diff options
Diffstat (limited to 'src/crypto.c')
| -rw-r--r-- | src/crypto.c | 1694 |
1 files changed, 1694 insertions, 0 deletions
diff --git a/src/crypto.c b/src/crypto.c new file mode 100644 index 0000000..97bef62 --- /dev/null +++ b/src/crypto.c @@ -0,0 +1,1694 @@ +/* SPDX-License-Identifier: MIT + * + * Copyright (C) 2015-2021 Jason A. Donenfeld <Jason@zx2c4.com>. All Rights Reserved. + */ + +#include <sys/types.h> +#include <sys/endian.h> +#include <sys/systm.h> + +#include "crypto.h" + +#ifndef ARRAY_SIZE +#define ARRAY_SIZE(x) (sizeof(x) / sizeof((x)[0])) +#endif +#ifndef noinline +#define noinline __attribute__((noinline)) +#endif +#ifndef __aligned +#define __aligned(x) __attribute__((aligned(x))) +#endif +#ifndef DIV_ROUND_UP +#define DIV_ROUND_UP(n,d) (((n) + (d) - 1) / (d)) +#endif + +#define le32_to_cpup(a) le32toh(*(a)) +#define le64_to_cpup(a) le64toh(*(a)) +#define cpu_to_le32(a) htole32(a) +#define cpu_to_le64(a) htole64(a) + +static inline uint32_t get_unaligned_le32(const uint8_t *a) +{ + uint32_t l; + __builtin_memcpy(&l, a, sizeof(l)); + return le32_to_cpup(&l); +} +static inline uint64_t get_unaligned_le64(const uint8_t *a) +{ + uint64_t l; + __builtin_memcpy(&l, a, sizeof(l)); + return le64_to_cpup(&l); +} +static inline void put_unaligned_le32(uint32_t s, uint8_t *d) +{ + uint32_t l = cpu_to_le32(s); + __builtin_memcpy(d, &l, sizeof(l)); +} +static inline void cpu_to_le32_array(uint32_t *buf, unsigned int words) +{ + while (words--) { + *buf = cpu_to_le32(*buf); + ++buf; + } +} +static inline void le32_to_cpu_array(uint32_t *buf, unsigned int words) +{ + while (words--) { + *buf = le32_to_cpup(buf); + ++buf; + } +} + +static inline uint32_t rol32(uint32_t word, unsigned int shift) +{ + return (word << (shift & 31)) | (word >> ((-shift) & 31)); +} +static inline uint32_t ror32(uint32_t word, unsigned int shift) +{ + return (word >> (shift & 31)) | (word << ((-shift) & 31)); +} + +static void xor_cpy(uint8_t *dst, const uint8_t *src1, const uint8_t *src2, + size_t len) +{ + size_t i; + + for (i = 0; i < len; ++i) + dst[i] = src1[i] ^ src2[i]; +} + +#define QUARTER_ROUND(x, a, b, c, d) ( \ + x[a] += x[b], \ + x[d] = rol32((x[d] ^ x[a]), 16), \ + x[c] += x[d], \ + x[b] = rol32((x[b] ^ x[c]), 12), \ + x[a] += x[b], \ + x[d] = rol32((x[d] ^ x[a]), 8), \ + x[c] += x[d], \ + x[b] = rol32((x[b] ^ x[c]), 7) \ +) + +#define C(i, j) (i * 4 + j) + +#define DOUBLE_ROUND(x) ( \ + /* Column Round */ \ + QUARTER_ROUND(x, C(0, 0), C(1, 0), C(2, 0), C(3, 0)), \ + QUARTER_ROUND(x, C(0, 1), C(1, 1), C(2, 1), C(3, 1)), \ + QUARTER_ROUND(x, C(0, 2), C(1, 2), C(2, 2), C(3, 2)), \ + QUARTER_ROUND(x, C(0, 3), C(1, 3), C(2, 3), C(3, 3)), \ + /* Diagonal Round */ \ + QUARTER_ROUND(x, C(0, 0), C(1, 1), C(2, 2), C(3, 3)), \ + QUARTER_ROUND(x, C(0, 1), C(1, 2), C(2, 3), C(3, 0)), \ + QUARTER_ROUND(x, C(0, 2), C(1, 3), C(2, 0), C(3, 1)), \ + QUARTER_ROUND(x, C(0, 3), C(1, 0), C(2, 1), C(3, 2)) \ +) + +#define TWENTY_ROUNDS(x) ( \ + DOUBLE_ROUND(x), \ + DOUBLE_ROUND(x), \ + DOUBLE_ROUND(x), \ + DOUBLE_ROUND(x), \ + DOUBLE_ROUND(x), \ + DOUBLE_ROUND(x), \ + DOUBLE_ROUND(x), \ + DOUBLE_ROUND(x), \ + DOUBLE_ROUND(x), \ + DOUBLE_ROUND(x) \ +) + +enum chacha20_lengths { + CHACHA20_NONCE_SIZE = 16, + CHACHA20_KEY_SIZE = 32, + CHACHA20_KEY_WORDS = CHACHA20_KEY_SIZE / sizeof(uint32_t), + CHACHA20_BLOCK_SIZE = 64, + CHACHA20_BLOCK_WORDS = CHACHA20_BLOCK_SIZE / sizeof(uint32_t), + HCHACHA20_NONCE_SIZE = CHACHA20_NONCE_SIZE, + HCHACHA20_KEY_SIZE = CHACHA20_KEY_SIZE +}; + +enum chacha20_constants { /* expand 32-byte k */ + CHACHA20_CONSTANT_EXPA = 0x61707865U, + CHACHA20_CONSTANT_ND_3 = 0x3320646eU, + CHACHA20_CONSTANT_2_BY = 0x79622d32U, + CHACHA20_CONSTANT_TE_K = 0x6b206574U +}; + +struct chacha20_ctx { + union { + uint32_t state[16]; + struct { + uint32_t constant[4]; + uint32_t key[8]; + uint32_t counter[4]; + }; + }; +}; + +static void chacha20_init(struct chacha20_ctx *ctx, + const uint8_t key[CHACHA20_KEY_SIZE], + const uint64_t nonce) +{ + ctx->constant[0] = CHACHA20_CONSTANT_EXPA; + ctx->constant[1] = CHACHA20_CONSTANT_ND_3; + ctx->constant[2] = CHACHA20_CONSTANT_2_BY; + ctx->constant[3] = CHACHA20_CONSTANT_TE_K; + ctx->key[0] = get_unaligned_le32(key + 0); + ctx->key[1] = get_unaligned_le32(key + 4); + ctx->key[2] = get_unaligned_le32(key + 8); + ctx->key[3] = get_unaligned_le32(key + 12); + ctx->key[4] = get_unaligned_le32(key + 16); + ctx->key[5] = get_unaligned_le32(key + 20); + ctx->key[6] = get_unaligned_le32(key + 24); + ctx->key[7] = get_unaligned_le32(key + 28); + ctx->counter[0] = 0; + ctx->counter[1] = 0; + ctx->counter[2] = nonce & 0xffffffffU; + ctx->counter[3] = nonce >> 32; +} + +static void chacha20_block(struct chacha20_ctx *ctx, uint32_t *stream) +{ + uint32_t x[CHACHA20_BLOCK_WORDS]; + int i; + + for (i = 0; i < ARRAY_SIZE(x); ++i) + x[i] = ctx->state[i]; + + TWENTY_ROUNDS(x); + + for (i = 0; i < ARRAY_SIZE(x); ++i) + stream[i] = cpu_to_le32(x[i] + ctx->state[i]); + + ctx->counter[0] += 1; +} + +static void chacha20(struct chacha20_ctx *ctx, uint8_t *out, const uint8_t *in, + uint32_t len) +{ + uint32_t buf[CHACHA20_BLOCK_WORDS]; + + while (len >= CHACHA20_BLOCK_SIZE) { + chacha20_block(ctx, buf); + xor_cpy(out, in, (uint8_t *)buf, CHACHA20_BLOCK_SIZE); + len -= CHACHA20_BLOCK_SIZE; + out += CHACHA20_BLOCK_SIZE; + in += CHACHA20_BLOCK_SIZE; + } + if (len) { + chacha20_block(ctx, buf); + xor_cpy(out, in, (uint8_t *)buf, len); + } +} + +static void hchacha20(uint32_t derived_key[CHACHA20_KEY_WORDS], + const uint8_t nonce[HCHACHA20_NONCE_SIZE], + const uint8_t key[HCHACHA20_KEY_SIZE]) +{ + uint32_t x[] = { CHACHA20_CONSTANT_EXPA, + CHACHA20_CONSTANT_ND_3, + CHACHA20_CONSTANT_2_BY, + CHACHA20_CONSTANT_TE_K, + get_unaligned_le32(key + 0), + get_unaligned_le32(key + 4), + get_unaligned_le32(key + 8), + get_unaligned_le32(key + 12), + get_unaligned_le32(key + 16), + get_unaligned_le32(key + 20), + get_unaligned_le32(key + 24), + get_unaligned_le32(key + 28), + get_unaligned_le32(nonce + 0), + get_unaligned_le32(nonce + 4), + get_unaligned_le32(nonce + 8), + get_unaligned_le32(nonce + 12) + }; + + TWENTY_ROUNDS(x); + + memcpy(derived_key + 0, x + 0, sizeof(uint32_t) * 4); + memcpy(derived_key + 4, x + 12, sizeof(uint32_t) * 4); +} + +enum poly1305_lengths { + POLY1305_BLOCK_SIZE = 16, + POLY1305_KEY_SIZE = 32, + POLY1305_MAC_SIZE = 16 +}; + +struct poly1305_internal { + uint32_t h[5]; + uint32_t r[5]; + uint32_t s[4]; +}; + +struct poly1305_ctx { + struct poly1305_internal state; + uint32_t nonce[4]; + uint8_t data[POLY1305_BLOCK_SIZE]; + size_t num; +}; + +static void poly1305_init_core(struct poly1305_internal *st, + const uint8_t key[16]) +{ + /* r &= 0xffffffc0ffffffc0ffffffc0fffffff */ + st->r[0] = (get_unaligned_le32(&key[0])) & 0x3ffffff; + st->r[1] = (get_unaligned_le32(&key[3]) >> 2) & 0x3ffff03; + st->r[2] = (get_unaligned_le32(&key[6]) >> 