x64_128(mul, r1, s3) add128(t[4], mul) mul64x64_128(mul, r2, s2) add128(t[4], mul)
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#endif
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r1 *= 19;
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r2 *= 19;
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r3 *= 19;
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r4 *= 19;
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#if defined(HAVE_NATIVE_UINT128)
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t[0] += ((uint128_t) r4) * s1 + ((uint128_t) r1) * s4 + ((uint128_t) r2) * s3 + ((uint128_t) r3) * s2;
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t[1] += ((uint128_t) r4) * s2 + ((uint128_t) r2) * s4 + ((uint128_t) r3) * s3;
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t[2] += ((uint128_t) r4) * s3 + ((uint128_t) r3) * s4;
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t[3] += ((uint128_t) r4) * s4;
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#else
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mul64x64_128(mul, r4, s1) add128(t[0], mul) mul64x64_128(mul, r1, s4) add128(t[0], mul) mul64x64_128(mul, r2, s3) add128(t[0], mul) mul64x64_128(mul, r3, s2) add128(t[0], mul)
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mul64x64_128(mul, r4, s2) add128(t[1], mul) mul64x64_128(mul, r2, s4) add128(t[1], mul) mul64x64_128(mul, r3, s3) add128(t[1], mul)
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mul64x64_128(mul, r4, s3) add128(t[2], mul) mul64x64_128(mul, r3, s4) add128(t[2], mul)
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mul64x64_128(mul, r4, s4) add128(t[3], mul)
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#endif
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r0 = lo128(t[0]) & reduce_mask_51; shr128(c, t[0], 51);
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add128_64(t[1], c) r1 = lo128(t[1]) & reduce_mask_51; shr128(c, t[1], 51);
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add128_64(t[2], c) r2 = lo128(t[2]) & reduce_mask_51; shr128(c, t[2], 51);
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add128_64(t[3], c) r3 = lo128(t[3]) & reduce_mask_51; shr128(c, t[3], 51);
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add128_64(t[4], c) r4 = lo128(t[4]) & reduce_mask_51; shr128(c, t[4], 51);
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r0 += c * 19; c = r0 >> 51; r0 = r0 & reduce_mask_51;
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r1 += c;
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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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}
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DONNA_NOINLINE static void
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curve25519_mul_noinline(bignum25519 out, const bignum25519 in2, const bignum25519 in) {
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curve25519_mul(out, in2, in);
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}
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/* out = in^(2 * count) */
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DONNA_NOINLINE static void
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curve25519_square_times(bignum25519 out, const bignum25519 in, uint64_t count) {
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#if !defined(HAVE_NATIVE_UINT128)
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uint128_t mul;
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#endif
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uint128_t t[5];
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uint64_t r0,r1,r2,r3,r4,c;
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uint64_t d0,d1,d2,d4,d419;
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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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do {
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d0 = r0 * 2;
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d1 = r1 * 2;
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d2 = r2 * 2 * 19;
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d419 = r4 * 19;
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d4 = d419 * 2;
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#if defined(HAVE_NATIVE_UINT128)
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t[0] = ((uint128_t) r0) * r0 + ((uint128_t) d4) * r1 + (((uint128_t) d2) * (r3 ));
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t[1] = ((uint128_t) d0) * r1 + ((uint128_t) d4) * r2 + (((uint128_t) r3) * (r3 * 19));
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t[2] = ((uint128_t) d0) * r2 + ((uint128_t) r1) * r1 + (((uint128_t) d4) * (r3 ));
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t[3] = ((uint128_t) d0) * r3 + ((uint128_t) d1) * r2 + (((uint128_t) r4) * (d419 ));
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t[4] = ((uint128_t) d0) * r4 + ((uint128_t) d1) * r3 + (((uint128_t) r2) * (r2 ));
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#else
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mul64x64_128(t[0], r0, r0) mul64x64_128(mul, d4, r1) add128(t[0], mul) mul64x64_128(mul, d2, r3) add128(t[0], mul)
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mul64x64_128(t[1], d0, r1) mul64x64_128(mul, d4, r2) add128(t[1], mul) mul64x64_128(mul, r3, r3 * 19) add128(t[1], mul)
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mul64x64_128(t[2], d0, r2) mul64x64_128(mul, r1, r1) add128(t[2], mul) mul64x64_128(mul, d4, r3) add128(t[2], mul)
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mul64x64_128(t[3], d0, r3) mul64x64_128(mul, d1, r2) add128(t[3], mul) mul64x64_128(mul, r4, d419) add128(t[3], mul)
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mul64x64_128(t[4], d0, r4) mul64x64_128(mul, d1, r3) add128(t[4], mul) mul64x64_128(mul, r2, r2) add128(t[4], mul)
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#endif
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r0 = lo128(t[0]) & reduce_mask_51;
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r1 = lo128(t[1]) & reduce_mask_51; shl128(c, t[0], 13); r1 += c;
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r2 = lo128(t[2]) & reduce_mask_51; shl128(c, t[1], 13); r2 += c;
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r3 = lo128(t[3]) & reduce_mask_51; shl128(c, t[2], 13); r3 += c;
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r4 = lo128(t[4]) & reduce_mask_51; shl128(c, t[3], 13); r4 += c;
