diff options
Diffstat (limited to 'deps/openssl/openssl/crypto/ec/curve448')
-rw-r--r-- | deps/openssl/openssl/crypto/ec/curve448/arch_32/arch_intrinsics.h | 27 | ||||
-rw-r--r-- | deps/openssl/openssl/crypto/ec/curve448/arch_32/f_impl.c | 95 | ||||
-rw-r--r-- | deps/openssl/openssl/crypto/ec/curve448/arch_32/f_impl.h | 60 | ||||
-rw-r--r-- | deps/openssl/openssl/crypto/ec/curve448/curve448.c | 727 | ||||
-rw-r--r-- | deps/openssl/openssl/crypto/ec/curve448/curve448_lcl.h | 38 | ||||
-rw-r--r-- | deps/openssl/openssl/crypto/ec/curve448/curve448_tables.c | 475 | ||||
-rw-r--r-- | deps/openssl/openssl/crypto/ec/curve448/curve448utils.h | 78 | ||||
-rw-r--r-- | deps/openssl/openssl/crypto/ec/curve448/ed448.h | 195 | ||||
-rw-r--r-- | deps/openssl/openssl/crypto/ec/curve448/eddsa.c | 346 | ||||
-rw-r--r-- | deps/openssl/openssl/crypto/ec/curve448/f_generic.c | 204 | ||||
-rw-r--r-- | deps/openssl/openssl/crypto/ec/curve448/field.h | 168 | ||||
-rw-r--r-- | deps/openssl/openssl/crypto/ec/curve448/point_448.h | 301 | ||||
-rw-r--r-- | deps/openssl/openssl/crypto/ec/curve448/scalar.c | 235 | ||||
-rw-r--r-- | deps/openssl/openssl/crypto/ec/curve448/word.h | 81 |
14 files changed, 3030 insertions, 0 deletions
diff --git a/deps/openssl/openssl/crypto/ec/curve448/arch_32/arch_intrinsics.h b/deps/openssl/openssl/crypto/ec/curve448/arch_32/arch_intrinsics.h new file mode 100644 index 0000000000..48081c7717 --- /dev/null +++ b/deps/openssl/openssl/crypto/ec/curve448/arch_32/arch_intrinsics.h @@ -0,0 +1,27 @@ +/* + * Copyright 2017-2018 The OpenSSL Project Authors. All Rights Reserved. + * Copyright 2016 Cryptography Research, Inc. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + * + * Originally written by Mike Hamburg + */ + +#ifndef HEADER_ARCH_32_ARCH_INTRINSICS_H +# define HEADER_ARCH_32_ARCH_INTRINSICS_H + +#include "internal/constant_time_locl.h" + +# define ARCH_WORD_BITS 32 + +#define word_is_zero(a) constant_time_is_zero_32(a) + +static ossl_inline uint64_t widemul(uint32_t a, uint32_t b) +{ + return ((uint64_t)a) * b; +} + +#endif /* HEADER_ARCH_32_ARCH_INTRINSICS_H */ diff --git a/deps/openssl/openssl/crypto/ec/curve448/arch_32/f_impl.c b/deps/openssl/openssl/crypto/ec/curve448/arch_32/f_impl.c new file mode 100644 index 0000000000..8a89d276ed --- /dev/null +++ b/deps/openssl/openssl/crypto/ec/curve448/arch_32/f_impl.c @@ -0,0 +1,95 @@ +/* + * Copyright 2017-2018 The OpenSSL Project Authors. All Rights Reserved. + * Copyright 2014 Cryptography Research, Inc. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + * + * Originally written by Mike Hamburg + */ + +#include "field.h" + +void gf_mul(gf_s * RESTRICT cs, const gf as, const gf bs) +{ + const uint32_t *a = as->limb, *b = bs->limb; + uint32_t *c = cs->limb; + uint64_t accum0 = 0, accum1 = 0, accum2 = 0; + uint32_t mask = (1 << 28) - 1; + uint32_t aa[8], bb[8]; + int i, j; + + for (i = 0; i < 8; i++) { + aa[i] = a[i] + a[i + 8]; + bb[i] = b[i] + b[i + 8]; + } + + for (j = 0; j < 8; j++) { + accum2 = 0; + for (i = 0; i < j + 1; i++) { + accum2 += widemul(a[j - i], b[i]); + accum1 += widemul(aa[j - i], bb[i]); + accum0 += widemul(a[8 + j - i], b[8 + i]); + } + accum1 -= accum2; + accum0 += accum2; + accum2 = 0; + for (i = j + 1; i < 8; i++) { + accum0 -= widemul(a[8 + j - i], b[i]); + accum2 += widemul(aa[8 + j - i], bb[i]); + accum1 += widemul(a[16 + j - i], b[8 + i]); + } + accum1 += accum2; + accum0 += accum2; + c[j] = ((uint32_t)(accum0)) & mask; + c[j + 8] = ((uint32_t)(accum1)) & mask; + accum0 >>= 28; + accum1 >>= 28; + } + + accum0 += accum1; + accum0 += c[8]; + accum1 += c[0]; + c[8] = ((uint32_t)(accum0)) & mask; + c[0] = ((uint32_t)(accum1)) & mask; + + accum0 >>= 28; + accum1 >>= 28; + c[9] += ((uint32_t)(accum0)); + c[1] += ((uint32_t)(accum1)); +} + +void gf_mulw_unsigned(gf_s * RESTRICT cs, const gf as, uint32_t b) +{ + const uint32_t *a = as->limb; + uint32_t *c = cs->limb; + uint64_t accum0 = 0, accum8 = 0; + uint32_t mask = (1 << 28) - 1; + int i; + + assert(b <= mask); + + for (i = 0; i < 8; i++) { + accum0 += widemul(b, a[i]); + accum8 += widemul(b, a[i + 8]); + c[i] = accum0 & mask; + accum0 >>= 28; + c[i + 8] = accum8 & mask; + accum8 >>= 28; + } + + accum0 += accum8 + c[8]; + c[8] = ((uint32_t)accum0) & mask; + c[9] += (uint32_t)(accum0 >> 28); + + accum8 += c[0]; + c[0] = ((uint32_t)accum8) & mask; + c[1] += (uint32_t)(accum8 >> 28); +} + +void gf_sqr(gf_s * RESTRICT cs, const gf as) +{ + gf_mul(cs, as, as); /* Performs better with a dedicated square */ +} diff --git a/deps/openssl/openssl/crypto/ec/curve448/arch_32/f_impl.h b/deps/openssl/openssl/crypto/ec/curve448/arch_32/f_impl.h new file mode 100644 index 0000000000..bbde84a038 --- /dev/null +++ b/deps/openssl/openssl/crypto/ec/curve448/arch_32/f_impl.h @@ -0,0 +1,60 @@ +/* + * Copyright 2017-2018 The OpenSSL Project Authors. All Rights Reserved. + * Copyright 2014-2016 Cryptography Research, Inc. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + * + * Originally written by Mike Hamburg + */ + +#ifndef HEADER_ARCH_32_F_IMPL_H +# define HEADER_ARCH_32_F_IMPL_H + +# define GF_HEADROOM 2 +# define LIMB(x) ((x) & ((1 << 28) - 1)), ((x) >> 28) +# define FIELD_LITERAL(a, b, c, d, e, f, g, h) \ + {{LIMB(a), LIMB(b), LIMB(c), LIMB(d), LIMB(e), LIMB(f), LIMB(g), LIMB(h)}} + +# define LIMB_PLACE_VALUE(i) 28 + +void gf_add_RAW(gf out, const gf a, const gf b) +{ + unsigned int i; + + for (i = 0; i < NLIMBS; i++) + out->limb[i] = a->limb[i] + b->limb[i]; +} + +void gf_sub_RAW(gf out, const gf a, const gf b) +{ + unsigned int i; + + for (i = 0; i < NLIMBS; i++) + out->limb[i] = a->limb[i] - b->limb[i]; +} + +void gf_bias(gf a, int amt) +{ + unsigned int i; + uint32_t co1 = ((1 << 28) - 1) * amt, co2 = co1 - amt; + + for (i = 0; i < NLIMBS; i++) + a->limb[i] += (i == NLIMBS / 2) ? co2 : co1; +} + +void gf_weak_reduce(gf a) +{ + uint32_t mask = (1 << 28) - 1; + uint32_t tmp = a->limb[NLIMBS - 1] >> 28; + unsigned int i; + + a->limb[NLIMBS / 2] += tmp; + for (i = NLIMBS - 1; i > 0; i--) + a->limb[i] = (a->limb[i] & mask) + (a->limb[i - 1] >> 28); + a->limb[0] = (a->limb[0] & mask) + tmp; +} + +#endif /* HEADER_ARCH_32_F_IMPL_H */ diff --git a/deps/openssl/openssl/crypto/ec/curve448/curve448.c b/deps/openssl/openssl/crypto/ec/curve448/curve448.c new file mode 100644 index 0000000000..7dc68c8853 --- /dev/null +++ b/deps/openssl/openssl/crypto/ec/curve448/curve448.c @@ -0,0 +1,727 @@ +/* + * Copyright 2017-2018 The OpenSSL Project Authors. All Rights Reserved. + * Copyright 2015-2016 Cryptography Research, Inc. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + * + * Originally written by Mike Hamburg + */ +#include <openssl/crypto.h> +#include "word.h" +#include "field.h" + +#include "point_448.h" +#include "ed448.h" +#include "curve448_lcl.h" + +#define COFACTOR 4 + +#define C448_WNAF_FIXED_TABLE_BITS 5 +#define C448_WNAF_VAR_TABLE_BITS 3 + +#define EDWARDS_D (-39081) + +static const curve448_scalar_t precomputed_scalarmul_adjustment = { + { + { + SC_LIMB(0xc873d6d54a7bb0cf), SC_LIMB(0xe933d8d723a70aad), + SC_LIMB(0xbb124b65129c96fd), SC_LIMB(0x00000008335dc163) + } + } +}; + +#define TWISTED_D (EDWARDS_D - 1) + +#define WBITS C448_WORD_BITS /* NB this may be different from ARCH_WORD_BITS */ + +/* Inverse. */ +static void gf_invert(gf y, const gf x, int assert_nonzero) +{ + mask_t ret; + gf t1, t2; + + gf_sqr(t1, x); /* o^2 */ + ret = gf_isr(t2, t1); /* +-1/sqrt(o^2) = +-1/o */ + (void)ret; + if (assert_nonzero) + assert(ret); + gf_sqr(t1, t2); + gf_mul(t2, t1, x); /* not direct to y in case of alias. */ + gf_copy(y, t2); +} + +/** identity = (0,1) */ +const curve448_point_t curve448_point_identity = + { {{{{0}}}, {{{1}}}, {{{1}}}, {{{0}}}} }; + +static void point_double_internal(curve448_point_t p, const curve448_point_t q, + int before_double) +{ + gf