4) & 0x3ffc0ff; + st->r[3] = (get_unaligned_le32(&key[9]) >> 6) & 0x3f03fff; + st->r[4] = (get_unaligned_le32(&key[12]) >> 8) & 0x00fffff; + + /* s = 5*r */ + st->s[0] = st->r[1] * 5; + st->s[1] = st->r[2] * 5; + st->s[2] = st->r[3] * 5; + st->s[3] = st->r[4] * 5; + + /* h = 0 */ + st->h[0] = 0; + st->h[1] = 0; + st->h[2] = 0; + st->h[3] = 0; + st->h[4] = 0; +} + +static void poly1305_blocks_core(struct poly1305_internal *st, + const uint8_t *input, size_t len, + const uint32_t padbit) +{ + const uint32_t hibit = padbit << 24; + uint32_t r0, r1, r2, r3, r4; + uint32_t s1, s2, s3, s4; + uint32_t h0, h1, h2, h3, h4; + uint64_t d0, d1, d2, d3, d4; + uint32_t c; + + r0 = st->r[0]; + r1 = st->r[1]; + r2 = st->r[2]; + r3 = st->r[3]; + r4 = st->r[4]; + + s1 = st->s[0]; + s2 = st->s[1]; + s3 = st->s[2]; + s4 = st->s[3]; + + h0 = st->h[0]; + h1 = st->h[1]; + h2 = st->h[2]; + h3 = st->h[3]; + h4 = st->h[4]; + + while (len >= POLY1305_BLOCK_SIZE) { + /* h += m[i] */ + h0 += (get_unaligned_le32(&input[0])) & 0x3ffffff; + h1 += (get_unaligned_le32(&input[3]) >> 2) & 0x3ffffff; + h2 += (get_unaligned_le32(&input[6]) >> 4) & 0x3ffffff; + h3 += (get_unaligned_le32(&input[9]) >> 6) & 0x3ffffff; + h4 += (get_unaligned_le32(&input[12]) >> 8) | hibit; + + /* h *= r */ + d0 = ((uint64_t)h0 * r0) + ((uint64_t)h1 * s4) + + ((uint64_t)h2 * s3) + ((uint64_t)h3 * s2) + + ((uint64_t)h4 * s1); + d1 = ((uint64_t)h0 * r1) + ((uint64_t)h1 * r0) + + ((uint64_t)h2 * s4) + ((uint64_t)h3 * s3) + + ((uint64_t)h4 * s2); + d2 = ((uint64_t)h0 * r2) + ((uint64_t)h1 * r1) + + ((uint64_t)h2 * r0) + ((uint64_t)h3 * s4) + + ((uint64_t)h4 * s3); + d3 = ((uint64_t)h0 * r3) + ((uint64_t)h1 * r2) + + ((uint64_t)h2 * r1) + ((uint64_t)h3 * r0) + + ((uint64_t)h4 * s4); + d4 = ((uint64_t)h0 * r4) + ((uint64_t)h1 * r3) + + ((uint64_t)h2 * r2) + ((uint64_t)h3 * r1) + + ((uint64_t)h4 * r0); + + /* (partial) h %= p */ + c = (uint32_t)(d0 >> 26); + h0 = (uint32_t)d0 & 0x3ffffff; + d1 += c; + c = (uint32_t)(d1 >> 26); + h1 = (uint32_t)d1 & 0x3ffffff; + d2 += c; + c = (uint32_t)(d2 >> 26); + h2 = (uint32_t)d2 & 0x3ffffff; + d3 += c; + c = (uint32_t)(d3 >> 26); + h3 = (uint32_t)d3 & 0x3ffffff; + d4 += c; + c = (uint32_t)(d4 >> 26); + h4 = (uint32_t)d4 & 0x3ffffff; + h0 += c * 5; + c = (h0 >> 26); + h0 = h0 & 0x3ffffff; + h1 += c; + + input += POLY1305_BLOCK_SIZE; + len -= POLY1305_BLOCK_SIZE; + } + + st->h[0] = h0; + st->h[1] = h1; + st->h[2] = h2; + st->h[3] = h3; + st->h[4] = h4; +} + +static void poly1305_emit_core(struct poly1305_internal *st, uint8_t mac[16], + const uint32_t nonce[4]) +{ + uint32_t h0, h1, h2, h3, h4, c; + uint32_t g0, g1, g2, g3, g4; + uint64_t f; + uint32_t mask; + + /* fully carry h */ + h0 = st->h[0]; + h1 = st->h[1]; + h2 = st->h[2]; + h3 = st->h[3]; + h4 = st->h[4]; + + c = h1 >> 26; + h1 = h1 & 0x3ffffff; + h2 += c; + c = h2 >> 26; + h2 = h2 & 0x3ffffff; + h3 += c; + c = h3 >> 26; + h3 = h3 & 0x3ffffff; + h4 += c; + c = h4 >> 26; + h4 = h4 & 0x3ffffff; + h0 += c * 5; + c = h0 >> 26; + h0 = h0 & 0x3ffffff; + h1 += c; + + /* compute h + -p */ + g0 = h0 + 5; + c = g0 >> 26; + g0 &= 0x3ffffff; + g1 = h1 + c; + c = g1 >> 26; + g1 &= 0x3ffffff; + g2 = h2 + c; + c = g2 >> 26; + g2 &= 0x3ffffff; + g3 = h3 + c; + c = g3 >> 26; + g3 &= 0x3ffffff; + g4 = h4 + c - (1UL << 26); + + /* select h if h < p, or h + -p if h >= p */ + mask = (g4 >> ((sizeof(uint32_t) * 8) - 1)) - 1; + g0 &= mask; + g1 &= mask; + g2 &= mask; + g3 &= mask; + g4 &= mask; + mask = ~mask; + + h0 = (h0 & mask) | g0; + h1 = (h1 & mask) | g1; + h2 = (h2 & mask) | g2; + h3 = (h3 & mask) | g3; + h4 = (h4 & mask) | g4; + + /* h = h % (2^128) */ + h0 = ((h0) | (h1 << 26)) & 0xffffffff; + h1 = ((h1 >> 6) | (h2 << 20)) & 0xffffffff; + h2 = ((h2 >> 12) | (h3 << 14)) & 0xffffffff; + h3 = ((h3 >> 18) | (h4 << 8)) & 0xffffffff; + + /* mac = (h + nonce) % (2^128) */ + f = (uint64_t)h0 + nonce[0]; + h0 = (uint32_t)f; + f = (uint64_t)h1 + nonce[1] + (f >> 32); + h1 = (uint32_t)f; + f = (uint64_t)h2 + nonce[2] + (f >> 32); + h2 = (uint32_t)f; + f = (uint64_t)h3 + nonce[3] + (f >> 32); + h3 = (uint32_t)f; + + put_unaligned_le32(h0, &mac[0]); + put_unaligned_le32(h1, &mac[4]); + put_unaligned_le32(h2, &mac[8]); + put_unaligned_le32(h3, &mac[12]); +} + +static void poly1305_init(struct poly1305_ctx *ctx, + const uint8_t key[POLY1305_KEY_SIZE]) +{ + ctx->nonce[0] = get_unaligned_le32(&key[16]); + ctx->nonce[1] = get_unaligned_le32(&key[20]); + ctx->nonce[2] = get_unaligned_le32(&key[24]); + ctx->nonce[3] = get_unaligned_le32(&key[28]); + + poly1305_init_core(&ctx->state, key); + + ctx->num = 0; +} + +static void poly1305_update(struct poly1305_ctx *ctx, const uint8_t *input, + size_t len) +{ + const size_t num = ctx->num; + size_t rem; + + if (num) { + rem = POLY1305_BLOCK_SIZE - num; + if (len < rem) { + memcpy(ctx->data + num, input, len); + ctx->num = num + len; + return; + } + memcpy(ctx->data + num, input, rem); + poly1305_blocks_core(&ctx->state, ctx->data, + POLY1305_BLOCK_SIZE, 1); + input += rem; + len -= rem; + } + + rem = len % POLY1305_BLOCK_SIZE; + len -= rem; + + if (len >= POLY1305_BLOCK_SIZE) { + poly1305_blocks_core(&ctx->state, input, len, 1); + input += len; + } + + if (rem) + memcpy(ctx->data, input, rem); + + ctx->num = rem; +} + +static void poly1305_final(struct poly1305_ctx *ctx, + uint8_t mac[POLY1305_MAC_SIZE]) +{ + size_t num = ctx->num; + + if (num) { + ctx->data[num++] = 1; + while (num < POLY1305_BLOCK_SIZE) + ctx->data[num++] = 0; + poly1305_blocks_core(&ctx->state, ctx->data, + POLY1305_BLOCK_SIZE, 0); + } + + poly1305_emit_core(&ctx->state, mac, ctx->nonce); + + explicit_bzero(ctx, sizeof(*ctx)); +} + + +static const uint8_t pad0[16] = { 0 }; + +void +chacha20poly1305_encrypt(uint8_t *dst, const uint8_t *src, const size_t src_len, + const uint8_t *ad, const size_t ad_len, + const uint64_t nonce, + const uint8_t key[CHACHA20POLY1305_KEY_SIZE]) +{ + struct poly1305_ctx poly1305_state; + struct chacha20_ctx chacha20_state; + union { + uint8_t block0[POLY1305_KEY_SIZE]; + uint64_t lens[2]; + } b = { { 0 } }; + + chacha20_init(&chacha20_state, key, nonce); + chacha20(&chacha20_state, b.block0, b.block0, sizeof(b.block0)); + poly1305_init(&poly1305_state, b.block0); + + poly1305_update(&poly1305_state, ad, ad_len); + poly1305_update(&poly1305_state, pad0, (0x10 - ad_len) & 0xf); + + chacha20(&chacha20_state, dst, src, src_len); + + poly1305_update(&poly1305_state, dst, src_len); + poly1305_update(&poly1305_state, pad0, (0x10 - src_len) & 0xf); + + b.lens[0] = cpu_to_le64(ad_len); + b.lens[1] = cpu_to_le64(src_len); + poly1305_update(&poly1305_state, (uint8_t *)b.lens, sizeof(b.lens)); + + poly1305_final(&poly1305_state, dst + src_len); + + explicit_bzero(&chacha20_state, sizeof(chacha20_state)); + explicit_bzero(&b, sizeof(b)); +} + +bool +chacha20poly1305_decrypt(uint8_t *dst, const