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shl128(c, t[4], 13); r0 += c * 19;
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c = r0 >> 51; r0 &= reduce_mask_51;
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r1 += c ; c = r1 >> 51; r1 &= reduce_mask_51;
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r2 += c ; c = r2 >> 51; r2 &= reduce_mask_51;
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r3 += c ; c = r3 >> 51; r3 &= reduce_mask_51;
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r4 += c ; c = r4 >> 51; r4 &= reduce_mask_51;
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r0 += c * 19;
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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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}
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DONNA_INLINE static void
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curve25519_square(bignum25519 out, const bignum25519 in) {
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#if !defined(HAVE_NATIVE_UINT128)
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uint128_t mul;
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#endif
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uint128_t t[5];
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uint64_t r0,r1,r2,r3,r4,c;
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uint64_t d0,d1,d2,d4,d419;
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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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d0 = r0 * 2;
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d1 = r1 * 2;
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d2 = r2 * 2 * 19;
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d419 = r4 * 19;
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d4 = d419 * 2;
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#if defined(HAVE_NATIVE_UINT128)
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t[0] = ((uint128_t) r0) * r0 + ((uint128_t) d4) * r1 + (((uint128_t) d2) * (r3 ));
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t[1] = ((uint128_t) d0) * r1 + ((uint128_t) d4) * r2 + (((uint128_t) r3) * (r3 * 19));
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t[2] = ((uint128_t) d0) * r2 + ((uint128_t) r1) * r1 + (((uint128_t) d4) * (r3 ));
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t[3] = ((uint128_t) d0) * r3 + ((uint128_t) d1) * r2 + (((uint128_t) r4) * (d419 ));
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t[4] = ((uint128_t) d0) * r4 + ((uint128_t) d1) * r3 + (((uint128_t) r2) * (r2 ));
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#else
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mul64x64_128(t[0], r0, r0) mul64x64_128(mul, d4, r1) add128(t[0], mul) mul64x64_128(mul, d2, r3) add128(t[0], mul)
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mul64x64_128(t[1], d0, r1) mul64x64_128(mul, d4, r2) add128(t[1], mul) mul64x64_128(mul, r3, r3 * 19) add128(t[1], mul)
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mul64x64_128(t[2], d0, r2) mul64x64_128(mul, r1, r1) add128(t[2], mul) mul64x64_128(mul, d4, r3) add128(t[2], mul)
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mul64x64_128(t[3], d0, r3) mul64x64_128(mul, d1, r2) add128(t[3], mul) mul64x64_128(mul, r4, d419) add128(t[3], mul)
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mul64x64_128(t[4], d0, r4) mul64x64_128(mul, d1, r3) add128(t[4], mul) mul64x64_128(mul, r2, r2) add128(t[4], mul)
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#endif
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r0 = lo128(t[0]) & reduce_mask_51; shr128(c, t[0], 51);
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add128_64(t[1], c) r1 = lo128(t[1]) & reduce_mask_51; shr128(c, t[1], 51);
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add128_64(t[2], c) r2 = lo128(t[2]) & reduce_mask_51; shr128(c, t[2], 51);
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add128_64(t[3], c) r3 = lo128(t[3]) & reduce_mask_51; shr128(c, t[3], 51);
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add128_64(t[4], c) r4 = lo128(t[4]) & reduce_mask_51; shr128(c, t[4], 51);
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r0 += c * 19; c = r0 >> 51; r0 = r0 & reduce_mask_51;
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r1 += c;
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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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}
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/* Take a little-endian, 32-byte number and expand it into polynomial form */
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DONNA_INLINE static void
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curve25519_expand(bignum25519 out, const unsigned char *in) {
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static const union { uint8_t b[2]; uint16_t s; } endian_check = {{1,0}};
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uint64_t x0,x1,x2,x3;
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if (endian_check.s == 1) {
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x0 = *(uint64_t *)(in + 0);
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x1 = *(uint64_t *)(in + 8);
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x2 = *(uint64_t *)(in + 16);
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x3 = *(uint64_t *)(in + 24);
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} else {
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#define F(s) \
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((((uint64_t)in[s + 0]) ) | \
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(((uint64_t)in[s + 1]) << 8) | \
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(((uint64_t)in[s + 2]) << 16) | \
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(((uint64_t)in[s + 3]) << 24) | \
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(((uint64_t)in[s + 4]) << 32) | \
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(((uint64_t)in[s + 5]) << 40) | \
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(((uint64_t)in[s + 6]) << 48) | \
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(((uint64_t)in[s + 7]) << 56))
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x0 = F(0);
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x1 = F(8);
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x2 = F(16);