a, b, c, d; + + gf_sqr(c, q->x); + gf_sqr(a, q->y); + gf_add_nr(d, c, a); /* 2+e */ + gf_add_nr(p->t, q->y, q->x); /* 2+e */ + gf_sqr(b, p->t); + gf_subx_nr(b, b, d, 3); /* 4+e */ + gf_sub_nr(p->t, a, c); /* 3+e */ + gf_sqr(p->x, q->z); + gf_add_nr(p->z, p->x, p->x); /* 2+e */ + gf_subx_nr(a, p->z, p->t, 4); /* 6+e */ + if (GF_HEADROOM == 5) + gf_weak_reduce(a); /* or 1+e */ + gf_mul(p->x, a, b); + gf_mul(p->z, p->t, a); + gf_mul(p->y, p->t, d); + if (!before_double) + gf_mul(p->t, b, d); +} + +void curve448_point_double(curve448_point_t p, const curve448_point_t q) +{ + point_double_internal(p, q, 0); +} + +/* Operations on [p]niels */ +static ossl_inline void cond_neg_niels(niels_t n, mask_t neg) +{ + gf_cond_swap(n->a, n->b, neg); + gf_cond_neg(n->c, neg); +} + +static void pt_to_pniels(pniels_t b, const curve448_point_t a) +{ + gf_sub(b->n->a, a->y, a->x); + gf_add(b->n->b, a->x, a->y); + gf_mulw(b->n->c, a->t, 2 * TWISTED_D); + gf_add(b->z, a->z, a->z); +} + +static void pniels_to_pt(curve448_point_t e, const pniels_t d) +{ + gf eu; + + gf_add(eu, d->n->b, d->n->a); + gf_sub(e->y, d->n->b, d->n->a); + gf_mul(e->t, e->y, eu); + gf_mul(e->x, d->z, e->y); + gf_mul(e->y, d->z, eu); + gf_sqr(e->z, d->z); +} + +static void niels_to_pt(curve448_point_t e, const niels_t n) +{ + gf_add(e->y, n->b, n->a); + gf_sub(e->x, n->b, n->a); + gf_mul(e->t, e->y, e->x); + gf_copy(e->z, ONE); +} + +static void add_niels_to_pt(curve448_point_t d, const niels_t e, + int before_double) +{ + gf a, b, c; + + gf_sub_nr(b, d->y, d->x); /* 3+e */ + gf_mul(a, e->a, b); + gf_add_nr(b, d->x, d->y); /* 2+e */ + gf_mul(d->y, e->b, b); + gf_mul(d->x, e->c, d->t); + gf_add_nr(c, a, d->y); /* 2+e */ + gf_sub_nr(b, d->y, a); /* 3+e */ + gf_sub_nr(d->y, d->z, d->x); /* 3+e */ + gf_add_nr(a, d->x, d->z); /* 2+e */ + gf_mul(d->z, a, d->y); + gf_mul(d->x, d->y, b); + gf_mul(d->y, a, c); + if (!before_double) + gf_mul(d->t, b, c); +} + +static void sub_niels_from_pt(curve448_point_t d, const niels_t e, + int before_double) +{ + gf a, b, c; + + gf_sub_nr(b, d->y, d->x); /* 3+e */ + gf_mul(a, e->b, b); + gf_add_nr(b, d->x, d->y); /* 2+e */ + gf_mul(d->y, e->a, b); + gf_mul(d->x, e->c, d->t); + gf_add_nr(c, a, d->y); /* 2+e */ + gf_sub_nr(b, d->y, a); /* 3+e */ + gf_add_nr(d->y, d->z, d->x); /* 2+e */ + gf_sub_nr(a, d->z, d->x); /* 3+e */ + gf_mul(d->z, a, d->y); + gf_mul(d->x, d->y, b); + gf_mul(d->y, a, c); + if (!before_double) + gf_mul(d->t, b, c); +} + +static void add_pniels_to_pt(curve448_point_t p, const pniels_t pn, + int before_double) +{ + gf L0; + + gf_mul(L0, p->z, pn->z); + gf_copy(p->z, L0); + add_niels_to_pt(p, pn->n, before_double); +} + +static void sub_pniels_from_pt(curve448_point_t p, const pniels_t pn, + int before_double) +{ + gf L0; + + gf_mul(L0, p->z, pn->z); + gf_copy(p->z, L0); + sub_niels_from_pt(p, pn->n, before_double); +} + +c448_bool_t curve448_point_eq(const curve448_point_t p, + const curve448_point_t q) +{ + mask_t succ; + gf a, b; + + /* equality mod 2-torsion compares x/y */ + gf_mul(a, p->y, q->x); + gf_mul(b, q->y, p->x); + succ = gf_eq(a, b); + + return mask_to_bool(succ); +} + +c448_bool_t curve448_point_valid(const curve448_point_t p) +{ + mask_t out; + gf a, b, c; + + gf_mul(a, p->x, p->y); + gf_mul(b, p->z, p->t); + out = gf_eq(a, b); + gf_sqr(a, p->x); + gf_sqr(b, p->y); + gf_sub(a, b, a); + gf_sqr(b, p->t); + gf_mulw(c, b, TWISTED_D); + gf_sqr(b, p->z); + gf_add(b, b, c); + out &= gf_eq(a, b); + out &= ~gf_eq(p->z, ZERO); + return mask_to_bool(out); +} + +static ossl_inline void constant_time_lookup_niels(niels_s * RESTRICT ni, + const niels_t * table, + int nelts, int idx) +{ + constant_time_lookup(ni, table, sizeof(niels_s), nelts, idx); +} + +void curve448_precomputed_scalarmul(curve448_point_t out, + const curve448_precomputed_s * table, + const curve448_scalar_t scalar) +{ + unsigned int i, j, k; + const unsigned int n = COMBS_N, t = COMBS_T, s = COMBS_S; + niels_t ni; + curve448_scalar_t scalar1x; + + curve448_scalar_add(scalar1x, scalar, precomputed_scalarmul_adjustment); + curve448_scalar_halve(scalar1x, scalar1x); + + for (i = s; i > 0; i--) { + if (i != s) + point_double_internal(out, out, 0); + + for (j = 0; j < n; j++) { + int tab = 0; + mask_t invert; + + for (k = 0; k < t; k++) { + unsigned int bit = (i - 1) + s * (k + j * t); + + if (bit < C448_SCALAR_BITS) + tab |= + (scalar1x->limb[bit / WBITS] >> (bit % WBITS) & 1) << k; + } + + invert = (tab >> (t - 1)) - 1; + tab ^= invert; + tab &= (1 << (t - 1)) - 1; + + constant_time_lookup_niels(ni, &table->table[j << (t - 1)], + 1 << (t - 1), tab); + + cond_neg_niels(ni, invert); + if ((i != s) || j != 0) + add_niels_to_pt(out, ni, j == n - 1 && i != 1); + else + niels_to_pt(out, ni); + } + } + + OPENSSL_cleanse(ni, sizeof(ni)); + OPENSSL_cleanse(scalar1x, sizeof(scalar1x)); +} + +void curve448_point_mul_by_ratio_and_encode_like_eddsa( + uint8_t enc[EDDSA_448_PUBLIC_BYTES], + const curve448_point_t p) +{ + gf x, y, z, t; + curve448_point_t q; + + /* The point is now on the twisted curve. Move it to untwisted. */ + curve448_point_copy(q, p); + + { + /* 4-isogeny: 2xy/(y^+x^2), (y^2-x^2)/(2z^2-y^2+x^2) */ + gf u; + + gf_sqr(x, q->x); + gf_sqr(t, q->y); + gf_add(u, x, t); + gf_add(z, q->y, q->x); + gf_sqr(y, z); + gf_sub(y, y, u); + gf_sub(z, t, x); + gf_sqr(x, q->z); + gf_add(t, x, x); + gf_sub(t, t, z); + gf_mul(x, t, y); + gf_mul(y, z, u); + gf_mul(z, u, t); + OPENSSL_cleanse(u, sizeof(u)); + } + + /* Affinize */ + gf_invert(z, z, 1); + gf_mul(t, x, z); + gf_mul(x, y, z); + + /* Encode */ + enc[EDDSA_448_PRIVATE_BYTES - 1] = 0; + gf_serialize(enc, x, 1); + enc[EDDSA_448_PRIVATE_BYTES - 1] |= 0x80 & gf_lobit(t); + + OPENSSL_cleanse(x, sizeof(x)); + OPENSSL_cleanse(y, sizeof(y)); + OPENSSL_cleanse(z, sizeof(z)); + OPENSSL_cleanse(t, sizeof(t)); + curve448_point_destroy(q); +} + +c448_error_t curve448_point_decode_like_eddsa_and_mul_by_ratio( + curve448_point_t p, + const uint8_t enc[EDDSA_448_PUBLIC_BYTES]) +{ + uint8_t enc2[EDDSA_448_PUBLIC_BYTES]; + mask_t low; + mask_t succ; + + memcpy(enc2, enc, sizeof(enc2)); + + low = ~word_is_zero(enc2[EDDSA_448_PRIVATE_BYTES - 1] & 0x80); + enc2[EDDSA_448_PRIVATE_BYTES - 1] &= ~0x80; + + succ = gf_deserialize(p->y, enc2, 1, 0); + succ &= word_is_zero(enc2[EDDSA_448_PRIVATE_BYTES - 1]); + + gf_sqr(p->x, p->y); + gf_sub(p->z, ONE, p->x); /* num = 1-y^2 */ + gf_mulw(p->t, p->x, EDWARDS_D); /* dy^2 */ + gf_sub(p->t, ONE, p->t); /* denom = 1-dy^2 or 1-d + dy^2 */ + + gf_mul(p->x, p->z, p->t); + succ &= gf_isr(p->t, p->x); /* 1/sqrt(num * denom) */ + + gf_mul(p->x, p->t, p->z); /* sqrt(num / denom) */ + gf_cond_neg(p->x, gf_lobit(p->x) ^ low); + gf_copy(p->z, ONE); + + { + gf a, b, c, d; + + /* 4-isogeny 2xy/(y^2-ax^2), (y^2+ax^2)/(2-y^2-ax^2) */ + gf_sqr(c, p->x); + gf_sqr(a, p->y); + gf_add(d, c, a); + gf_add(p->t, p->y, p->x); + gf_sqr(b, p->t); + gf_sub(b, b, d); + gf_sub(p->t, a, c); + gf_sqr(p->x, p->z); + gf_add(p->z, p->x, p->x); + gf_sub(a, p->z, d); + gf_mul(p->x, a, b); + gf_mul(p->z, p->t, a); + gf_mul(p->y, p->t, d); + gf_mul(p->t, b, d); + OPENSSL_cleanse(a, sizeof(a)); + OPENSSL_cleanse(b, sizeof(b)); + OPENSSL_cleanse(c, sizeof(c)); + OPENSSL_cleanse(d, sizeof(d)); + } + + OPENSSL_cleanse(enc2, sizeof(enc2)); + assert(curve448_point_valid(p) || ~succ); + + return c448_succeed_if(mask_to_bool(succ)); +} + +c448_error_t x448_int(uint8_t out[X_PUBLIC_BYTES], + const uint8_t base[X_PUBLIC_BYTES], + const uint8_t scalar[X_PRIVATE_BYTES]) +{ + gf x1, x2, z2, x3, z3, t1, t2; + int t; + mask_t swap = 0; + mask_t nz; + + (void)gf_deserialize(x1, base, 1, 0); + gf_copy(x2, ONE); + gf_copy(z2, ZERO); + gf_copy(x3, x1); + gf_copy(z3, ONE); + + for (t = X_PRIVATE_BITS - 1; t >= 0; t--) { + uint8_t sb = scalar[t / 8]; + mask_t k_t; + + /* Scalar conditioning */ + if (t / 8 == 0) + sb &= -(uint8_t)COFACTOR; + else if (t == X_PRIVATE_BITS - 1) + sb = -1; + + k_t = (sb >> (t % 8)) & 1; + k_t = 0 - k_t; /* set to all 0s or all 1s */ + + swap ^= k_t; + gf_cond_swap(x2, x3, swap); + gf_cond_swap(z2, z3, swap); + swap = k_t; + + /* + * The "_nr" below skips coefficient reduction. In the following + * comments, "2+e" is saying that the coefficients are at most 2+epsilon + * times the reduction limit. + */ + gf_add_nr(t1, x2, z2); /* A = x2 + z2 */ /* 2+e */ + gf_sub_nr(t2, x2, z2); /* B = x2 - z2 */ /* 3+e */ + gf_sub_nr(z2, x3, z3); /* D = x3 - z3 */ /* 3+e */ + gf_mul(x2, t1, z2); /* DA */ + gf_add_nr(z2, z3, x3); /* C = x3 + z3 */ /* 2+e */ + gf_mul(x3, t2, z2); /* CB */ + gf_sub_nr(z3, x2, x3); /* DA-CB */ /* 3+e */ + gf_sqr(z2, z3); /* (DA-CB)^2 */ + gf_mul(z3, x1, z2); /* z3 = x1(DA-CB)^2 */ + gf_add_nr(z2, x2, x3); /* (DA+CB) */ /* 2+e */ + gf_sqr(x3, z2); /* x3 = (DA+CB)^2 */ + + gf_sqr(z2, t1); /* AA = A^2 */ + gf_sqr(t1, t2); /* BB = B^2 */ + gf_mul(x2, z2, t1); /* x2 = AA*BB */ + gf_sub_nr(t2, z2, t1); /* E = AA-BB */ /* 3+e */ + + gf_mulw(t1, t2, -EDWARDS_D); /* E*-d = a24*E */ + gf_add_nr(t1, t1, z2); /* AA + a24*E */ /* 2+e */ + gf_mul(z2, t2, t1); /* z2 = E(AA+a24*E) */ + } + + /* Finish */ + gf_cond_swap(x2, x3, swap); + gf_cond_swap(z2, z3, swap); + gf_invert(z2, z2, 0); + gf_mul(x1, x2, z2); + gf_serialize(out, x1, 1); + nz = ~gf_eq(x1, ZERO); + + OPENSSL_cleanse(x1, sizeof(x1)); + OPENSSL_cleanse(x2, sizeof(x2)); + OPENSSL_cleanse(z2, sizeof(z2)); + OPENSSL_cleanse(x3, sizeof(x3)); + OPENSSL_cleanse(z3, sizeof(z3)); + OPENSSL_cleanse(t1, sizeof(t1)); + OPENSSL_cleanse(t2, sizeof(t2)); + + return c448_succeed_if(mask_to_bool(nz)); +} + +void curve448_point_mul_by_ratio_and_encode_like_x448(uint8_t + out[X_PUBLIC_BYTES], + const curve448_point_t p) +{ + curve448_point_t q; + + curve448_point_copy(q, p); + gf_invert(q->t, q->x, 0); /* 1/x */ + gf_mul(q->z, q->t, q->y); /* y/x */ + gf_sqr(q->y, q->z); /* (y/x)^2 */ + gf_serialize(out, q->y, 1); + curve448_point_destroy(q); +} + +void x448_derive_public_key(uint8_t out[X_PUBLIC_BYTES], + const uint8_t scalar[X_PRIVATE_BYTES]) +{ + /* Scalar conditioning */ + uint8_t scalar2[X_PRIVATE_BYTES]; + curve448_scalar_t the_scalar; + curve448_point_t p; + unsigned int i; + + memcpy(scalar2, scalar, sizeof(scalar2)); + scalar2[0] &= -(uint8_t)COFACTOR; + + scalar2[X_PRIVATE_BYTES - 1] &= ~((0u - 1u) << ((X_PRIVATE_BITS + 7) % 8)); + scalar2[X_PRIVATE_BYTES - 1] |= 1 << ((X_PRIVATE_BITS + 7) % 8); + + curve448_scalar_decode_long(the_scalar, scalar2, sizeof(scalar2)); + + /* Compensate for the encoding ratio */ + for (i = 1; i < X448_ENCODE_RATIO; i <<= 1) + curve448_scalar_halve(the_scalar, the_scalar); + + curve448_precomputed_scalarmul(p, curve448_precomputed_base, the_scalar); + curve448_point_mul_by_ratio_and_encode_like_x448(out, p); + curve448_point_destroy(p); +} + +/* Control for variable-time scalar multiply algorithms. */ +struct smvt_control { + int power, addend; +}; + +#if defined(__GNUC__) && (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ > 3)) +# define NUMTRAILINGZEROS __builtin_ctz +#else +# define NUMTRAILINGZEROS numtrailingzeros +static uint32_t numtrailingzeros(uint32_t i) +{ + uint32_t tmp; + uint32_t num = 31; + + if (i == 0) + return 32; + + tmp = i << 16; + if (tmp != 0) { + i = tmp; + num -= 16; + } + tmp = i << 8; + if (tmp != 0) { + i = tmp; + num -= 8; + } + tmp = i << 4; + if (tmp != 0) { + i = tmp; + num -= 4; + } + tmp = i << 2; + if (tmp != 0) { + i = tmp; + num -= 2; + } + tmp = i << 1; + if (tmp != 0) + num--; + + return num; +} +#endif + +static int recode_wnaf(struct smvt_control *control, + /* [nbits/(table_bits + 1) + 3] */ + const curve448_scalar_t scalar, + unsigned int table_bits) +{ + unsigned int table_size = C448_SCALAR_BITS / (table_bits + 1) + 3; + int position = table_size - 1; /* at the end */ + uint64_t current = scalar->limb[0] & 0xFFFF; + uint32_t mask = (1 << (table_bits + 1)) - 1; + unsigned int w; + const unsigned int B_OVER_16 = sizeof(scalar->limb[0]) / 2; + unsigned int n, i; + + /* place the end marker */ + control[position].power = -1; + control[position].addend = 0; + position--; + + /* + * PERF: Could negate scalar if it's large. But then would need more cases + * in the actual code that uses it, all for an expected reduction of like + * 1/5 op. Probably not worth it. + */ + + for (w = 1; w < (C448_SCALAR_BITS - 1) / 16 + 3; w++) { + if (w < (C448_SCALAR_BITS - 1) / 16 + 1) { + /* Refill the 16 high bits of current */ + current += (uint32_t)((scalar->limb[w / B_OVER_16] + >> (16 * (w % B_OVER_16))) << 16); + } + + while (current & 0xFFFF) { + uint32_t pos = NUMTRAILINGZEROS((uint32_t)current); + uint32_t odd = (uint32_t)current >> pos; + int32_t delta = odd & mask; + + assert(position >= 0); + if (odd & (1 << (table_bits + 1))) + delta -= (1 << (table_bits + 1)); + current -= delta * (1 << pos); + control[position].power = pos + 16 * (w - 1); + control[position].addend = delta; + position--; + } + current >>= 16; + } + assert(current == 0); + + position++; + n = table_size - position; + for (i = 0; i < n; i++) + control[i] = control[i + position]; + + return n - 1; +} + +static void prepare_wnaf_table(pniels_t * output, + const curve448_point_t working, + unsigned int tbits) +{ + curve448_point_t tmp; + int i; + pniels_t twop; + + pt_to_pniels(output[0], working); + + if (tbits == 0) + return; + + curve448_point_double(tmp, working); + pt_to_pniels(twop, tmp); + + add_pniels_to_pt(tmp, output[0], 0); + pt_to_pniels(output[1], tmp); + + for (i = 2; i < 1 << tbits; i++) { + add_pniels_to_pt(tmp, twop, 0); + pt_to_pniels(output[i], tmp); + } + + curve448_point_destroy(tmp); + OPENSSL_cleanse(twop, sizeof(twop)); +} + +void curve448_base_double_scalarmul_non_secret(curve448_point_t combo, + const curve448_scalar_t scalar1, + const curve448_point_t base2, + const curve448_scalar_t scalar2) +{ + const int table_bits_var = C448_WNAF_VAR_TABLE_BITS; + const int table_bits_pre = C448_WNAF_FIXED_TABLE_BITS; + struct smvt_control control_var[C448_SCALAR_BITS / + (C448_WNAF_VAR_TABLE_BITS + 1) + 3]; + struct smvt_control control_pre[C448_SCALAR_BITS / + (C448_WNAF_FIXED_TABLE_BITS + 1) + 3]; + int ncb_pre = recode_wnaf(control_pre, scalar1, table_bits_pre); + int ncb_var = recode_wnaf(control_var, scalar2, table_bits_var); + pniels_t precmp_var[1 << C448_WNAF_VAR_TABLE_BITS]; + int contp = 0, contv = 0, i; + + prepare_wnaf_table(precmp_var, base2, table_bits_var); + i = control_var[0].power; + + if (i < 0) { + curve448_point_copy(combo, curve448_point_identity); + return; + } + if (i > control_pre[0].power) { + pniels_to_pt(combo, precmp_var[control_var[0].addend >> 1]); + contv++; + } else if (i == control_pre[0].power && i >= 0) { + pniels_to_pt(combo, precmp_var[control_var[0].addend >> 1]); + add_niels_to_pt(combo, curve448_wnaf_base[control_pre[0].addend >> 1], + i); + contv++; + contp++; + } else { + i = control_pre[0].power; + niels_to_pt(combo, curve448_wnaf_base[control_pre[0].addend >> 1]); + contp++; + } + + for (i--; i >= 0; i--) { + int cv = (i == control_var[contv].power); + int cp = (i == control_pre[contp].power); + + point_double_internal(combo, combo, i && !