uint8_t *src, const size_t src_len, + const uint8_t *ad, const size_t ad_len, + const uint64_t nonce, + const uint8_t key[CHACHA20POLY1305_KEY_SIZE]) +{ + struct poly1305_ctx poly1305_state; + struct chacha20_ctx chacha20_state; + bool ret; + size_t dst_len; + union { + uint8_t block0[POLY1305_KEY_SIZE]; + uint8_t mac[POLY1305_MAC_SIZE]; + uint64_t lens[2]; + } b = { { 0 } }; + + if (src_len < POLY1305_MAC_SIZE) + return false; + + chacha20_init(&chacha20_state, key, nonce); + chacha20(&chacha20_state, b.block0, b.block0, sizeof(b.block0)); + poly1305_init(&poly1305_state, b.block0); + + poly1305_update(&poly1305_state, ad, ad_len); + poly1305_update(&poly1305_state, pad0, (0x10 - ad_len) & 0xf); + + dst_len = src_len - POLY1305_MAC_SIZE; + poly1305_update(&poly1305_state, src, dst_len); + poly1305_update(&poly1305_state, pad0, (0x10 - dst_len) & 0xf); + + b.lens[0] = cpu_to_le64(ad_len); + b.lens[1] = cpu_to_le64(dst_len); + poly1305_update(&poly1305_state, (uint8_t *)b.lens, sizeof(b.lens)); + + poly1305_final(&poly1305_state, b.mac); + + ret = timingsafe_bcmp(b.mac, src + dst_len, POLY1305_MAC_SIZE) == 0; + if (ret) + chacha20(&chacha20_state, dst, src, dst_len); + + explicit_bzero(&chacha20_state, sizeof(chacha20_state)); + explicit_bzero(&b, sizeof(b)); + + return ret; +} + +void +xchacha20poly1305_encrypt(uint8_t *dst, const uint8_t *src, + const size_t src_len, const uint8_t *ad, + const size_t ad_len, + const uint8_t nonce[XCHACHA20POLY1305_NONCE_SIZE], + const uint8_t key[CHACHA20POLY1305_KEY_SIZE]) +{ + uint32_t derived_key[CHACHA20_KEY_WORDS]; + + hchacha20(derived_key, nonce, key); + cpu_to_le32_array(derived_key, ARRAY_SIZE(derived_key)); + chacha20poly1305_encrypt(dst, src, src_len, ad, ad_len, + get_unaligned_le64(nonce + 16), + (uint8_t *)derived_key); + explicit_bzero(derived_key, CHACHA20POLY1305_KEY_SIZE); +} + +bool +xchacha20poly1305_decrypt(uint8_t *dst, const uint8_t *src, + const size_t src_len, const uint8_t *ad, + const size_t ad_len, + const uint8_t nonce[XCHACHA20POLY1305_NONCE_SIZE], + const uint8_t key[CHACHA20POLY1305_KEY_SIZE]) +{ + bool ret; + uint32_t derived_key[CHACHA20_KEY_WORDS]; + + hchacha20(derived_key, nonce, key); + cpu_to_le32_array(derived_key, ARRAY_SIZE(derived_key)); + ret = chacha20poly1305_decrypt(dst, src, src_len, ad, ad_len, + get_unaligned_le64(nonce + 16), + (uint8_t *)derived_key); + explicit_bzero(derived_key, CHACHA20POLY1305_KEY_SIZE); + return ret; +} + + +static const uint32_t blake2s_iv[8] = { + 0x6A09E667UL, 0xBB67AE85UL, 0x3C6EF372UL, 0xA54FF53AUL, + 0x510E527FUL, 0x9B05688CUL, 0x1F83D9ABUL, 0x5BE0CD19UL +}; + +static const uint8_t blake2s_sigma[10][16] = { + { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 }, + { 14, 10, 4, 8, 9, 15, 13, 6, 1, 12, 0, 2, 11, 7, 5, 3 }, + { 11, 8, 12, 0, 5, 2, 15, 13, 10, 14, 3, 6, 7, 1, 9, 4 }, + { 7, 9, 3, 1, 13, 12, 11, 14, 2, 6, 5, 10, 4, 0, 15, 8 }, + { 9, 0, 5, 7, 2, 4, 10, 15, 14, 1, 11, 12, 6, 8, 3, 13 }, + { 2, 12, 6, 10, 0, 11, 8, 3, 4, 13, 7, 5, 15, 14, 1, 9 }, + { 12, 5, 1, 15, 14, 13, 4, 10, 0, 7, 6, 3, 9, 2, 8, 11 }, + { 13, 11, 7, 14, 12, 1, 3, 9, 5, 0, 15, 4, 8, 6, 2, 10 }, + { 6, 15, 14, 9, 11, 3, 0, 8, 12, 2, 13, 7, 1, 4, 10, 5 }, + { 10, 2, 8, 4, 7, 6, 1, 5, 15, 11, 9, 14, 3, 12, 13, 0 }, +}; + +static inline void blake2s_set_lastblock(struct blake2s_state *state) +{ + state->f[0] = -1; +} + +static inline void blake2s_increment_counter(struct blake2s_state *state, + const uint32_t inc) +{ + state->t[0] += inc; + state->t[1] += (state->t[0] < inc); +} + +static inline void blake2s_init_param(struct blake2s_state *state, + const uint32_t param) +{ + int i; + + memset(state, 0, sizeof(*state)); + for (i = 0; i < 8; ++i) + state->h[i] = blake2s_iv[i]; + state->h[0] ^= param; +} + +void blake2s_init(struct blake2s_state *state, const size_t outlen) +{ + blake2s_init_param(state, 0x01010000 | outlen); + state->outlen = outlen; +} + +void blake2s_init_key(struct blake2s_state *state, const size_t outlen, + const uint8_t *key, const size_t keylen) +{ + uint8_t block[BLAKE2S_BLOCK_SIZE] = { 0 }; + + blake2s_init_param(state, 0x01010000 | keylen << 8 | outlen); + state->outlen = outlen; + memcpy(block, key, keylen); + blake2s_update(state, block, BLAKE2S_BLOCK_SIZE); + explicit_bzero(block, BLAKE2S_BLOCK_SIZE); +} + +static inline void blake2s_compress(struct blake2s_state *state, + const uint8_t *block, size_t nblocks, + const uint32_t inc) +{ + uint32_t m[16]; + uint32_t v[16]; + int i; + + while (nblocks > 0) { + blake2s_increment_counter(state, inc); + memcpy(m, block, BLAKE2S_BLOCK_SIZE); + le32_to_cpu_array(m, ARRAY_SIZE(m)); + memcpy(v, state->h, 32); + v[ 8] = blake2s_iv[0]; + v[ 9] = blake2s_iv[1]; + v[10] = blake2s_iv[2]; + v[11] = blake2s_iv[3]; + v[12] = blake2s_iv[4] ^ state->t[0]; + v[13] = blake2s_iv[5] ^ state->t[1]; + v[14] = blake2s_iv[6] ^ state->f[0]; + v[15] = blake2s_iv[7] ^ state->f[1]; + +#define G(r, i, a, b, c, d) do { \ + a += b + m[blake2s_sigma[r][2 * i + 0]]; \ + d = ror32(d ^ a, 16); \ + c += d; \ + b = ror32(b ^ c, 12); \ + a += b + m[blake2s_sigma[r][2 * i + 1]]; \ + d = ror32(d ^ a, 8); \ + c += d; \ + b = ror32(b ^ c, 7); \ +} while (0) + +#define ROUND(r) do { \ + G(r, 0, v[0], v[ 4], v[ 8], v[12]); \ + G(r, 1, v[1], v[ 5], v[ 9], v[13]); \ + G(r, 2, v[2], v[ 6], v[10], v[14]); \ + G(r, 3, v[3], v[ 7], v[11], v[15]); \ + G(r, 4, v[0], v[ 5], v[10], v[15]); \ + G(r, 5, v[1], v[ 6], v[11], v[12]); \ + G(r, 6, v[2], v[ 7], v[ 8], v[13]); \ + G(r, 7, v[3], v[ 4], v[ 9], v[14]); \ +} while (0) + ROUND(0); + ROUND(1); + ROUND(2); + ROUND(3); + ROUND(4); + ROUND(5); + ROUND(6); + ROUND(7); + ROUND(8); + ROUND(9); + +#undef G +#undef ROUND + + for (i = 0; i < 8; ++i) + state->h[i] ^= v[i] ^ v[i + 8]; + + block += BLAKE2S_BLOCK_SIZE; + --nblocks; + } +} + +void blake2s_update(struct blake2s_state *state, const uint8_t *in, size_t inlen) +{ + const size_t fill = BLAKE2S_BLOCK_SIZE - state->buflen; + + if (!inlen) + return; + if (inlen > fill) { + memcpy(state->buf + state->buflen, in, fill); + blake2s_compress(state, state->buf, 1, BLAKE2S_BLOCK_SIZE); + state->buflen = 0; + in += fill; + inlen -= fill; + } + if (inlen > BLAKE2S_BLOCK_SIZE) { + const size_t nblocks = DIV_ROUND_UP(inlen, BLAKE2S_BLOCK_SIZE); + /* Hash one less (full) block than strictly possible */ + blake2s_compress(state, in, nblocks - 1, BLAKE2S_BLOCK_SIZE); + in += BLAKE2S_BLOCK_SIZE * (nblocks - 1); + inlen -= BLAKE2S_BLOCK_SIZE * (nblocks - 1); + } + memcpy(state->buf + state->buflen, in, inlen); + state->buflen += inlen; +} + +void blake2s_final(struct blake2s_state *state, uint8_t *out) +{ + blake2s_set_lastblock(state); + memset(state->buf + state->buflen, 0, + BLAKE2S_BLOCK_SIZE - state->buflen); /* Padding */ + blake2s_compress(state, state->buf, 