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x3 = F(24);
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}
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out[0] = x0 & reduce_mask_51; x0 = (x0 >> 51) | (x1 << 13);
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out[1] = x0 & reduce_mask_51; x1 = (x1 >> 38) | (x2 << 26);
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out[2] = x1 & reduce_mask_51; x2 = (x2 >> 25) | (x3 << 39);
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out[3] = x2 & reduce_mask_51; x3 = (x3 >> 12);
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out[4] = x3 & reduce_mask_51;
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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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DONNA_INLINE static void
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curve25519_contract(unsigned char *out, const bignum25519 input) {
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uint64_t t[5];
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uint64_t f, i;
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t[0] = input[0];
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t[1] = input[1];
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t[2] = input[2];
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t[3] = input[3];
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t[4] = input[4];
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#define curve25519_contract_carry() \
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t[1] += t[0] >> 51; t[0] &= reduce_mask_51; \
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t[2] += t[1] >> 51; t[1] &= reduce_mask_51; \
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t[3] += t[2] >> 51; t[2] &= reduce_mask_51; \
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t[4] += t[3] >> 51; t[3] &= reduce_mask_51;
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#define curve25519_contract_carry_full() curve25519_contract_carry() \
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t[0] += 19 * (t[4] >> 51); t[4] &= reduce_mask_51;
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#define curve25519_contract_carry_final() curve25519_contract_carry() \
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t[4] &= reduce_mask_51;
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curve25519_contract_carry_full()
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curve25519_contract_carry_full()
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/* now t is between 0 and 2^255-1, properly carried. */
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/* case 1: between 0 and 2^255-20. case 2: between 2^255-19 and 2^255-1. */
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t[0] += 19;
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curve25519_contract_carry_full()
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/* now between 19 and 2^255-1 in both cases, and offset by 19. */
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t[0] += (reduce_mask_51 + 1) - 19;
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t[1] += (reduce_mask_51 + 1) - 1;
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t[2] += (reduce_mask_51 + 1) - 1;
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t[3] += (reduce_mask_51 + 1) - 1;
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t[4] += (reduce_mask_51 + 1) - 1;
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/* now between 2^255 and 2^256-20, and offset by 2^255. */
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curve25519_contract_carry_final()
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#define write51full(n,shift) \
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f = ((t[n] >> shift) | (t[n+1] << (51 - shift))); \
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for (i = 0; i < 8; i++, f >>= 8) *out++ = (unsigned char)f;
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#define write51(n) write51full(n,13*n)
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write51(0)
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write51(1)
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write51(2)
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write51(3)
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}
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#if !defined(ED25519_GCC_64BIT_CHOOSE)
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/* out = (flag) ? in : out */
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DONNA_INLINE static void
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curve25519_move_conditional_bytes(uint8_t out[96], const uint8_t in[96], uint64_t flag) {
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const uint64_t nb = flag - 1, b = ~nb;
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const uint64_t *inq = (const uint64_t *)in;
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uint64_t *outq = (uint64_t *)out;
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outq[0] = (outq[0] & nb) | (inq[0] & b);
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outq[1] = (outq[1] & nb) | (inq[1] & b);
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outq[2] = (outq[2] & nb) | (inq[2] & b);
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outq[3] = (outq[3] & nb) | (inq[3] & b);
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outq[4] = (outq[4] & nb) | (inq[4] & b);
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outq[5] = (outq[5] & nb) | (inq[5] & b);
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outq[6] = (outq[6] & nb) | (inq[6] & b);
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outq[7] = (outq[7] & nb) | (inq[7] & b);
|
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outq[8] = (outq[8] & nb) | (inq[8] & b);
|
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outq[9] = (outq[9] & nb) | (inq[9] & b);
|
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outq[10] = (outq[10] & nb) | (inq[10] & b);
|
|
outq[11] = (outq[11] & nb) | (inq[11] & b);
|
|
}
|
|
|
|
/* if (iswap) swap(a, b) */
|
|
DONNA_INLINE static void
|
|
curve25519_swap_conditional(bignum25519 a, bignum25519 b, uint64_t iswap) {
|
|
const uint64_t swap = (uint64_t)(-(int64_t)iswap);
|
|
uint64_t x0,x1,x2,x3,x4;
|
|
|
|
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;
|
|
}
|
|
|
|
#endif /* ED25519_GCC_64BIT_CHOOSE */
|
|
|
|
#define ED25519_64BIT_TABLES
|
|
|