1, state->buflen); + cpu_to_le32_array(state->h, ARRAY_SIZE(state->h)); + memcpy(out, state->h, state->outlen); + explicit_bzero(state, sizeof(*state)); +} + +void blake2s(uint8_t *out, const uint8_t *in, const uint8_t *key, + const size_t outlen, const size_t inlen, const size_t keylen) +{ + struct blake2s_state state; + + if (keylen) + blake2s_init_key(&state, outlen, key, keylen); + else + blake2s_init(&state, outlen); + + blake2s_update(&state, in, inlen); + blake2s_final(&state, out); +} + +void blake2s_hmac(uint8_t *out, const uint8_t *in, const uint8_t *key, const size_t outlen, + const size_t inlen, const size_t keylen) +{ + struct blake2s_state state; + uint8_t x_key[BLAKE2S_BLOCK_SIZE] __aligned(sizeof(uint32_t)) = { 0 }; + uint8_t i_hash[BLAKE2S_HASH_SIZE] __aligned(sizeof(uint32_t)); + int i; + + if (keylen > BLAKE2S_BLOCK_SIZE) { + blake2s_init(&state, BLAKE2S_HASH_SIZE); + blake2s_update(&state, key, keylen); + blake2s_final(&state, x_key); + } else + memcpy(x_key, key, keylen); + + for (i = 0; i < BLAKE2S_BLOCK_SIZE; ++i) + x_key[i] ^= 0x36; + + blake2s_init(&state, BLAKE2S_HASH_SIZE); + blake2s_update(&state, x_key, BLAKE2S_BLOCK_SIZE); + blake2s_update(&state, in, inlen); + blake2s_final(&state, i_hash); + + for (i = 0; i < BLAKE2S_BLOCK_SIZE; ++i) + x_key[i] ^= 0x5c ^ 0x36; + + blake2s_init(&state, BLAKE2S_HASH_SIZE); + blake2s_update(&state, x_key, BLAKE2S_BLOCK_SIZE); + blake2s_update(&state, i_hash, BLAKE2S_HASH_SIZE); + blake2s_final(&state, i_hash); + + memcpy(out, i_hash, outlen); + explicit_bzero(x_key, BLAKE2S_BLOCK_SIZE); + explicit_bzero(i_hash, BLAKE2S_HASH_SIZE); +} + + +/* Below here is fiat's implementation of x25519. + * + * Copyright (C) 2015-2016 The fiat-crypto Authors. + * Copyright (C) 2018-2021 Jason A. Donenfeld <Jason@zx2c4.com>. All Rights Reserved. + * + * This is a machine-generated formally verified implementation of Curve25519 + * ECDH from: <https://github.com/mit-plv/fiat-crypto>. Though originally + * machine generated, it has been tweaked to be suitable for use in the kernel. + * It is optimized for 32-bit machines and machines that cannot work efficiently + * with 128-bit integer types. + */ + +/* fe means field element. Here the field is \Z/(2^255-19). An element t, + * entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77 + * t[3]+2^102 t[4]+...+2^230 t[9]. + * fe limbs are bounded by 1.125*2^26,1.125*2^25,1.125*2^26,1.125*2^25,etc. + * Multiplication and carrying produce fe from fe_loose. + */ +typedef struct fe { uint32_t v[10]; } fe; + +/* fe_loose limbs are bounded by 3.375*2^26,3.375*2^25,3.375*2^26,3.375*2^25,etc + * Addition and subtraction produce fe_loose from (fe, fe). + */ +typedef struct fe_loose { uint32_t v[10]; } fe_loose; + +static inline void fe_frombytes_impl(uint32_t h[10], const uint8_t *s) +{ + /* Ignores top bit of s. */ + uint32_t a0 = get_unaligned_le32(s); + uint32_t a1 = get_unaligned_le32(s+4); + uint32_t a2 = get_unaligned_le32(s+8); + uint32_t a3 = get_unaligned_le32(s+12); + uint32_t a4 = get_unaligned_le32(s+16); + uint32_t a5 = get_unaligned_le32(s+20); + uint32_t a6 = get_unaligned_le32(s+24); + uint32_t a7 = get_unaligned_le32(s+28); + h[0] = a0&((1<<26)-1); /* 26 used, 32-26 left. 26 */ + h[1] = (a0>>26) | ((a1&((1<<19)-1))<< 6); /* (32-26) + 19 = 6+19 = 25 */ + h[2] = (a1>>19) | ((a2&((1<<13)-1))<<13); /* (32-19) + 13 = 13+13 = 26 */ + h[3] = (a2>>13) | ((a3&((1<< 6)-1))<<19); /* (32-13) + 6 = 19+ 6 = 25 */ + h[4] = (a3>> 6); /* (32- 6) = 26 */ + h[5] = a4&((1<<25)-1); /* 25 */ + h[6] = (a4>>25) | ((a5&((1<<19)-1))<< 7); /* (32-25) + 19 = 7+19 = 26 */ + h[7] = (a5>>19) | ((a6&((1<<12)-1))<<13); /* (32-19) + 12 = 13+12 = 25 */ + h[8] = (a6>>12) | ((a7&((1<< 6)-1))<<20); /* (32-12) + 6 = 20+ 6 = 26 */ + h[9] = (a7>> 6)&((1<<25)-1); /* 25 */ +} + +static inline void fe_frombytes(fe *h, const uint8_t *s) +{ + fe_frombytes_impl(h->v, s); +} + +static inline uint8_t /*bool*/ +addcarryx_u25(uint8_t /*bool*/ c, uint32_t a, uint32_t b, uint32_t *low) +{ + /* This function extracts 25 bits of result and 1 bit of carry + * (26 total), so a 32-bit intermediate is sufficient. + */ + uint32_t x = a + b + c; + *low = x & ((1 << 25) - 1); + return (x >> 25) & 1; +} + +static inline uint8_t /*bool*/ +addcarryx_u26(uint8_t /*bool*/ c, uint32_t a, uint32_t b, uint32_t *low) +{ + /* This function extracts 26 bits of result and 1 bit of carry + * (27 total), so a 32-bit intermediate is sufficient. + */ + uint32_t x = a + b + c; + *low = x & ((1 << 26) - 1); + return (x >> 26) & 1; +} + +static inline uint8_t /*bool*/ +subborrow_u25(uint8_t /*bool*/ c, uint32_t a, uint32_t b, uint32_t *low) +{ + /* This function extracts 25 bits of result and 1 bit of borrow + * (26 total), so a 32-bit intermediate is sufficient. + */ + uint32_t x = a - b - c; + *low = x & ((1 << 25) - 1); + return x >> 31; +} + +static inline uint8_t /*bool*/ +subborrow_u26(uint8_t /*bool*/ c, uint32_t a, uint32_t b, uint32_t *low) +{ + /* This function extracts 26 bits of result and 1 bit of borrow + *(27 total), so a 32-bit intermediate is sufficient. + */ + uint32_t x = a - b - c; + *low = x & ((1 << 26) - 1); + return x >> 31; +} + +static inline uint32_t cmovznz32(uint32_t t, uint32_t z, uint32_t nz) +{ + t = -!!t; /* all set if nonzero, 0 if 0 */ + return (t&nz) | ((~t)&z); +} + +static inline void fe_freeze(uint32_t out[10], const uint32_t in1[10]) +{ + const uint32_t x17 = in1[9]; + const uint32_t x18 = in1[8]; + const uint32_t x16 = in1[7]; + const uint32_t x14 = in1[6]; + const uint32_t x12 = in1[5]; + const uint32_t x10 = in1[4]; + const uint32_t x8 = in1[3]; + const uint32_t x6 = in1[2]; + const uint32_t x4 = in1[1]; + const uint32_t x2 = in1[0]; + uint32_t x20; uint8_t/*bool*/ x21 = subborrow_u26(0x0, x2, 0x3ffffed, &x20); + uint32_t x23; uint8_t/*bool*/ x24 = subborrow_u25(x21, x4, 0x1ffffff, &x23); + uint32_t x26; uint8_t/*bool*/ x27 = subborrow_u26(x24, x6, 0x3ffffff, &x26); + uint32_t x29; uint8_t/*bool*/ x30 = subborrow_u25(x27, x8, 0x1ffffff, &x29); + uint32_t x32; uint8_t/*bool*/ x33 = subborrow_u26(x30, x10, 0x3ffffff, &x32); + uint32_t x35; uint8_t/*bool*/ x36 = subborrow_u25(x33, x12, 0x1ffffff, &x35); + uint32_t x38; uint8_t/*bool*/ x39 = subborrow_u26(x36, x14, 0x3ffffff, &x38); + uint32_t x41; uint8_t/*bool*/ x42 = subborrow_u25(x39, x16, 0x1ffffff, &x41); + uint32_t x44; uint8_t/*bool*/ x45 = subborrow_u26(x42, x18, 0x3ffffff, &x44); + uint32_t x47; uint8_t/*bool*/ x48 = subborrow_u25(x45, x17, 0x1ffffff, &x47); + uint32_t x49 = cmovznz32(x48, 0x0, 0xffffffff); + uint32_t x50 = (x49 & 0x3ffffed); + uint32_t x52; uint8_t/*bool*/ x53 = addcarryx_u26(0x0, x20, x50, &x52); + uint32_t x54 = (x49 & 0x1ffffff); + uint32_t x56; uint8_t/*bool*/ x57 = addcarryx_u25(x53, x23, x54, &x56); + uint32_t x58 = (x49 & 0x3ffffff); + uint32_t x60; uint8_t/*bool*/ x61 = addcarryx_u26(x57, x26, x58, &x60); + uint32_t x62 = (x49 & 0x1ffffff); + uint32_t x64; uint8_t/*bool*/ x65 = addcarryx_u25(x61, x29, x62, &x64); + uint32_t x66 = (x49 & 0x3ffffff); + uint32_t x68; uint8_t/*bool*/ x69 = addcarryx_u26(x65, x32, x66, &x68); + uint32_t x70 = (x49 & 0x1ffffff); + uint32_t x72; uint8_t/*bool*/ x73 = addcarryx_u25(x69, x35, x70, &x72); + uint32_t x74 = (x49 & 0x3ffffff); + uint32_t x76; uint8_t/*bool*/ x77 = addcarryx_u26(x73, x38, x74, &x76); + uint32_t x78 = (x49 & 0x1ffffff); + uint32_t x80; uint8_t/*bool*/ x81 = addcarryx_u25(x77, x41, x78, &x80); + uint32_t x82 = (x49 & 0x3ffffff); + uint32_t x84; uint8_t/*bool*/ x85 = addcarryx_u26(x81, x44, x82, &x84); + uint32_t x86 = (x49 & 0x1ffffff); + uint32_t x88; addcarryx_u25(x85, x47, x86, &x88); + out[0] = x52; + out[1] = x56; + out[2] = x60; + out[3] = x64; + out[4] = x68; + out[5] = x72; + out[6] = x76; + out[7] = x80; + out[8] = x84; + out[9] = x88; +} + +static inline void fe_tobytes(uint8_t s[32], const fe *f) +{ + uint32_t h[10]; + fe_freeze(h, f->v); + s[0] = h[0] >> 0; + s[1] = h[0] >> 8; + s[2] = h[0] >> 16; + s[3] = (h[0] >> 24) | (h[1] << 2); + s[4] = h[1] >> 6; + s[5] = h[1] >> 14; + s[6] = (h[1] >> 22) | (h[2] << 3); + s[7] = h[2] >> 5; + s[8] = h[2] >> 13; + s[9] = (h[2] >> 21) | (h[3] << 5); + s[10] = h[3] >> 3; + s[11] = h[3] >> 11; + s[12] = (h[3] >> 19) | (h[4] << 6); + s[13] = h[4] >> 2; + s[14] = h[4] >> 10; + s[15] = h[4] >> 18; + s[16] = h[5] >> 0; + s[17] = h[5] >> 8; + s[18] = h[5] >> 16; + s[19] = (h[5] >> 24) | (h[6] << 1); + s[20] = h[6] >> 7; + s[21] = h[6] >> 15; + s[22] = (h[6] >> 23) | (h[7] << 3); + s[23] = h[7] >> 5; + s[24] = h[7] >> 13; + s[25] = (h[7] >> 21) | (h[8] << 4); + s[26] = h[8] >> 4; + s[27] = h[8] >> 12; + s[28] = (h[8] >> 20) | (h[9] << 6); + s[29] = h[9] >> 2; + s[30] = h[9] >> 10; + s[31] = h[9] >> 18; +} + +/* h = f */ +static inline void fe_copy(fe *h, const fe *f) +{ + memmove(h, f, sizeof(uint32_t) * 10); +} + +static inline void fe_copy_lt(fe_loose *h, const fe *f) +{ + memmove(h, f, sizeof(uint32_t) * 10); +} + +/* h = 0 */ +static inline void fe_0(fe *h) +{ + memset(h, 0, sizeof(uint32_t) * 10); +} + +/* h = 1 */ +static inline void fe_1(fe *h) +{ + memset(h, 0, sizeof(uint32_t) * 10); + h->v[0] = 1; +} + +static void fe_add_impl(uint32_t out[10], const uint32_t in1[10], const uint32_t in2[10]) +{ + const uint32_t x20 = in1[9]; + const uint32_t x21 = in1[8]; + const uint32_t x19 = in1[7]; + const uint32_t x17 = in1[6]; + const uint32_t x15 = in1[5]; + const uint32_t x13 = in1[4]; + const uint32_t x11 = in1[3]; + const uint32_t x9 = in1[2]; + const uint32_t x7 = in1[1]; + const uint32_t x5 = in1[0]; + const uint32_t x38 = in2[9]; + const uint32_t x39 = in2[8]; + const uint32_t x37 = in2[7]; + const uint32_t x35 = in2[6]; + const uint32_t x33 = in2[5]; + const uint32_t x31 = in2[4]; + const uint32_t x29 = in2[3]; + const uint32_t x27 = in2[2]; + const uint32_t x25 = in2[1]; + const uint32_t x23 = in2[0]; + out[0] = (x5 + x23); + out[1] = (x7 + x25); + out[2] = (x9 + x27); + out[3] = (x11 + x29); + out[4] = (x13 + x31); + out[5] = (x15 + x33); + out[6] = (x17 + x35); + out[7] = (x19 + x37); + out[8] = (x21 + x39); + out[9] = (x20 + x38); +} + +/* h = f + g + * Can overlap h with f or g. + */ +static inline void fe_add(fe_loose *h, const fe *f, const fe *g) +{ + fe_add_impl(h->v, f->v, g->v); +} + +static void fe_sub_impl(uint32_t out[10], const uint32_t in1[10], const uint32_t in2[10]) +{ + const uint32_t x20 = in1[9]; + const uint32_t x21 = in1[8]; + const uint32_t x19 = in1[7]; + const uint32_t x17 = in1[6]; + const uint32_t x15 = in1[5]; + const uint32_t x13 = in1[4]; + const uint32_t x11 = in1[3]; + const uint32_t x9 = in1[2]; + const uint32_t x7 = in1[1]; + const uint32_t x5 = in1[0]; + const uint32_t x38 = in2[9]; + const uint32_t x39 = in2[8]; + const uint32_t x37 = in2[7]; + const uint32_t x35 = in2[6]; + const uint32_t x33 = in2[5]; + const uint32_t x31 = in2[4]; + const uint32_t x29 = in2[3]; + const uint32_t x27 = in2[2]; + const uint32_t x25 = in2[1]; + const uint32_t x23 = in2[0]; + out[0] = ((0x7ffffda + x5) - x23); + out[1] = ((0x3fffffe + x7) - x25); + out[2] = ((0x7fffffe + x9) - x27); + out[3] = ((0x3fffffe + x11) - x29); + out[4] = ((0x7fffffe + x13) - x31); + out[5] = ((0x3fffffe + x15) - x33); + out[6] = ((0x7fffffe + x17) - x35); + out[7] = ((0x3fffffe + x19) - x37); + out[8] = ((0x7fffffe + x21) - x39); + out[9] = ((0x3fffffe + x20) - x38); +} + +/* h = f - g + * Can overlap h with f or g. + */ +static inline void fe_sub(fe_loose *h, const fe *f, const fe *g) +{ + fe_sub_impl(h->v, f->v, g->v); +} + +static void fe_mul_impl(uint32_t out[10], const uint32_t in1[10], const uint32_t in2[10]) +{ + const uint32_t x20 = in1[9]; + const uint32_t x21 = in1[8]; + const uint32_t x19 = in1[7]; + const uint32_t x17 = in1[6]; + const uint32_t x15 = in1[5]; + const uint32_t x13 = in1[4]; + const uint32_t x11 = in1[3]; + const uint32_t x9 = in1[2]; + const uint32_t x7 = in1[1]; + const uint32_t x5 = in1[0]; + const uint32_t x38 = in2[9]; + const uint32_t x39 = in2[8]; + const uint32_t x37 = in2[7]; + const uint32_t x35 = in2[6]; + const uint32_t x33 = in2[5]; + const uint32_t x31 = in2[4]; + const uint32_t x29 = in2[3]; + const uint32_t x27 = in2[2]; + const uint32_t x25 = in2[1]; + const uint32_t x23 = in2[0]; + uint64_t x40 = ((uint64_t)x23 * x5); + uint64_t x41 = (((uint64_t)x23 * x7) + ((uint64_t)x25 * x5)); + uint64_t x42 = ((((uint64_t)(0x2 * x25) * x7) + ((uint64_t)x23 * x9)) + ((uint64_t)x27 * x5)); + uint64_t x43 = (((((uint64_t)x25 * x9) + ((uint64_t)x27 * x7)) + ((uint64_t)x23 * x11)) + ((uint64_t)x29 * x5)); + uint64_t x44 = (((((uint64_t)x27 * x9) + (0x2 * (((uint64_t)x25 * x11) + ((uint64_t)x29 * x7)))) + ((uint64_t)x23 * x13)) + ((uint64_t)x31 * x5)); + uint64_t x45 = (((((((uint64_t)x27 * x11) + ((uint64_t)x29 * x9)) + ((uint64_t)x25 * x13)) + ((uint64_t)x31 * x7)) + ((uint64_t)x23 * x15)) + ((uint64_t)x33 * x5)); + uint64_t x46 = (((((0x2 * ((((uint64_t)x29 * x11) + ((uint64_t)x25 * x15)) + ((uint64_t)x33 * x7))) + ((uint64_t)x27 * x13)) + ((uint64_t)x31 * x9)) + ((uint64_t)x23 * x17)) + ((uint64_t)x35 * x5)); + uint64_t x47 = (((((((((uint64_t)x29 * x13) + ((uint64_t)x31 * x11)) + ((uint64_t)x27 * x15)) + ((uint64_t)x33 * x9)) + ((uint64_t)x25 * x17)) + ((uint64_t)x35 * x7)) + ((uint64_t)x23 * x19)) + ((uint64_t)x37 * x5)); + uint64_t x48 = (((((((uint64_t)x31 * x13) + (0x2 * (((((uint64_t)x29 * x15) + ((uint64_t)x33 * x11)) + ((uint64_t)x25 * x19)) + ((uint64_t)x37 * x7)))) + ((uint64_t)x27 * x17)) + ((uint64_t)x35 * x9)) + ((uint64_t)x23 * x21)) + ((uint64_t)x39 * x5)); + uint64_t x49 = (((((((((((uint64_t)x31 * x15) + ((uint64_t)x33 * x13)) + ((uint64_t)x29 * x17)) + ((uint64_t)x35 * x11)) + ((uint64_t)x27 * x19)) + ((uint64_t)x37 * x9)) + ((uint64_t)x25 * x21)) + ((uint64_t)x39 * x7)) + ((uint64_t)x23 * x20)) + ((uint64_t)x38 * x5)); + uint64_t x50 = (((((0x2 * ((((((uint64_t)x33 * x15) + ((uint64_t)x29 * x19)) + ((uint64_t)x37 * x11)) + ((uint64_t)x25 * x20)) + ((uint64_t)x38 * x7))) + ((uint64_t)x31 * x17)) + ((uint64_t)x35 * x13)) + ((uint64_t)x27 * x21)) + ((uint64_t)x39 * x9)); + uint64_t x51 = (((((((((uint64_t)x33 * x17) + ((uint64_t)x35 * x15)) + ((uint64_t)x31 * x19)) + ((uint64_t)x37 * x13)) + ((uint64_t)x29 * x21)) + ((uint64_t)x39 * x11)) + ((uint64_t)x27 * x20)) + ((uint64_t)x38 * x9)); + uint64_t x52 = (((((uint64_t)x35 * x17) + (0x2 * (((((uint64_t)x33 * x19) + ((uint64_t)x37 * x15)) + ((uint64_t)x29 * x20)) + ((uint64_t)x38 * x11)))) + ((uint64_t)x31 * x21)) + ((uint64_t)x39 * x13)); + uint64_t x53 = (((((((uint64_t)x35 * x19) + ((uint64_t)x37 * x17)) + ((uint64_t)x33 * x21)) + ((uint64_t)x39 * x15)) + ((uint64_t)x31 * x20)) + ((uint64_t)x38 * x13)); + uint64_t x54 = (((0x2 * ((((uint64_t)x37 * x19) + ((uint64_t)x33 * x20)) + ((uint64_t)x38 * x15))) + ((uint64_t)x35 * x21)) + ((uint64_t)x39 * x17)); + uint64_t x55 = (((((uint64_t)x37 * x21) + ((uint64_t)x39 * x19)) + ((uint64_t)x35 * x20)) + ((uint64_t)x38 * x17)); + uint64_t x56 = (((uint64_t)x39 * x21) + (0x2 * (((uint64_t)x37 * x20) + ((uint64_t)x38 * x19)))); + uint64_t x57 = (((uint64_t)x39 * x20) + ((uint64_t)x38 * x21)); + uint64_t x58 = ((uint64_t)(0x2 * x38) * x20); + uint64_t x59 = (x48 + (x58 << 0x4)); + uint64_t x60 = (x59 + (x58 << 0x1)); + uint64_t x61 = (x60 + x58); + uint64_t x62 = (x47 + (x57 << 0x4)); + uint64_t x63 = (x62 + (x57 << 0x1)); + uint64_t x64 = (x63 + x57); + uint64_t x65 = (x46 + (x56 << 0x4)); + uint64_t x66 = (x65 + (x56 << 0x1)); + uint64_t x67 = (x66 + x56); + uint64_t x68 = (x45 + (x55 << 0x4)); + uint64_t x69 = (x68 + (x55 << 0x1)); + uint64_t x70 = (x69 + x55); + uint64_t x71 = (x44 + (x54 << 0x4)); + uint64_t x72 = (x71 + (x54 << 0x1)); + uint64_t x73 = (x72 + x54); + uint64_t x74 = (x43 + (x53 << 0x4)); + uint64_t x75 = (x74 + (x53 << 0x1)); + uint64_t x76 = (x75 + x53); + uint64_t x77 = (x42 + (x52 << 0x4)); + uint64_t x78 = (x77 + (x52 << 0x1)); + uint64_t x79 = (x78 + x52); + uint64_t x80 = (x41 + (x51 << 0x4)); + uint64_t x81 = (x80 + (x51 << 0x1)); + uint64_t x82 = (x81 + x51); + uint64_t x83 = (x40 + (x50 << 0x4)); + uint64_t x84 = (x83 + (x50 << 0x1)); + uint64_t x85 = (x84 + x50); + uint64_t x86 = (x85 >> 0x1a); + uint32_t x87 = ((uint32_t)x85 & 0x3ffffff); + uint64_t x88 = (x86 + x82); + uint64_t x89 = (x88 >> 0x19); + uint32_t x90 = ((uint32_t)x88 & 0x1ffffff); + uint64_t x91 = (x89 + x79); + uint64_t x92 = (x91 >> 0x1a); + uint32_t x93 = ((uint32_t)x91 & 0x3ffffff); + uint64_t x94 = (x92 + x76); + uint64_t x95 = (x94 >> 0x19); + uint32_t x96 = ((uint32_t)x94 & 0x1ffffff); + uint64_t x97 = (x95 + x73); + uint64_t x98 = (x97 >> 0x1a); + uint32_t x99 = ((uint32_t)x97 & 0x3ffffff); + uint64_t x100 = (x98 + x70); + uint64_t x101 = (x100 >> 0x19); + uint32_t x102 = ((uint32_t)x100 & 0x1ffffff); + uint64_t x103 = (x101 + x67); + uint64_t x104 = (x103 >> 0x1a); + uint32_t x105 = ((uint32_t)x103 & 0x3ffffff); + uint64_t x106 = (x104 + x64); + uint64_t x107 = (x106 >> 0x19); + uint32_t x108 = ((uint32_t)x106 & 0x1ffffff); + uint64_t x109 = (x107 + x61); + uint64_t x110 = (x109 >> 0x1a); + uint32_t x111 = ((uint32_t)x109 & 0x3ffffff); + uint64_t x112 = (x110 + x49); + uint64_t x113 = (x112 >> 0x19); + uint32_t x114 = ((uint32_t)x112 & 0x1ffffff); + uint64_t x115 = (x87 + (0x13 * x113)); + uint32_t x116 = (uint32_t) (x115 >> 0x1a); + uint32_t x117 = ((uint32_t)x115 & 0x3ffffff); + uint32_t x118 = (x116 + x90); + uint32_t x119 = (x118 >> 0x19); + uint32_t x120 = (x118 & 0x1ffffff); + out[0] = x117; + out[1] = x120; + out[2] = (x119 + x93); + out[3] = x96; + out[4] = x99; + out[5] = x102; + out[6] = x105; + out[7] = x108; + out[8] = x111; + out[9] = x114; +} + +static inline void fe_mul_ttt(fe *h, const fe *f, const fe *g) +{ + fe_mul_impl(h->v, f->v, g->v); +} + +static inline void fe_mul_tlt(fe *h, const fe_loose *f, const fe *g) +{ + fe_mul_impl(h->v, f->v, g->v); +} + +static inline void +fe_mul_tll(fe *h, const fe_loose *f, const fe_loose *g) +{ + fe_mul_impl(h->v, f->v, g->v); +} + +static void fe_sqr_impl(uint32_t out[10], const uint32_t in1[10]) +{ + const uint32_t x17 = in1[9]; + const uint32_t x18 = in1[8]; + const uint32_t x16 = in1[7]; + const uint32_t x14 = in1[6]; + const uint32_t x12 = in1[5]; + const uint32_t x10 = in1[4]; + const uint32_t x8 = in1[3]; + const uint32_t x6 = in1[2]; + const uint32_t x4 = in1[1]; + const uint32_t x2 = in1[0]; + uint64_t x19 = ((uint64_t)x2 * x2); + uint64_t x20 = ((uint64_t)(0x2 * x2) * x4); + uint64_t x21 = (0x2 * (((uint64_t)x4 * x4) + ((uint64_t)x2 * x6))); + uint64_t x22 = (0x2 * (((uint64_t)x4 * x6) + ((uint64_t)x2 * x8))); + uint64_t x23 = ((((uint64_t)x6 * x6) + ((uint64_t)(0x4 * x4) * x8)) + ((uint64_t)(0x2 * x2) * x10)); + uint64_t x24 = (0x2 * ((((uint64_t)x6 * x8) + ((uint64_t)x4 * x10)) + ((uint64_t)x2 * x12))); + uint64_t x25 = (0x2 * (((((uint64_t)x8 * x8) + ((uint64_t)x6 * x10)) + ((uint64_t)x2 * x14)) + ((uint64_t)(0x2 * x4) * x12))); + uint64_t x26 = (0x2 * (((((uint64_t)x8 * x10) + ((uint64_t)x6 * x12)) + ((uint64_t)x4 * x14)) + ((uint64_t)x2 * x16))); + uint64_t x27 = (((uint64_t)x10 * x10) + (0x2 * ((((uint64_t)x6 * x14) + ((uint64_t)x2 * x18)) + (0x2 * (((uint64_t)x4 * x16) + ((uint64_t)x8 * x12)))))); + uint64_t x28 = (0x2 * ((((((uint64_t)x10 * x12) + ((uint64_t)x8 * x14)) + ((uint64_t)x6 * x16)) + ((uint64_t)x4 * x18)) + ((uint64_t)x2 * x17))); + uint64_t x29 = (0x2 * (((((uint64_t)x12 * x12) + ((uint64_t)x10 * x14)) + ((uint64_t)x6 * x18)) + (0x2 * (((uint64_t)x8 * x16) + ((uint64_t)x4 * x17))))); + uint64_t x30 = (0x2 * (((((uint64_t)x12 * x14) + ((uint64_t)x10 * x16)) + ((uint64_t)x8 * x18)) + ((uint64_t)x6 * x17))); + uint64_t x31 = (((uint64_t)x14 * x14) + (0x2 * (((uint64_t)x10 * x18) + (0x2 * (((uint64_t)x12 * x16) + ((uint64_t)x8 * x17)))))); + uint64_t x32 = (0x2 * ((((uint64_t)x14 * x16) + ((uint64_t)x12 * x18)) + ((uint64_t)x10 * x17))); + uint64_t x33 = (0x2 * ((((uint64_t)x16 * x16) + ((uint64_t)x14 * x18)) + ((uint64_t)(0x2 * x12) * x17))); + uint64_t x34 = (0x2 * (((uint64_t)x16 * x18) + ((uint64_t)x14 * x17))); + uint64_t x35 = (((uint64_t)x18 * x18) + ((uint64_t)(0x4 * x16) * x17)); + uint64_t x36 = ((uint64_t)(0x2 * x18) * x17); + uint64_t x37 = ((uint64_t)(0x2 * x17) * x17); + uint64_t x38 = (x27 + (x37 << 0x4)); + uint64_t x39 = (x38 + (x37 << 0x1)); + uint64_t x40 = (x39 + x37); + uint64_t x41 = (x26 + (x36 << 0x4)); + uint64_t x42 = (x41 + (x36 << 0x1)); + uint64_t x43 = (x42 + x36); + uint64_t x44 = (x25 + (x35 << 0x4)); + uint64_t x45 = (x44 + (x35 << 0x1)); + uint64_t x46 = (x45 + x35); + uint64_t x47 = (x24 + (x34 << 0x4)); + uint64_t x48 = (x47 + (x34 << 0x1)); + uint64_t x49 = (x48 + x34); + uint64_t x50 = (x23 + (x33 << 0x4)); + uint64_t x51 = (x50 + (x33 << 0x1)); + uint64_t x52 = (x51 + x33); + uint64_t x53 = (x22 + (x32 << 0x4)); + uint64_t x54 = (x53 + (x32 << 0x1)); + uint64_t x55 = (x54 + x32); + uint64_t x56 = (x21 + (x31 << 0x4)); + uint64_t x57 = (x56 + (x31 << 0x1)); + uint64_t x58 = (x57 + x31); + uint64_t x59 = (x20 + (x30 << 0x4)); + uint64_t x60 = (x59 + (x30 << 0x1)); + uint64_t x61 = (x60 + x30); + uint64_t x62 = (x19 + (x29 << 0x4)); + uint64_t x63 = (x62 + (x29 << 0x1)); + uint64_t x64 = (x63 + x29); + uint64_t x65 = (x64 >> 0x1a); + uint32_t x66 = ((uint32_t)x64 & 0x3ffffff); + uint64_t x67 = (x65 + x61); + uint64_t x68 = (x67 >> 0x19); + uint32_t x69 = ((uint32_t)x67 & 0x1ffffff); + uint64_t x70 = (x68 + x58); + uint64_t x71 = (x70 >> 0x1a); + uint32_t x72 = ((uint32_t)x70 & 0x3ffffff); + uint64_t x73 = (x71 + x55); + uint64_t x74 = (x73 >> 0x19); + uint32_t x75 = ((uint32_t)x73 & 0x1ffffff); + uint64_t x76 = (x74 + x52); + uint64_t x77 = (x76 >> 0x1a); + uint32_t x78 = ((uint32_t)x76 & 0x3ffffff); + uint64_t x79 = (x77 + x49); + uint64_t x80 = (x79 >> 0x19); + uint32_t x81 = ((uint32_t)x79 & 0x1ffffff); + uint64_t x82 = (x80 + x46); + uint64_t x83 = (x82 >> 0x1a); + uint32_t x84 = ((uint32_t)x82 & 0x3ffffff); + uint64_t x85 = (x83 + x43); + uint64_t x86 = (x85 >> 0x19); + uint32_t x87 = ((uint32_t)x85 & 0x1ffffff); + uint64_t x88 = (x86 + x40); + uint64_t x89 = (x88 >> 0x1a); + uint32_t x90 = ((uint32_t)x88 & 0x3ffffff); + uint64_t x91 = (x89 + x28); + uint64_t x92 = (x91 >> 0x19); + uint32_t x93 = ((uint32_t)x91 & 0x1ffffff); + uint64_t x94 = (x66 + (0x13 * x92)); + uint32_t x95 = (uint32_t) (x94 >> 0x1a); + uint32_t x96 = ((uint32_t)x94 & 0x3ffffff); + uint32_t x97 = (x95 + x69); + uint32_t x98 = (x97 >> 0x19); + uint32_t x99 = (x97 & 0x1ffffff); + out[0] = x96; + out[1] = x99; + out[2] = (x98 + x72); + out[3] = x75; + out[4] = x78; + out[5] = x81; + out[6] = x84; + out[7] = x87; + out[8] = x90; + out[9] = x93; +} + +static inline void fe_sq_tl(fe *h, const fe_loose *f) +{ + fe_sqr_impl(h->v, f->v); +} + +static inline void fe_sq_tt(fe *h, const fe *f) +{ + fe_sqr_impl(h->v, f->v); +} + +static inline void fe_loose_invert(fe *out, const fe_loose *z) +{ + fe t0; + fe t1; + fe t2; + fe t3; + int i; + + fe_sq_tl(&t0, z); + fe_sq_tt(&t1, &t0); + for (i = 1; i < 2; ++i) + fe_sq_tt(&t1, &t1); + fe_mul_tlt(&t1, z, &t1); + fe_mul_ttt(&t0, &t0, &t1); + fe_sq_tt(&t2, &t0); + fe_mul_ttt(&t1, &t1, &t2); + fe_sq_tt(&t2, &t1); + for (i = 1; i < 5; ++i) + fe_sq_tt(&t2, &t2); + fe_mul_ttt(&t1, &t2, &t1); + fe_sq_tt(&t2, &t1); + for (i = 1; i < 10; ++i) + fe_sq_tt(&t2, &t2); + fe_mul_ttt(&t2, &t2, &t1); + fe_sq_tt(&t3, &t2); + for (i = 1; i < 20; ++i) + fe_sq_tt(&t3, &t3); + fe_mul_ttt(&t2, &t3, &t2); + fe_sq_tt(&t2, &t2); + for (i = 1; i < 10; ++i) + fe_sq_tt(&t2, &t2); + fe_mul_ttt(&t1, &t2, &t1); + fe_sq_tt(&t2, &t1); + for (i = 1; i < 50; ++i) + fe_sq_tt(&t2, &t2); + fe_mul_ttt(&t2, &t2, &t1); + fe_sq_tt(&t3, &t2); + for (i = 1; i < 100; ++i) + fe_sq_tt(&t3, &t3); + fe_mul_ttt(&t2, &t3, &t2); + fe_sq_tt(&t2, &t2); + for (i = 1; i < 50; ++i) + fe_sq_tt(&t2, &t2); + fe_mul_ttt(&t1, &t2, &t1); + fe_sq_tt(&t1, &t1); + for (i = 1; i < 5; ++i) + fe_sq_tt(&t1, &t1); + fe_mul_ttt(out, &t1, &t0); +} + +static inline void fe_invert(fe *out, const fe *z) +{ + fe_loose l; + fe_copy_lt(&l, z); + fe_loose_invert(out, &l); +} + +/* Replace (f,g) with (g,f) if b == 1; + * replace (f,g) with (f,g) if b == 0. + * + * Preconditions: b in {0,1} + */ +static inline void fe_cswap(fe *f, fe *g, unsigned int b) +{ + unsigned i; + b = 0 - b; + for (i = 0; i < 10; i++) { + uint32_t x = f->v[i] ^ g->v[i]; + x &= b; + f->v[i] ^= x; + g->v[i] ^= x; + } +} + +/* NOTE: based on fiat-crypto fe_mul, edited for in2=121666, 0, 0.*/ +static inline void fe_mul_121666_impl(uint32_t out[10], const uint32_t in1[10]) +{ + const uint32_t x20 = in1[9]; + const uint32_t x21 = in1[8]; + const uint32_t x19 = in1[7]; + const uint32_t x17 = in1[6]; + const uint32_t x15 = in1[5]; + const uint32_t x13 = in1[4]; + const uint32_t x11 = in1[3]; + const uint32_t x9 = in1[2]; + const uint32_t x7 = in1[1]; + const uint32_t x5 = in1[0]; + const uint32_t x38 = 0; + const uint32_t x39 = 0; + const uint32_t x37 = 0; + const uint32_t x35 = 0; + const uint32_t x33 = 0; + const uint32_t x31 = 0; + const uint32_t x29 = 0; + const uint32_t x27 = 0; + const uint32_t x25 = 0; + const uint32_t x23 = 121666; + uint64_t x40 = ((uint64_t)x23 * x5); + uint64_t x41 = (((uint64_t)x23 * x7) + ((uint64_t)x25 * x5)); + uint64_t x42 = ((((uint64_t)(0x2 * x25) * x7) + ((uint64_t)x23 * x9)) + ((uint64_t)x27 * x5)); + uint64_t x43 = (((((uint64_t)x25 * x9) + ((uint64_t)x27 * x7)) + ((uint64_t)x23 * x11)) + ((uint64_t)x29 * x5)); + uint64_t x44 = (((((uint64_t)x27 * x9) + (0x2 * (((uint64_t)x25 * x11) + ((uint64_t)x29 * x7)))) + ((uint64_t)x23 * x13)) + ((uint64_t)x31 * x5)); + uint64_t x45 = (((((((uint64_t)x27 * x11) + ((uint64_t)x29 * x9)) + ((uint64_t)x25 * x13)) + ((uint64_t)x31 * x7)) + ((uint64_t)x23 * x15)) + ((uint64_t)x33 * x5)); + uint64_t x46 = (((((0x2 * ((((uint64_t)x29 * x11) + ((uint64_t)x25 * x15)) + ((uint64_t)x33 * x7))) + ((uint64_t)x27 * x13)) + ((uint64_t)x31 * x9)) + ((uint64_t)x23 * x17)) + ((uint64_t)x35 * x5)); + uint64_t x47 = (((((((((uint64_t)x29 * x13) + ((uint64_t)x31 * x11)) + ((uint64_t)x27 * x15)) + ((uint64_t)x33 * x9)) + ((uint64_t)x25 * x17)) + ((uint64_t)x35 * x7)) + ((uint64_t)x23 * x19)) + ((uint64_t)x37 * x5)); + uint64_t x48 = (((((((uint64_t)x31 * x13) + (0x2 * (((((uint64_t)x29 * x15) + ((uint64_t)x33 * x11)) + ((uint64_t)x25 * x19)) + ((uint64_t)x37 * x7)))) + ((uint64_t)x27 * x17)) + ((uint64_t)x35 * x9)) + ((uint64_t)x23 * x21)) + ((uint64_t)x39 * x5)); + uint64_t x49 = (((((((((((uint64_t)x31 * x15) + ((uint64_t)x33 * x13)) + ((uint64_t)x29 * x17)) + ((uint64_t)x35 * x11)) + ((uint64_t)x27 * x19)) + ((uint64_t)x37 * x9)) + ((uint64_t)x25 * x21)) + ((uint64_t)x39 * x7)) + ((uint64_t)x23 * x20)) + ((uint64_t)x38 * x5)); + uint64_t x50 = (((((0x2 * ((((((uint64_t)x33 * x15) + ((uint64_t)x29 * x19)) + ((uint64_t)x37 * x11)) + ((uint64_t)x25 * x20)) + ((uint64_t)x38 * x7))) + ((uint64_t)x31 * x17)) + ((uint64_t)x35 * x13)) + ((uint64_t)x27 * x21)) + ((uint64_t)x39 * x9)); + uint64_t x51 = (((((((((uint64_t)x33 * x17) + ((uint64_t)x35 * x15)) + ((uint64_t)x31 * x19)) + ((uint64_t)x37 * x13)) + ((uint64_t)x29 * x21)) + ((uint64_t)x39 * x11)) + ((uint64_t)x27 * x20)) + ((uint64_t)x38 * x9)); + uint64_t x52 = (((((uint64_t)x35 * x17) + (0x2 * (((((uint64_t)x33 * x19) + ((uint64_t)x37 * x15)) + ((uint64_t)x29 * x20)) + ((uint64_t)x38 * x11)))) + ((uint64_t)x31 * x21)) + ((uint64_t)x39 * x13)); + uint64_t x53 = (((((((uint64_t)x35 * x19) + ((uint64_t)x37 * x17)) + ((uint64_t)x33 * x21)) + ((uint64_t)x39 * x15)) + ((uint64_t)x31 * x20)) + ((uint64_t)x38 * x13)); + uint64_t x54 = (((0x2 * ((((uint64_t)x37 * x19) + ((uint64_t)x33 * x20)) + ((uint64_t)x38 * x15))) + ((uint64_t)x35 * x21)) + ((uint64_t)x39 * x17)); + uint64_t x55 = (((((uint64_t)x37 * x21) + ((uint64_t)x39 * x19)) + ((uint64_t)x35 * x20)) + ((uint64_t)x38 * x17)); + uint64_t x56 = (((uint64_t)x39 * x21) + (0x2 * (((uint64_t)x37 * x20) + ((uint64_t)x38 * x19)))); + uint64_t x57 = (((uint64_t)x39 * x20) + ((uint64_t)x38 * x21)); + uint64_t x58 = ((uint64_t)(0x2 * x38) * x20); + uint64_t x59 = (x48 + (x58 << 0x4)); + uint64_t x60 = (x59 + (x58 << 0x1)); + uint64_t x61 = (x60 + x58); + uint64_t x62 = (x47 + (x57 << 0x4)); + uint64_t x63 = (x62 + (x57 << 0x1)); + uint64_t x64 = (x63 + x57); + uint64_t x65 = (x46 + (x56 << 0x4)); + uint64_t x66 = (x65 + (x56 << 0x1)); + uint64_t x67 = (x66 + x56); + uint64_t x68 = (x45 + (x55 << 0x4)); + uint64_t x69 = (x68 + (x55 << 0x1)); + uint64_t x70 = (x69 + x55); + uint64_t x71 = (x44 + (x54 << 0x4)); + uint64_t x72 = (x71 + (x54 << 0x1)); + uint64_t x73 = (x72 + x54); + uint64_t x74 = (x43 + (x53 << 0x4)); + uint64_t x75 = (x74 + (x53 << 0x1)); + uint64_t x76 = (x75 + x53); + uint64_t x77 = (x42 + (x52 << 0x4)); + uint64_t x78 = (x77 + (x52 << 0x1)); + uint64_t x79 = (x78 + x52); + uint64_t x80 = (x41 + (x51 << 0x4)); + uint64_t x81 = (x80 + (x51 << 0x1)); + uint64_t x82 = (x81 + x51); + uint64_t x83 = (x40 + (x50 << 0x4)); + uint64_t x84 = (x83 + (x50 << 0x1)); + uint64_t x85 = (x84 + x50); + uint64_t x86 = (x85 >> 0x1a); + uint32_t x87 = ((uint32_t)x85 & 0x3ffffff); + uint64_t x88 = (x86 + x82); + uint64_t x89 = (x88 >> 0x19); + uint32_t x90 = ((uint32_t)x88 & 0x1ffffff); + uint64_t x91 = (x89 + x79); + uint64_t x92 = (x91 >> 0x1a); + uint32_t x93 = ((uint32_t)x91 & 0x3ffffff); + uint64_t x94 = (x92 + x76); + uint64_t x95 = (x94 >> 0x19); + uint32_t x96 = ((uint32_t)x94 & 0x1ffffff); + uint64_t x97 = (x95 + x73); + uint64_t x98 = (x97 >> 0x1a); + uint32_t x99 = ((uint32_t)x97 & 0x3ffffff); + uint64_t x100 = (x98 + x70); + uint64_t x101 = (x100 >> 0x19); + uint32_t x102 = ((uint32_t)x100 & 0x1ffffff); + uint64_t x103 = (x101 + x67); + uint64_t x104 = (x103 >> 0x1a); + uint32_t x105 = ((uint32_t)x103 & 0x3ffffff); + uint64_t x106 = (x104 + x64); + uint64_t x107 = (x106 >> 0x19); + uint32_t x108 = ((uint32_t)x106 & 0x1ffffff); + uint64_t x109 = (x107 + x61); + uint64_t x110 = (x109 >> 0x1a); + uint32_t x111 = ((uint32_t)x109 & 0x3ffffff); + uint64_t x112 = (x110 + x49); + uint64_t x113 = (x112 >> 0x19); + uint32_t x114 = ((uint32_t)x112 & 0x1ffffff); + uint64_t x115 = (x87 + (0x13 * x113)); + uint32_t x116 = (uint32_t) (x115 >> 0x1a); + uint32_t x117 = ((uint32_t)x115 & 0x3ffffff); + uint32_t x118 = (x116 + x90); + uint32_t x119 = (x118 >> 0x19); + uint32_t x120 = (x118 & 0x1ffffff); + out[0] = x117; + out[1] = x120; + out[2] = (x119 + x93); + out[3] = x96; + out[4] = x99; + out[5] = x102; + out[6] = x105; + out[7] = x108; + out[8] = x111; + out[9] = x114; +} + +static inline void fe_mul121666(fe *h, const fe_loose *f) +{ + fe_mul_121666_impl(h->v, f->v); +} + +static const uint8_t curve25519_null_point[CURVE25519_KEY_SIZE]; + +bool curve25519(uint8_t out[CURVE25519_KEY_SIZE], + const uint8_t scalar[CURVE25519_KEY_SIZE], + const uint8_t point[CURVE25519_KEY_SIZE]) +{ + fe x1, x2, z2, x3, z3; + fe_loose x2l, z2l, x3l; + unsigned swap = 0; + int pos; + uint8_t e[32]; + + memcpy(e, scalar, 32); + curve25519_clamp_secret(e); + + /* The following implementation was transcribed to Coq and proven to + * correspond to unary scalar multiplication in affine coordinates given + * that x1 != 0 is the x coordinate of some point on the curve. It was + * also checked in Coq that doing a ladderstep with x1 = x3 = 0 gives + * z2' = z3' = 0, and z2 = z3 = 0 gives z2' = z3' = 0. The statement was + * quantified over the underlying field, so it applies to Curve25519 + * itself and the quadratic twist of Curve25519. It was not proven in + * Coq that prime-field arithmetic correctly simulates extension-field + * arithmetic on prime-field values. The decoding of the byte array + * representation of e was not considered. + * + * Specification of Montgomery curves in affine coordinates: + * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Spec/MontgomeryCurve.v#L27> + * + * Proof that these form a group that is isomorphic to a Weierstrass + * curve: + * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/AffineProofs.v#L35> + * + * Coq transcription and correctness proof of the loop + * (where scalarbits=255): + * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZ.v#L118> + * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L278> + * preconditions: 0 <= e < 2^255 (not necessarily e < order), + * fe_invert(0) = 0 + */ + fe_frombytes(&x1, point); + fe_1(&x2); + fe_0(&z2); + fe_copy(&x3, &x1); + fe_1(&z3); + + for (pos = 254; pos >= 0; --pos) { + fe tmp0, tmp1; + fe_loose tmp0l, tmp1l; + /* loop invariant as of right before the test, for the case + * where x1 != 0: + * pos >= -1; if z2 = 0 then x2 is nonzero; if z3 = 0 then x3 + * is nonzero + * let r := e >> (pos+1) in the following equalities of + * projective points: + * to_xz (r*P) === if swap then (x3, z3) else (x2, z2) + * to_xz ((r+1)*P) === if swap then (x2, z2) else (x3, z3) + * x1 is the nonzero x coordinate of the nonzero + * point (r*P-(r+1)*P) + */ + unsigned b = 1 & (e[pos / 8] >> (pos & 7)); + swap ^= b; + fe_cswap(&x2, &x3, swap); + fe_cswap(&z2, &z3, swap); + swap = b; + /* Coq transcription of ladderstep formula (called from + * transcribed loop): + * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZ.v#L89> + * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L131> + * x1 != 0 <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L217> + * x1 = 0 <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L147> + */ + fe_sub(&tmp0l, &x3, &z3); + fe_sub(&tmp1l, &x2, &z2); + fe_add(&x2l, &x2, &z2); + fe_add(&z2l, &x3, &z3); + fe_mul_tll(&z3, &tmp0l, &x2l); + fe_mul_tll(&z2, &z2l, &tmp1l); + fe_sq_tl(&tmp0, &tmp1l); + fe_sq_tl(&tmp1, &x2l); + fe_add(&x3l, &z3, &z2); + fe_sub(&z2l, &z3, &z2); + fe_mul_ttt(&x2, &tmp1, &tmp0); + fe_sub(&tmp1l, &tmp1, &tmp0); + fe_sq_tl(&z2, &z2l); + fe_mul121666(&z3, &tmp1l); + fe_sq_tl(&x3, &x3l); + fe_add(&tmp0l, &tmp0, &z3); + fe_mul_ttt(&z3, &x1, &z2); + fe_mul_tll(&z2, &tmp1l, &tmp0l); + } + /* here pos=-1, so r=e, so to_xz (e*P) === if swap then (x3, z3) + * else (x2, z2) + */ + fe_cswap(&x2, &x3, swap); + fe_cswap(&z2, &z3, swap); + + fe_invert(&z2, &z2); + fe_mul_ttt(&x2, &x2, &z2); + fe_tobytes(out, &x2); + + explicit_bzero(&x1, sizeof(x1)); + explicit_bzero(&x2, sizeof(x2)); + explicit_bzero(&z2, sizeof(z2)); + explicit_bzero(&x3, sizeof(x3)); + explicit_bzero(&z3, sizeof(z3)); + explicit_bzero(&x2l, sizeof(x2l)); + explicit_bzero(&z2l, sizeof(z2l)); + explicit_bzero(&x3l, sizeof(x3l)); + explicit_bzero(&e, sizeof(e)); + + return timingsafe_bcmp(out, curve25519_null_point, CURVE25519_KEY_SIZE) != 0; +} |