(cv || cp)); + + if (cv) { + assert(control_var[contv].addend); + + if (control_var[contv].addend > 0) + add_pniels_to_pt(combo, + precmp_var[control_var[contv].addend >> 1], + i && !cp); + else + sub_pniels_from_pt(combo, + precmp_var[(-control_var[contv].addend) + >> 1], i && !cp); + contv++; + } + + if (cp) { + assert(control_pre[contp].addend); + + if (control_pre[contp].addend > 0) + add_niels_to_pt(combo, + curve448_wnaf_base[control_pre[contp].addend + >> 1], i); + else + sub_niels_from_pt(combo, + curve448_wnaf_base[(-control_pre + [contp].addend) >> 1], i); + contp++; + } + } + + /* This function is non-secret, but whatever this is cheap. */ + OPENSSL_cleanse(control_var, sizeof(control_var)); + OPENSSL_cleanse(control_pre, sizeof(control_pre)); + OPENSSL_cleanse(precmp_var, sizeof(precmp_var)); + + assert(contv == ncb_var); + (void)ncb_var; + assert(contp == ncb_pre); + (void)ncb_pre; +} + +void curve448_point_destroy(curve448_point_t point) +{ + OPENSSL_cleanse(point, sizeof(curve448_point_t)); +} + +int X448(uint8_t out_shared_key[56], const uint8_t private_key[56], + const uint8_t peer_public_value[56]) +{ + return x448_int(out_shared_key, peer_public_value, private_key) + == C448_SUCCESS; +} + +void X448_public_from_private(uint8_t out_public_value[56], + const uint8_t private_key[56]) +{ + x448_derive_public_key(out_public_value, private_key); +} diff --git a/deps/openssl/openssl/crypto/ec/curve448/curve448_lcl.h b/deps/openssl/openssl/crypto/ec/curve448/curve448_lcl.h new file mode 100644 index 0000000000..2bc3bd84c8 --- /dev/null +++ b/deps/openssl/openssl/crypto/ec/curve448/curve448_lcl.h @@ -0,0 +1,38 @@ +/* + * Copyright 2017-2018 The OpenSSL Project Authors. All Rights Reserved. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + */ +#ifndef HEADER_CURVE448_LCL_H +# define HEADER_CURVE448_LCL_H +# include "curve448utils.h" + +int X448(uint8_t out_shared_key[56], const uint8_t private_key[56], + const uint8_t peer_public_value[56]); + +void X448_public_from_private(uint8_t out_public_value[56], + const uint8_t private_key[56]); + +int ED448_sign(uint8_t *out_sig, const uint8_t *message, size_t message_len, + const uint8_t public_key[57], const uint8_t private_key[57], + const uint8_t *context, size_t context_len); + +int ED448_verify(const uint8_t *message, size_t message_len, + const uint8_t signature[114], const uint8_t public_key[57], + const uint8_t *context, size_t context_len); + +int ED448ph_sign(uint8_t *out_sig, const uint8_t hash[64], + const uint8_t public_key[57], const uint8_t private_key[57], + const uint8_t *context, size_t context_len); + +int ED448ph_verify(const uint8_t hash[64], const uint8_t signature[114], + const uint8_t public_key[57], const uint8_t *context, + size_t context_len); + +int ED448_public_from_private(uint8_t out_public_key[57], + const uint8_t private_key[57]); + +#endif /* HEADER_CURVE448_LCL_H */ diff --git a/deps/openssl/openssl/crypto/ec/curve448/curve448_tables.c b/deps/openssl/openssl/crypto/ec/curve448/curve448_tables.c new file mode 100644 index 0000000000..a1185b1eee --- /dev/null +++ b/deps/openssl/openssl/crypto/ec/curve448/curve448_tables.c @@ -0,0 +1,475 @@ +/* + * Copyright 2017-2018 The OpenSSL Project Authors. All Rights Reserved. + * Copyright 2015-2016 Cryptography Research, Inc. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + * + * Originally written by Mike Hamburg + */ +#include "field.h" + +#include "point_448.h" + +static const curve448_precomputed_s curve448_precomputed_base_table = { + { + {{ + {FIELD_LITERAL(0x00cc3b062366f4cc,0x003d6e34e314aa3c,0x00d51c0a7521774d,0x0094e060eec6ab8b,0x00d21291b4d80082,0x00befed12b55ef1e,0x00c3dd2df5c94518,0x00e0a7b112b8d4e6)}, + {FIELD_LITERAL(0x0019eb5608d8723a,0x00d1bab52fb3aedb,0x00270a7311ebc90c,0x0037c12b91be7f13,0x005be16cd8b5c704,0x003e181acda888e1,0x00bc1f00fc3fc6d0,0x00d3839bfa319e20)}, + {FIELD_LITERAL(0x003caeb88611909f,0x00ea8b378c4df3d4,0x00b3295b95a5a19a,0x00a65f97514bdfb5,0x00b39efba743cab1,0x0016ba98b862fd2d,0x0001508812ee71d7,0x000a75740eea114a)}, + }}, {{ + {FIELD_LITERAL(0x00ebcf0eb649f823,0x00166d332e98ea03,0x0059ddf64f5cd5f6,0x0047763123d9471b,0x00a64065c53ef62f,0x00978e44c480153d,0x000b5b2a0265f194,0x0046a24b9f32965a)}, + {FIELD_LITERAL(0x00b9eef787034df0,0x0020bc24de3390cd,0x000022160bae99bb,0x00ae66e886e97946,0x0048d4bbe02cbb8b,0x0072ba97b34e38d4,0x00eae7ec8f03e85a,0x005ba92ecf808b2c)}, + {FIELD_LITERAL(0x00c9cfbbe74258fd,0x00843a979ea9eaa7,0x000cbb4371cfbe90,0x0059bac8f7f0a628,0x004b3dff882ff530,0x0011869df4d90733,0x00595aa71f4abfc2,0x0070e2d38990c2e6)}, + }}, {{ + {FIELD_LITERAL(0x00de2010c0a01733,0x00c739a612e24297,0x00a7212643141d7c,0x00f88444f6b67c11,0x00484b7b16ec28f2,0x009c1b8856af9c68,0x00ff4669591fe9d6,0x0054974be08a32c8)}, + {FIELD_LITERAL(0x0010de3fd682ceed,0x008c07642d83ca4e,0x0013bb064e00a1cc,0x009411ae27870e11,0x00ea8e5b4d531223,0x0032fe7d2aaece2e,0x00d989e243e7bb41,0x000fe79a508e9b8b)}, + {FIELD_LITERAL(0x005e0426b9bfc5b1,0x0041a5b1d29ee4fa,0x0015b0def7774391,0x00bc164f1f51af01,0x00d543b0942797b9,0x003c129b6398099c,0x002b114c6e5adf18,0x00b4e630e4018a7b)}, + }}, {{ + {FIELD_LITERAL(0x00d490afc95f8420,0x00b096bf50c1d9b9,0x00799fd707679866,0x007c74d9334afbea,0x00efaa8be80ff4ed,0x0075c4943bb81694,0x00c21c2fca161f36,0x00e77035d492bfee)}, + {FIELD_LITERAL(0x006658a190dd6661,0x00e0e9bab38609a6,0x0028895c802237ed,0x006a0229c494f587,0x002dcde96c9916b7,0x00d158822de16218,0x00173b917a06856f,0x00ca78a79ae07326)}, + {FIELD_LITERAL(0x00e35bfc79caced4,0x0087238a3e1fe3bb,0x00bcbf0ff4ceff5b,0x00a19c1c94099b91,0x0071e102b49db976,0x0059e3d004eada1e,0x008da78afa58a47e,0x00579c8ebf269187)}, + }}, {{ + {FIELD_LITERAL(0x00a16c2905eee75f,0x009d4bcaea2c7e1d,0x00d3bd79bfad19df,0x0050da745193342c,0x006abdb8f6b29ab1,0x00a24fe0a4fef7ef,0x0063730da1057dfb,0x00a08c312c8eb108)}, + {FIELD_LITERAL(0x00b583be005375be,0x00a40c8f8a4e3df4,0x003fac4a8f5bdbf7,0x00d4481d872cd718,0x004dc8749cdbaefe,0x00cce740d5e5c975,0x000b1c1f4241fd21,0x00a76de1b4e1cd07)}, + {FIELD_LITERAL(0x007a076500d30b62,0x000a6e117b7f090f,0x00c8712ae7eebd9a,0x000fbd6c1d5f6ff7,0x003a7977246ebf11,0x00166ed969c6600e,0x00aa42e469c98bec,0x00dc58f307cf0666)}, + }}, {{ + {FIELD_LITERAL(0x004b491f65a9a28b,0x006a10309e8a55b7,0x00b67210185187ef,0x00cf6497b12d9b8f,0x0085778c56e2b1ba,0x0015b4c07a814d85,0x00686479e62da561,0x008de5d88f114916)}, + {FIELD_LITERAL(0x00e37c88d6bba7b1,0x003e4577e1b8d433,0x0050d8ea5f510ec0,0x0042fc9f2da9ef59,0x003bd074c1141420,0x00561b8b7b68774e,0x00232e5e5d1013a3,0x006b7f2cb3d7e73f)}, + {FIELD_LITERAL(0x004bdd0f0b41e6a0,0x001773057c405d24,0x006029f99915bd97,0x006a5ba70a17fe2f,0x0046111977df7e08,0x004d8124c89fb6b7,0x00580983b2bb2724,0x00207bf330d6f3fe)}, + }}, {{ + 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{FIELD_LITERAL(0x00b37396c3320791,0x00fc7b67175c5783,0x00c36d2cd73ecc38,0x0080ebcc0b328fc5,0x0043a5b22b35d35d,0x00466c9f1713c9da,0x0026ad346dcaa8da,0x007c684e701183a6)}, + {FIELD_LITERAL(0x00fd579ffb691713,0x00b76af4f81c412d,0x00f239de96110f82,0x00e965fb437f0306,0x00ca7e9436900921,0x00e487f1325fa24a,0x00633907de476380,0x00721c62ac5b8ea0)}, + {FIELD_LITERAL(0x00c0d54e542eb4f9,0x004ed657171c8dcf,0x00b743a4f7c2a39b,0x00fd9f93ed6cc567,0x00307fae3113e58b,0x0058aa577c93c319,0x00d254556f35b346,0x00491aada2203f0d)}, + }}, {{ + {FIELD_LITERAL(0x00dff3103786ff34,0x000144553b1f20c3,0x0095613baeb930e4,0x00098058275ea5d4,0x007cd1402b046756,0x0074d74e4d58aee3,0x005f93fc343ff69b,0x00873df17296b3b0)}, + {FIELD_LITERAL(0x00c4a1fb48635413,0x00b5dd54423ad59f,0x009ff5d53fd24a88,0x003c98d267fc06a7,0x002db7cb20013641,0x00bd1d6716e191f2,0x006dbc8b29094241,0x0044bbf233dafa2c)}, + {FIELD_LITERAL(0x0055838d41f531e6,0x00bf6a2dd03c81b2,0x005827a061c4839e,0x0000de2cbb36aac3,0x002efa29d9717478,0x00f9e928cc8a77ba,0x00c134b458def9ef,0x00958a182223fc48)}, + }}, {{ + {FIELD_LITERAL(0x000a9ee23c06881f,0x002c727d3d871945,0x00f47d971512d24a,0x00671e816f9ef31a,0x00883af2cfaad673,0x00601f98583d6c9a,0x00b435f5adc79655,0x00ad87b71c04bff2)}, + {FIELD_LITERAL(0x007860d99db787cf,0x00fda8983018f4a8,0x008c8866bac4743c,0x00ef471f84c82a3f,0x00abea5976d3b8e7,0x00714882896cd015,0x00b49fae584ddac5,0x008e33a1a0b69c81)}, + {FIELD_LITERAL(0x007b6ee2c9e8a9ec,0x002455dbbd89d622,0x006490cf4eaab038,0x00d925f6c3081561,0x00153b3047de7382,0x003b421f8bdceb6f,0x00761a4a5049da78,0x00980348c5202433)}, + }}, {{ + {FIELD_LITERAL(0x007f8a43da97dd5c,0x00058539c800fc7b,0x0040f3cf5a28414a,0x00d68dd0d95283d6,0x004adce9da90146e,0x00befa41c7d4f908,0x007603bc2e3c3060,0x00bdf360ab3545db)}, + {FIELD_LITERAL(0x00eebfd4e2312cc3,0x00474b2564e4fc8c,0x003303ef14b1da9b,0x003c93e0e66beb1d,0x0013619b0566925a,0x008817c24d901bf3,0x00b62bd8898d218b,0x0075a7716f1e88a2)}, + {FIELD_LITERAL(0x0009218da1e6890f,0x0026907f5fd02575,0x004dabed5f19d605,0x003abf181870249d,0x00b52fd048cc92c4,0x00b6dd51e415a5c5,0x00d9eb82bd2b4014,0x002c865a43b46b43)}, + }}, {{ + {FIELD_LITERAL(0x0070047189452f4c,0x00f7ad12e1ce78d5,0x00af1ba51ec44a8b,0x005f39f63e667cd6,0x00058eac4648425e,0x00d7fdab42bea03b,0x0028576a5688de15,0x00af973209e77c10)}, + {FIELD_LITERAL(0x00c338b915d8fef0,0x00a893292045c39a,0x0028ab4f2eba6887,0x0060743cb519fd61,0x0006213964093ac0,0x007c0b7a43f6266d,0x008e3557c4fa5bda,0x002da976de7b8d9d)}, + {FIELD_LITERAL(0x0048729f8a8b6dcd,0x00fe23b85cc4d323,0x00e7384d16e4db0e,0x004a423970678942,0x00ec0b763345d4ba,0x00c477b9f99ed721,0x00c29dad3777b230,0x001c517b466f7df6)}, + }}, {{ + {FIELD_LITERAL(0x006366c380f7b574,0x001c7d1f09ff0438,0x003e20a7301f5b22,0x00d3efb1916d28f6,0x0049f4f81060ce83,0x00c69d91ea43ced1,0x002b6f3e5cd269ed,0x005b0fb22ce9ec65)}, + {FIELD_LITERAL(0x00aa2261022d883f,0x00ebcca4548010ac,0x002528512e28a437,0x0070ca7676b66082,0x0084bda170f7c6d3,0x00581b4747c9b8bb,0x005c96a01061c7e2,0x00fb7c4a362b5273)}, + {FIELD_LITERAL(0x00c30020eb512d02,0x0060f288283a4d26,0x00b7ed13becde260,0x0075ebb74220f6e9,0x00701079fcfe8a1f,0x001c28fcdff58938,0x002e4544b8f4df6b,0x0060c5bc4f1a7d73)}, + }}, {{ + {FIELD_LITERAL(0x00ae307cf069f701,0x005859f222dd618b,0x00212d6c46ec0b0d,0x00a0fe4642afb62d,0x00420d8e4a0a8903,0x00a80ff639bdf7b0,0x0019bee1490b5d8e,0x007439e4b9c27a86)}, + {FIELD_LITERAL(0x00a94700032a093f,0x0076e96c225216e7,0x00a63a4316e45f91,0x007d8bbb4645d3b2,0x00340a6ff22793eb,0x006f935d4572aeb7,0x00b1fb69f00afa28,0x009e8f3423161ed3)}, + {FIELD_LITERAL(0x009ef49c6b5ced17,0x00a555e6269e9f0a,0x007e6f1d79ec73b5,0x009ac78695a32ac4,0x0001d77fbbcd5682,0x008cea1fee0aaeed,0x00f42bea82a53462,0x002e46ab96cafcc9)}, + }}, {{ + {FIELD_LITERAL(0x0051cfcc5885377a,0x00dce566cb1803ca,0x00430c7643f2c7d4,0x00dce1a1337bdcc0,0x0010d5bd7283c128,0x003b1b547f9b46fe,0x000f245e37e770ab,0x007b72511f022b37)}, + {FIELD_LITERAL(0x0060db815bc4786c,0x006fab25beedc434,0x00c610d06084797c,0x000c48f08537bec0,0x0031aba51c5b93da,0x007968fa6e01f347,0x0030070da52840c6,0x00c043c225a4837f)}, + {FIELD_LITERAL(0x001bcfd00649ee93,0x006dceb47e2a0fd5,0x00f2cebda0cf8fd0,0x00b6b9d9d1fbdec3,0x00815262e6490611,0x00ef7f5ce3176760,0x00e49cd0c998d58b,0x005fc6cc269ba57c)}, + }}, {{ + {FIELD_LITERAL(0x008940211aa0d633,0x00addae28136571d,0x00d68fdbba20d673,0x003bc6129bc9e21a,0x000346cf184ebe9a,0x0068774d741ebc7f,0x0019d5e9e6966557,0x0003cbd7f981b651)}, + {FIELD_LITERAL(0x004a2902926f8d3f,0x00ad79b42637ab75,0x0088f60b90f2d4e8,0x0030f54ef0e398c4,0x00021dc9bf99681e,0x007ebf66fde74ee3,0x004ade654386e9a4,0x00e7485066be4c27)}, + {FIELD_LITERAL(0x00445f1263983be0,0x004cf371dda45e6a,0x00744a89d5a310e7,0x001f20ce4f904833,0x00e746edebe66e29,0x000912ab1f6c153d,0x00f61d77d9b2444c,0x0001499cd6647610)}, + }} + } +}; +const struct curve448_precomputed_s *curve448_precomputed_base + = &curve448_precomputed_base_table; + +static const niels_t curve448_wnaf_base_table[32] = { + {{ + {FIELD_LITERAL(0x00303cda6feea532,0x00860f1d5a3850e4,0x00226b9fa4728ccd,0x00e822938a0a0c0c,0x00263a61c9ea9216,0x001204029321b828,0x006a468360983c65,0x0002846f0a782143)}, + {FIELD_LITERAL(0x00303cda6feea532,0x00860f1d5a3850e4,0x00226b9fa4728ccd,0x006822938a0a0c0c,0x00263a61c9ea9215,0x001204029321b828,0x006a468360983c65,0x0082846f0a782143)}, + {FIELD_LITERAL(0x00ef8e22b275198d,0x00b0eb141a0b0e8b,0x001f6789da3cb38c,0x006d2ff8ed39073e,0x00610bdb69a167f3,0x00571f306c9689b4,0x00f557e6f84b2df8,0x002affd38b2c86db)}, + }}, {{ + {FIELD_LITERAL(0x00cea0fc8d2e88b5,0x00821612d69f1862,0x0074c283b3e67522,0x005a195ba05a876d,0x000cddfe557feea4,0x008046c795bcc5e5,0x00540969f4d6e119,0x00d27f96d6b143d5)}, + {FIELD_LITERAL(0x000c3b1019d474e8,0x00e19533e4952284,0x00cc9810ba7c920a,0x00f103d2785945ac,0x00bfa5696cc69b34,0x00a8d3d51e9ca839,0x005623cb459586b9,0x00eae7ce1cd52e9e)}, + {FIELD_LITERAL(0x0005a178751dd7d8,0x002cc3844c69c42f,0x00acbfe5efe10539,0x009c20f43431a65a,0x008435d96374a7b3,0x009ee57566877bd3,0x0044691725ed4757,0x001e87bb2fe2c6b2)}, + }}, {{ + {FIELD_LITERAL(0x000cedc4debf7a04,0x002ffa45000470ac,0x002e9f9678201915,0x0017da1208c4fe72,0x007d558cc7d656cb,0x0037a827287cf289,0x00142472d3441819,0x009c21f166cf8dd1)}, + {FIELD_LITERAL(0x003ef83af164b2f2,0x000949a5a0525d0d,0x00f4498186cac051,0x00e77ac09ef126d2,0x0073ae0b2c9296e9,0x001c163f6922e3ed,0x0062946159321bea,0x00cfb79b22990b39)}, + {FIELD_LITERAL(0x00b001431ca9e654,0x002d7e5eabcc9a3a,0x0052e8114c2f6747,0x0079ac4f94487f92,0x00bffd919b5d749c,0x00261f92ad15e620,0x00718397b7a97895,0x00c1443e6ebbc0c4)}, + }}, {{ + {FIELD_LITERAL(0x00eacd90c1e0a049,0x008977935b149fbe,0x0004cb9ba11c93dc,0x009fbd5b3470844d,0x004bc18c9bfc22cf,0x0057679a991839f3,0x00ef15b76fb4092e,0x0074a5173a225041)}, + {FIELD_LITERAL(0x003f5f9d7ec4777b,0x00ab2e733c919c94,0x001bb6c035245ae5,0x00a325a49a883630,0x0033e9a9ea3cea2f,0x00e442a1eaa0e844,0x00b2116d5b0e71b8,0x00c16abed6d64047)}, + {FIELD_LITERAL(0x00c560b5ed051165,0x001945adc5d65094,0x00e221865710f910,0x00cc12bc9e9b8ceb,0x004faa9518914e35,0x0017476d89d42f6d,0x00b8f637c8fa1c8b,0x0088c7d2790864b8)}, + }}, {{ + {FIELD_LITERAL(0x00ef7eafc1c69be6,0x0085d3855778fbea,0x002c8d5b450cb6f5,0x004e77de5e1e7fec,0x0047c057893abded,0x001b430b85d51e16,0x00965c7b45640c3c,0x00487b2bb1162b97)}, + {FIELD_LITERAL(0x0099c73a311beec2,0x00a3eff38d8912ad,0x002efa9d1d7e8972,0x00f717ae1e14d126,0x002833f795850c8b,0x0066c12ad71486bd,0x00ae9889da4820eb,0x00d6044309555c08)}, + {FIELD_LITERAL(0x004b1c5283d15e41,0x00669d8ea308ff75,0x0004390233f762a1,0x00e1d67b83cb6cec,0x003eebaa964c78b1,0x006b0aff965eb664,0x00b313d4470bdc37,0x008814ffcb3cb9d8)}, + }}, {{ + {FIELD_LITERAL(0x009724b8ce68db70,0x007678b5ed006f3d,0x00bdf4b89c0abd73,0x00299748e04c7c6d,0x00ddd86492c3c977,0x00c5a7febfa30a99,0x00ed84715b4b02bb,0x00319568adf70486)}, + {FIELD_LITERAL(0x0070ff2d864de5bb,0x005a37eeb637ee95,0x0033741c258de160,0x00e6ca5cb1988f46,0x001ceabd92a24661,0x0030957bd500fe40,0x001c3362afe912c5,0x005187889f678bd2)}, + {FIELD_LITERAL(0x0086835fc62bbdc7,0x009c3516ca4910a1,0x00956c71f8d00783,0x0095c78fcf63235f,0x00fc7ff6ba05c222,0x00cdd8b3f8d74a52,0x00ac5ae16de8256e,0x00e9d4be8ed48624)}, + }}, {{ + {FIELD_LITERAL(0x00c0ce11405df2d8,0x004e3f37b293d7b6,0x002410172e1ac6db,0x00b8dbff4bf8143d,0x003a7b409d56eb66,0x003e0f6a0dfef9af,0x0081c4e4d3645be1,0x00ce76076b127623)}, + {FIELD_LITERAL(0x00f6ee0f98974239,0x0042d89af07d3a4f,0x00846b7fe84346b5,0x006a21fc6a8d39a1,0x00ac8bc2541ff2d9,0x006d4e2a77732732,0x009a39b694cc3f2f,0x0085c0aa2a404c8f)}, + {FIELD_LITERAL(0x00b261101a218548,0x00c1cae96424277b,0x00869da0a77dd268,0x00bc0b09f8ec83ea,0x00d61027f8e82ba9,0x00aa4c85999dce67,0x00eac3132b9f3fe1,0x00fb9b0cf1c695d2)}, + }}, {{ + {FIELD_LITERAL(0x0043079295512f0d,0x0046a009861758e0,0x003ee2842a807378,0x0034cc9d1298e4fa,0x009744eb4d31b3ee,0x00afacec96650cd0,0x00ac891b313761ae,0x00e864d6d26e708a)}, + {FIELD_LITERAL(0x00a84d7c8a23b491,0x0088e19aa868b27f,0x0005986d43e78ce9,0x00f28012f0606d28,0x0017ded7e10249b3,0x005ed4084b23af9b,0x00b9b0a940564472,0x00ad9056cceeb1f4)}, + {FIELD_LITERAL(0x00db91b357fe755e,0x00a1aa544b15359c,0x00af4931a0195574,0x007686124fe11aef,0x00d1ead3c7b9ef7e,0x00aaf5fc580f8c15,0x00e727be147ee1ec,0x003c61c1e1577b86)}, + }}, {{ + {FIELD_LITERAL(0x009d3fca983220cf,0x00cd11acbc853dc4,0x0017590409d27f1d,0x00d2176698082802,0x00fa01251b2838c8,0x00dd297a0d9b51c6,0x00d76c92c045820a,0x00534bc7c46c9033)}, + {FIELD_LITERAL(0x0080ed9bc9b07338,0x00fceac7745d2652,0x008a9d55f5f2cc69,0x0096ce72df301ac5,0x00f53232e7974d87,0x0071728c7ae73947,0x0090507602570778,0x00cb81cfd883b1b2)}, + {FIELD_LITERAL(0x005011aadea373da,0x003a8578ec896034,0x00f20a6535fa6d71,0x005152d31e5a87cf,0x002bac1c8e68ca31,0x00b0e323db4c1381,0x00f1d596b7d5ae25,0x00eae458097cb4e0)}, + }}, {{ + {FIELD_LITERAL(0x00920ac80f9b0d21,0x00f80f7f73401246,0x0086d37849b557d6,0x0002bd4b317b752e,0x00b26463993a42bb,0x002070422a73b129,0x00341acaa0380cb3,0x00541914dd66a1b2)}, + {FIELD_LITERAL(0x00c1513cd66abe8c,0x000139e01118944d,0x0064abbcb8080bbb,0x00b3b08202473142,0x00c629ef25da2403,0x00f0aec3310d9b7f,0x0050b2227472d8cd,0x00f6c8a922d41fb4)}, + {FIELD_LITERAL(0x001075ccf26b7b1f,0x00bb6bb213170433,0x00e9491ad262da79,0x009ef4f48d2d384c,0x008992770766f09d,0x001584396b6b1101,0x00af3f8676c9feef,0x0024603c40269118)}, + }}, {{ + {FIELD_LITERAL(0x009dd7b31319527c,0x001e7ac948d873a9,0x00fa54b46ef9673a,0x0066efb8d5b02fe6,0x00754b1d3928aeae,0x0004262ac72a6f6b,0x0079b7d49a6eb026,0x003126a753540102)}, + {FIELD_LITERAL(0x009666e24f693947,0x00f714311269d45f,0x0010ffac1d0c851c,0x0066e80c37363497,0x00f1f4ad010c60b0,0x0015c87408470ff7,0x00651d5e9c7766a4,0x008138819d7116de)}, + {FIELD_LITERAL(0x003934b11c57253b,0x00ef308edf21f46e,0x00e54e99c7a16198,0x0080d57135764e63,0x00751c27b946bc24,0x00dd389ce4e9e129,0x00a1a2bfd1cd84dc,0x002fae73e5149b32)}, + }}, {{ + {FIELD_LITERAL(0x00911657dffb4cdd,0x00c100b7cc553d06,0x00449d075ec467cc,0x007062100bc64e70,0x0043cf86f7bd21e7,0x00f401dc4b797dea,0x005224afb2f62e65,0x00d1ede3fb5a42be)}, + {FIELD_LITERAL(0x00f2ba36a41aa144,0x00a0c22d946ee18f,0x008aae8ef9a14f99,0x00eef4d79b19bb36,0x008e75ce3d27b1fc,0x00a65daa03b29a27,0x00d9cc83684eb145,0x009e1ed80cc2ed74)}, + {FIELD_LITERAL(0x00bed953d1997988,0x00b93ed175a24128,0x00871c5963fb6365,0x00ca2df20014a787,0x00f5d9c1d0b34322,0x00f6f5942818db0a,0x004cc091f49c9906,0x00e8a188a60bff9f)}, + }}, {{ + {FIELD_LITERAL(0x0032c7762032fae8,0x00e4087232e0bc21,0x00f767344b6e8d85,0x00bbf369b76c2aa2,0x008a1f46c6e1570c,0x001368cd9780369f,0x007359a39d079430,0x0003646512921434)}, + {FIELD_LITERAL(0x007c4b47ca7c73e7,0x005396221039734b,0x008b64ddf0e45d7e,0x00bfad5af285e6c2,0x008ec711c5b1a1a8,0x00cf663301237f98,0x00917ee3f1655126,0x004152f337efedd8)}, + {FIELD_LITERAL(0x0007c7edc9305daa,0x000a6664f273701c,0x00f6e78795e200b1,0x005d05b9ecd2473e,0x0014f5f17c865786,0x00c7fd2d166fa995,0x004939a2d8eb80e0,0x002244ba0942c199)}, + }}, {{ + {FIELD_LITERAL(0x00321e767f0262cf,0x002e57d776caf68e,0x00bf2c94814f0437,0x00c339196acd622f,0x001db4cce71e2770,0x001ded5ddba6eee2,0x0078608ab1554c8d,0x00067fe0ab76365b)}, + {FIELD_LITERAL(0x00f09758e11e3985,0x00169efdbd64fad3,0x00e8889b7d6dacd6,0x0035cdd58ea88209,0x00bcda47586d7f49,0x003cdddcb2879088,0x0016da70187e954b,0x009556ea2e92aacd)}, + {FIELD_LITERAL(0x008cab16bd1ff897,0x00b389972cdf753f,0x00ea8ed1e46dfdc0,0x004fe7ef94c589f4,0x002b8ae9b805ecf3,0x0025c08d892874a5,0x0023938e98d44c4c,0x00f759134cabf69c)}, + }}, {{ + {FIELD_LITERAL(0x006c2a84678e4b3b,0x007a194aacd1868f,0x00ed0225af424761,0x00da0a6f293c64b8,0x001062ac5c6a7a18,0x0030f5775a8aeef4,0x0002acaad76b7af0,0x00410b8fd63a579f)}, + {FIELD_LITERAL(0x001ec59db3d9590e,0x001e9e3f1c3f182d,0x0045a9c3ec2cab14,0x0008198572aeb673,0x00773b74068bd167,0x0012535eaa395434,0x0044dba9e3bbb74a,0x002fba4d3c74bd0e)}, + {FIELD_LITERAL(0x0042bf08fe66922c,0x003318b8fbb49e8c,0x00d75946004aa14c,0x00f601586b42bf1c,0x00c74cf1d912fe66,0x00abcb36974b30ad,0x007eb78720c9d2b8,0x009f54ab7bd4df85)}, + }}, {{ + {FIELD_LITERAL(0x00db9fc948f73826,0x00fa8b3746ed8ee9,0x00132cb65aafbeb2,0x00c36ff3fe7925b8,0x00837daed353d2fe,0x00ec661be0667cf4,0x005beb8ed2e90204,0x00d77dd69e564967)}, + {FIELD_LITERAL(0x0042e6268b861751,0x0008dd0469500c16,0x00b51b57c338a3fd,0x00cc4497d85cff6b,0x002f13d6b57c34a4,0x0083652eaf301105,0x00cc344294cc93a8,0x0060f4d02810e270)}, + {FIELD_LITERAL(0x00a8954363cd518b,0x00ad171124bccb7b,0x0065f46a4adaae00,0x001b1a5b2a96e500,0x0043fe24f8233285,0x0066996d8ae1f2c3,0x00c530f3264169f9,0x00c0f92d07cf6a57)}, + }}, {{ + {FIELD_LITERAL(0x0036a55c6815d943,0x008c8d1def993db3,0x002e0e1e8ff7318f,0x00d883a4b92db00a,0x002f5e781ae33906,0x001a72adb235c06d,0x00f2e59e736e9caa,0x001a4b58e3031914)}, + {FIELD_LITERAL(0x00d73bfae5e00844,0x00bf459766fb5f52,0x0061b4f5a5313cde,0x004392d4c3b95514,0x000d3551b1077523,0x0000998840ee5d71,0x006de6e340448b7b,0x00251aa504875d6e)}, + {FIELD_LITERAL(0x003bf343427ac342,0x00adc0a78642b8c5,0x0003b893175a8314,0x0061a34ade5703bc,0x00ea3ea8bb71d632,0x00be0df9a1f198c2,0x0046dd8e7c1635fb,0x00f1523fdd25d5e5)}, + }}, {{ + {FIELD_LITERAL(0x00633f63fc9dd406,0x00e713ff80e04a43,0x0060c6e970f2d621,0x00a57cd7f0df1891,0x00f2406a550650bb,0x00b064290efdc684,0x001eab0144d17916,0x00cd15f863c293ab)}, + {FIELD_LITERAL(0x0029cec55273f70d,0x007044ee275c6340,0x0040f637a93015e2,0x00338bb78db5aae9,0x001491b2a6132147,0x00a125d6cfe6bde3,0x005f7ac561ba8669,0x001d5eaea3fbaacf)}, + {FIELD_LITERAL(0x00054e9635e3be31,0x000e43f31e2872be,0x00d05b1c9e339841,0x006fac50bd81fd98,0x00cdc7852eaebb09,0x004ff519b061991b,0x009099e8107d4c85,0x00273e24c36a4a61)}, + }}, {{ + {FIELD_LITERAL(0x00070b4441ef2c46,0x00efa5b02801a109,0x00bf0b8c3ee64adf,0x008a67e0b3452e98,0x001916b1f2fa7a74,0x00d781a78ff6cdc3,0x008682ce57e5c919,0x00cc1109dd210da3)}, + {FIELD_LITERAL(0x00cae8aaff388663,0x005e983a35dda1c7,0x007ab1030d8e37f4,0x00e48940f5d032fe,0x006a36f9ef30b331,0x009be6f03958c757,0x0086231ceba91400,0x008bd0f7b823e7aa)}, + {FIELD_LITERAL(0x00cf881ebef5a45a,0x004ebea78e7c6f2c,0x0090da9209cf26a0,0x00de2b2e4c775b84,0x0071d6031c3c15ae,0x00d9e927ef177d70,0x00894ee8c23896fd,0x00e3b3b401e41aad)}, + }}, {{ + {FIELD_LITERAL(0x00204fef26864170,0x00819269c5dee0f8,0x00bfb4713ec97966,0x0026339a6f34df78,0x001f26e64c761dc2,0x00effe3af313cb60,0x00e17b70138f601b,0x00f16e1ccd9ede5e)}, + {FIELD_LITERAL(0x005d9a8353fdb2db,0x0055cc2048c698f0,0x00f6c4ac89657218,0x00525034d73faeb2,0x00435776fbda3c7d,0x0070ea5312323cbc,0x007a105d44d069fb,0x006dbc8d6dc786aa)}, + {FIELD_LITERAL(0x0017cff19cd394ec,0x00fef7b810922587,0x00e6483970dff548,0x00ddf36ad6874264,0x00e61778523fcce2,0x0093a66c0c93b24a,0x00fd367114db7f86,0x007652d7ddce26dd)}, + }}, {{ + {FIELD_LITERAL(0x00d92ced7ba12843,0x00aea9c7771e86e7,0x0046639693354f7b,0x00a628dbb6a80c47,0x003a0b0507372953,0x00421113ab45c0d9,0x00e545f08362ab7a,0x0028ce087b4d6d96)}, + {FIELD_LITERAL(0x00a67ee7cf9f99eb,0x005713b275f2ff68,0x00f1d536a841513d,0x00823b59b024712e,0x009c46b9d0d38cec,0x00cdb1595aa2d7d4,0x008375b3423d9af8,0x000ab0b516d978f7)}, + {FIELD_LITERAL(0x00428dcb3c510b0f,0x00585607ea24bb4e,0x003736bf1603687a,0x00c47e568c4fe3c7,0x003cd00282848605,0x0043a487c3b91939,0x004ffc04e1095a06,0x00a4c989a3d4b918)}, + }}, {{ + {FIELD_LITERAL(0x00a8778d0e429f7a,0x004c02b059105a68,0x0016653b609da3ff,0x00d5107bd1a12d27,0x00b4708f9a771cab,0x00bb63b662033f69,0x0072f322240e7215,0x0019445b59c69222)}, + {FIELD_LITERAL(0x00cf4f6069a658e6,0x0053ca52859436a6,0x0064b994d7e3e117,0x00cb469b9a07f534,0x00cfb68f399e9d47,0x00f0dcb8dac1c6e7,0x00f2ab67f538b3a5,0x0055544f178ab975)}, + {FIELD_LITERAL(0x0099b7a2685d538c,0x00e2f1897b7c0018,0x003adac8ce48dae3,0x00089276d5c50c0c,0x00172fca07ad6717,0x00cb1a72f54069e5,0x004ee42f133545b3,0x00785f8651362f16)}, + }}, {{ + {FIELD_LITERAL(0x0049cbac38509e11,0x0015234505d42cdf,0x00794fb0b5840f1c,0x00496437344045a5,0x0031b6d944e4f9b0,0x00b207318ac1f5d8,0x0000c840da7f5c5d,0x00526f373a5c8814)}, + {FIELD_LITERAL(0x002c7b7742d1dfd9,0x002cabeb18623c01,0x00055f5e3e044446,0x006c20f3b4ef54ba,0x00c600141ec6b35f,0x00354f437f1a32a3,0x00bac4624a3520f9,0x00c483f734a90691)}, + {FIELD_LITERAL(0x0053a737d422918d,0x00f7fca1d8758625,0x00c360336dadb04c,0x00f38e3d9158a1b8,0x0069ce3b418e84c6,0x005d1697eca16ead,0x00f8bd6a35ece13d,0x007885dfc2b5afea)}, + }}, {{ + {FIELD_LITERAL(0x00c3617ae260776c,0x00b20dc3e96922d7,0x00a1a7802246706a,0x00ca6505a5240244,0x002246b62d919782,0x001439102d7aa9b3,0x00e8af1139e6422c,0x00c888d1b52f2b05)}, + {FIELD_LITERAL(0x005b67690ffd41d9,0x005294f28df516f9,0x00a879272412fcb9,0x00098b629a6d1c8d,0x00fabd3c8050865a,0x00cd7e5b0a3879c5,0x00153238210f3423,0x00357cac101e9f42)}, + {FIELD_LITERAL(0x008917b454444fb7,0x00f59247c97e441b,0x00a6200a6815152d,0x0009a4228601d254,0x001c0360559bd374,0x007563362039cb36,0x00bd75b48d74e32b,0x0017f515ac3499e8)}, + }}, {{ + {FIELD_LITERAL(0x001532a7ffe41c5a,0x00eb1edce358d6bf,0x00ddbacc7b678a7b,0x008a7b70f3c841a3,0x00f1923bf27d3f4c,0x000b2713ed8f7873,0x00aaf67e29047902,0x0044994a70b3976d)}, + {FIELD_LITERAL(0x00d54e802082d42c,0x00a55aa0dce7cc6c,0x006477b96073f146,0x0082efe4ceb43594,0x00a922bcba026845,0x0077f19d1ab75182,0x00c2bb2737846e59,0x0004d7eec791dd33)}, + {FIELD_LITERAL(0x0044588d1a81d680,0x00b0a9097208e4f8,0x00212605350dc57e,0x0028717cd2871123,0x00fb083c100fd979,0x0045a056ce063fdf,0x00a5d604b4dd6a41,0x001dabc08ba4e236)}, + }}, {{ + {FIELD_LITERAL(0x00c4887198d7a7fa,0x00244f98fb45784a,0x0045911e15a15d01,0x001d323d374c0966,0x00967c3915196562,0x0039373abd2f3c67,0x000d2c5614312423,0x0041cf2215442ce3)}, + {FIELD_LITERAL(0x008ede889ada7f06,0x001611e91de2e135,0x00fdb9a458a471b9,0x00563484e03710d1,0x0031cc81925e3070,0x0062c97b3af80005,0x00fa733eea28edeb,0x00e82457e1ebbc88)}, + {FIELD_LITERAL(0x006a0df5fe9b6f59,0x00a0d4ff46040d92,0x004a7cedb6f93250,0x00d1df8855b8c357,0x00e73a46086fd058,0x0048fb0add6dfe59,0x001e03a28f1b4e3d,0x00a871c993308d76)}, + }}, {{ + {FIELD_LITERAL(0x0030dbb2d1766ec8,0x00586c0ad138555e,0x00d1a34f9e91c77c,0x0063408ad0e89014,0x00d61231b05f6f5b,0x0009abf569f5fd8a,0x00aec67a110f1c43,0x0031d1a790938dd7)}, + {FIELD_LITERAL(0x006cded841e2a862,0x00198d60af0ab6fb,0x0018f09db809e750,0x004e6ac676016263,0x00eafcd1620969cb,0x002c9784ca34917d,0x0054f00079796de7,0x00d9fab5c5972204)}, + {FIELD_LITERAL(0x004bd0fee2438a83,0x00b571e62b0f83bd,0x0059287d7ce74800,0x00fb3631b645c3f0,0x00a018e977f78494,0x0091e27065c27b12,0x007696c1817165e0,0x008c40be7c45ba3a)}, + }}, {{ + {FIELD_LITERAL(0x00a0f326327cb684,0x001c7d0f672680ff,0x008c1c81ffb112d1,0x00f8f801674eddc8,0x00e926d5d48c2a9d,0x005bd6d954c6fe9a,0x004c6b24b4e33703,0x00d05eb5c09105cc)}, + {FIELD_LITERAL(0x00d61731caacf2cf,0x002df0c7609e01c5,0x00306172208b1e2b,0x00b413fe4fb2b686,0x00826d360902a221,0x003f8d056e67e7f7,0x0065025b0175e989,0x00369add117865eb)}, + {FIELD_LITERAL(0x00aaf895aec2fa11,0x000f892bc313eb52,0x005b1c794dad050b,0x003f8ec4864cec14,0x00af81058d0b90e5,0x00ebe43e183997bb,0x00a9d610f9f3e615,0x007acd8eec2e88d3)}, + }}, {{ + {FIELD_LITERAL(0x0049b2fab13812a3,0x00846db32cd60431,0x000177fa578c8d6c,0x00047d0e2ad4bc51,0x00b158ba38d1e588,0x006a45daad79e3f3,0x000997b93cab887b,0x00c47ea42fa23dc3)}, + {FIELD_LITERAL(0x0012b6fef7aeb1ca,0x009412768194b6a7,0x00ff0d351f23ab93,0x007e8a14c1aff71b,0x006c1c0170c512bc,0x0016243ea02ab2e5,0x007bb6865b303f3e,0x0015ce6b29b159f4)}, + {FIELD_LITERAL(0x009961cd02e68108,0x00e2035d3a1d0836,0x005d51f69b5e1a1d,0x004bccb4ea36edcd,0x0069be6a7aeef268,0x0063f4dd9de8d5a7,0x006283783092ca35,0x0075a31af2c35409)}, + }}, {{ + {FIELD_LITERAL(0x00c412365162e8cf,0x00012283fb34388a,0x003e6543babf39e2,0x00eead6b3a804978,0x0099c0314e8b326f,0x00e98e0a8d477a4f,0x00d2eb96b127a687,0x00ed8d7df87571bb)}, + {FIELD_LITERAL(0x00777463e308cacf,0x00c8acb93950132d,0x00ebddbf4ca48b2c,0x0026ad7ca0795a0a,0x00f99a3d9a715064,0x000d60bcf9d4dfcc,0x005e65a73a437a06,0x0019d536a8db56c8)}, + {FIELD_LITERAL(0x00192d7dd558d135,0x0027cd6a8323ffa7,0x00239f1a412dc1e7,0x0046b4b3be74fc5c,0x0020c47a2bef5bce,0x00aa17e48f43862b,0x00f7e26c96342e5f,0x0008011c530f39a9)}, + }}, {{ + {FIELD_LITERAL(0x00aad4ac569bf0f1,0x00a67adc90b27740,0x0048551369a5751a,0x0031252584a3306a,0x0084e15df770e6fc,0x00d7bba1c74b5805,0x00a80ef223af1012,0x0089c85ceb843a34)}, + {FIELD_LITERAL(0x00c4545be4a54004,0x0099e11f60357e6c,0x001f3936d19515a6,0x007793df84341a6e,0x0051061886717ffa,0x00e9b0a660b28f85,0x0044ea685892de0d,0x000257d2a1fda9d9)}, + {FIELD_LITERAL(0x007e8b01b24ac8a8,0x006cf3b0b5ca1337,0x00f1607d3e36a570,0x0039b7fab82991a1,0x00231777065840c5,0x00998e5afdd346f9,0x00b7dc3e64acc85f,0x00baacc748013ad6)}, + }}, {{ + {FIELD_LITERAL(0x008ea6a4177580bf,0x005fa1953e3f0378,0x005fe409ac74d614,0x00452327f477e047,0x00a4018507fb6073,0x007b6e71951caac8,0x0012b42ab8a6ce91,0x0080eca677294ab7)}, + {FIELD_LITERAL(0x00a53edc023ba69b,0x00c6afa83ddde2e8,0x00c3f638b307b14e,0x004a357a64414062,0x00e4d94d8b582dc9,0x001739caf71695b7,0x0012431b2ae28de1,0x003b6bc98682907c)}, + {FIELD_LITERAL(0x008a9a93be1f99d6,0x0079fa627cc699c8,0x00b0cfb134ba84c8,0x001c4b778249419a,0x00df4ab3d9c44f40,0x009f596e6c1a9e3c,0x001979c0df237316,0x00501e953a919b87)}, + }} +}; +const niels_t *curve448_wnaf_base = curve448_wnaf_base_table; diff --git a/deps/openssl/openssl/crypto/ec/curve448/curve448utils.h b/deps/openssl/openssl/crypto/ec/curve448/curve448utils.h new file mode 100644 index 0000000000..9bf837993c --- /dev/null +++ b/deps/openssl/openssl/crypto/ec/curve448/curve448utils.h @@ -0,0 +1,78 @@ +/* + * Copyright 2017-2018 The OpenSSL Project Authors. All Rights Reserved. + * Copyright 2015 Cryptography Research, Inc. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + * + * Originally written by Mike Hamburg + */ + +#ifndef HEADER_CURVE448UTILS_H +# define HEADER_CURVE448UTILS_H + +# include <openssl/e_os2.h> + +/* + * Internal word types. Somewhat tricky. This could be decided separately per + * platform. However, the structs do need to be all the same size and + * alignment on a given platform to support dynamic linking, since even if you + * header was built with eg arch_neon, you might end up linking a library built + * with arch_arm32. + */ +# ifndef C448_WORD_BITS +# if (defined(__SIZEOF_INT128__) && (__SIZEOF_INT128__ == 16)) \ + && !defined(__sparc__) +# define C448_WORD_BITS 64 /* The number of bits in a word */ +# else +# define C448_WORD_BITS 32 /* The number of bits in a word */ +# endif +# endif + +# if C448_WORD_BITS == 64 +/* Word size for internal computations */ +typedef uint64_t c448_word_t; +/* Signed word size for internal computations */ +typedef int64_t c448_sword_t; +/* "Boolean" type, will be set to all-zero or all-one (i.e. -1u) */ +typedef uint64_t c448_bool_t; +/* Double-word size for internal computations */ +typedef __uint128_t c448_dword_t; +/* Signed double-word size for internal computations */ +typedef __int128_t c448_dsword_t; +# elif C448_WORD_BITS == 32 +/* Word size for internal computations */ +typedef uint32_t c448_word_t; +/* Signed word size for internal computations */ +typedef int32_t c448_sword_t; +/* "Boolean" type, will be set to all-zero or all-one (i.e. -1u) */ +typedef uint32_t c448_bool_t; +/* Double-word size for internal computations */ +typedef uint64_t c448_dword_t; +/* Signed double-word size for internal computations */ +typedef int64_t c448_dsword_t; +# else +# error "Only supporting C448_WORD_BITS = 32 or 64 for now" +# endif + +/* C448_TRUE = -1 so that C448_TRUE & x = x */ +# define C448_TRUE (0 - (c448_bool_t)1) + +/* C448_FALSE = 0 so that C448_FALSE & x = 0 */ +# define C448_FALSE 0 + +/* Another boolean type used to indicate success or failure. */ +typedef enum { + C448_SUCCESS = -1, /**< The operation succeeded. */ + C448_FAILURE = 0 /**< The operation failed. */ +} c448_error_t; + +/* Return success if x is true */ +static ossl_inline c448_error_t c448_succeed_if(c448_bool_t x) +{ + return (c448_error_t) x; +} + +#endif /* __C448_COMMON_H__ */ diff --git a/deps/openssl/openssl/crypto/ec/curve448/ed448.h b/deps/openssl/openssl/crypto/ec/curve448/ed448.h new file mode 100644 index 0000000000..5fe939e8e1 --- /dev/null +++ b/deps/openssl/openssl/crypto/ec/curve448/ed448.h @@ -0,0 +1,195 @@ +/* + * Copyright 2017-2018 The OpenSSL Project Authors. All Rights Reserved. + * Copyright 2015-2016 Cryptography Research, Inc. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + * + * Originally written by Mike Hamburg + */ + +#ifndef HEADER_ED448_H +# define HEADER_ED448_H + +# include "point_448.h" + +/* Number of bytes in an EdDSA public key. */ +# define EDDSA_448_PUBLIC_BYTES 57 + +/* Number of bytes in an EdDSA private key. */ +# define EDDSA_448_PRIVATE_BYTES EDDSA_448_PUBLIC_BYTES + +/* Number of bytes in an EdDSA private key. */ +# define EDDSA_448_SIGNATURE_BYTES (EDDSA_448_PUBLIC_BYTES + \ + EDDSA_448_PRIVATE_BYTES) + +/* EdDSA encoding ratio. */ +# define C448_EDDSA_ENCODE_RATIO 4 + +/* EdDSA decoding ratio. */ +# define C448_EDDSA_DECODE_RATIO (4 / 4) + +/* + * EdDSA key generation. This function uses a different (non-Decaf) encoding. + * + * pubkey (out): The public key. + * privkey (in): The private key. + */ +c448_error_t c448_ed448_derive_public_key( + uint8_t pubkey [EDDSA_448_PUBLIC_BYTES], + const uint8_t privkey [EDDSA_448_PRIVATE_BYTES]); + +/* + * EdDSA signing. + * + * signature (out): The signature. + * privkey (in): The private key. + * pubkey (in): The public key. + * message (in): The message to sign. + * message_len (in): The length of the message. + * prehashed (in): Nonzero if the message is actually the hash of something + * you want to sign. + * context (in): A "context" for this signature of up to 255 bytes. + * context_len (in): Length of the context. + * + * For Ed25519, it is unsafe to use the same key for both prehashed and + * non-prehashed messages, at least without some very careful protocol-level + * disambiguation. For Ed448 it is safe. + */ +c448_error_t c448_ed448_sign( + uint8_t signature[EDDSA_448_SIGNATURE_BYTES], + const uint8_t privkey[EDDSA_448_PRIVATE_BYTES], + const uint8_t pubkey[EDDSA_448_PUBLIC_BYTES], + const uint8_t *message, size_t message_len, + uint8_t prehashed, const uint8_t *context, + size_t context_len); + +/* + * EdDSA signing with prehash. + * + * signature (out): The signature. + * privkey (in): The private key. + * pubkey (in): The public key. + * hash (in): The hash of the message. This object will not be modified by the + * call. + * context (in): A "context" for this signature of up to 255 bytes. Must be the + * same as what was used for the prehash. + * context_len (in): Length of the context. + * + * For Ed25519, it is unsafe to use the same key for both prehashed and + * non-prehashed messages, at least without some very careful protocol-level + * disambiguation. For Ed448 it is safe. + */ +c448_error_t c448_ed448_sign_prehash( + uint8_t signature[EDDSA_448_SIGNATURE_BYTES], + const uint8_t privkey[EDDSA_448_PRIVATE_BYTES], + const uint8_t pubkey[EDDSA_448_PUBLIC_BYTES], + const uint8_t hash[64], + const uint8_t *context, + size_t context_len); + +/* + * EdDSA signature verification. + * + * Uses the standard (i.e. less-strict) verification formula. + * + * signature (in): The signature. + * pubkey (in): The public key. + * message (in): The message to verify. + * message_len (in): The length of the message. + * prehashed (in): Nonzero if the message is actually the hash of something you + * want to verify. + * context (in): A "context" for this signature of up to 255 bytes. + * context_len (in): Length of the context. + * + * For Ed25519, it is unsafe to use the same key for both prehashed and + * non-prehashed messages, at least without some very careful protocol-level + * disambiguation. For Ed448 it is safe. + */ +c448_error_t c448_ed448_verify(const uint8_t + signature[EDDSA_448_SIGNATURE_BYTES], + const uint8_t + pubkey[EDDSA_448_PUBLIC_BYTES], + const uint8_t *message, size_t message_len, + uint8_t prehashed, const uint8_t *context, + uint8_t context_len); + +/* + * EdDSA signature verification. + * + * Uses the standard (i.e. less-strict) verification formula. + * + * signature (in): The signature. + * pubkey (in): The public key. + * hash (in): The hash of the message. This object will not be modified by the + * call. + * context (in): A "context" for this signature of up to 255 bytes. Must be the + * same as what was used for the prehash. + * context_len (in): Length of the context. + * + * For Ed25519, it is unsafe to use the same key for both prehashed and + * non-prehashed messages, at least without some very careful protocol-level + * disambiguation. For Ed448 it is safe. + */ +c448_error_t c448_ed448_verify_prehash( + const uint8_t signature[EDDSA_448_SIGNATURE_BYTES], + const uint8_t pubkey[EDDSA_448_PUBLIC_BYTES], + const uint8_t hash[64], + const uint8_t *context, + uint8_t context_len); + +/* + * EdDSA point encoding. Used internally, exposed externally. + * Multiplies by C448_EDDSA_ENCODE_RATIO first. + * + * The multiplication is required because the EdDSA encoding represents + * the cofactor information, but the Decaf encoding ignores it (which + * is the whole point). So if you decode from EdDSA and re-encode to + * EdDSA, the cofactor info must get cleared, because the intermediate + * representation doesn't track it. + * + * The way we handle this is to multiply by C448_EDDSA_DECODE_RATIO when + * decoding, and by C448_EDDSA_ENCODE_RATIO when encoding. The product of + * these ratios is always exactly the cofactor 4, so the cofactor ends up + * cleared one way or another. But exactly how that shakes out depends on the + * base points specified in RFC 8032. + * + * The upshot is that if you pass the Decaf/Ristretto base point to + * this function, you will get C448_EDDSA_ENCODE_RATIO times the + * EdDSA base point. + * + * enc (out): The encoded point. + * p (in): The point. + */ +void curve448_point_mul_by_ratio_and_encode_like_eddsa( + uint8_t enc [EDDSA_448_PUBLIC_BYTES], + const curve448_point_t p); + +/* + * EdDSA point decoding. Multiplies by C448_EDDSA_DECODE_RATIO, and + * ignores cofactor information. + * + * See notes on curve448_point_mul_by_ratio_and_encode_like_eddsa + * + * enc (out): The encoded point. + * p (in): The point. + */ +c448_error_t curve448_point_decode_like_eddsa_and_mul_by_ratio( + curve448_point_t p, + const uint8_t enc[EDDSA_448_PUBLIC_BYTES]); + +/* + * EdDSA to ECDH private key conversion + * Using the appropriate hash function, hash the EdDSA private key + * and keep only the lower bytes to get the ECDH private key + * + * x (out): The ECDH private key as in RFC7748 + * ed (in): The EdDSA private key + */ +c448_error_t c448_ed448_convert_private_key_to_x448( + uint8_t x[X448_PRIVATE_BYTES], + const uint8_t ed[EDDSA_448_PRIVATE_BYTES]); + +#endif /* HEADER_ED448_H */ diff --git a/deps/openssl/openssl/crypto/ec/curve448/eddsa.c b/deps/openssl/openssl/crypto/ec/curve448/eddsa.c new file mode 100644 index 0000000000..909413a535 --- /dev/null +++ b/deps/openssl/openssl/crypto/ec/curve448/eddsa.c @@ -0,0 +1,346 @@ +/* + * Copyright 2017-2018 The OpenSSL Project Authors. All Rights Reserved. + * Copyright 2015-2016 Cryptography Research, Inc. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + * + * Originally written by Mike Hamburg + */ +#include <string.h> +#include <openssl/crypto.h> +#include <openssl/evp.h> +#include "curve448_lcl.h" +#include "word.h" +#include "ed448.h" +#include "internal/numbers.h" + +#define COFACTOR 4 + +static c448_error_t oneshot_hash(uint8_t *out, size_t outlen, + const uint8_t *in, size_t inlen) +{ + EVP_MD_CTX *hashctx = EVP_MD_CTX_new(); + + if (hashctx == NULL) + return C448_FAILURE; + + if (!EVP_DigestInit_ex(hashctx, EVP_shake256(), NULL) + || !EVP_DigestUpdate(hashctx, in, inlen) + || !EVP_DigestFinalXOF(hashctx, out, outlen)) { + EVP_MD_CTX_free(hashctx); + return C448_FAILURE; + } + + EVP_MD_CTX_free(hashctx); + return C448_SUCCESS; +} + +static void clamp(uint8_t secret_scalar_ser[EDDSA_448_PRIVATE_BYTES]) +{ + secret_scalar_ser[0] &= -COFACTOR; + secret_scalar_ser[EDDSA_448_PRIVATE_BYTES - 1] = 0; + secret_scalar_ser[EDDSA_448_PRIVATE_BYTES - 2] |= 0x80; +} + +static c448_error_t hash_init_with_dom(EVP_MD_CTX *hashctx, uint8_t prehashed, + uint8_t for_prehash, + const uint8_t *context, + size_t context_len) +{ + const char *dom_s = "SigEd448"; + uint8_t dom[2]; + + if (context_len > UINT8_MAX) + return C448_FAILURE; + + dom[0] = (uint8_t)(2 - (prehashed == 0 ? 1 : 0) + - (for_prehash == 0 ? 1 : 0)); + dom[1] = (uint8_t)context_len; + + if (!EVP_DigestInit_ex(hashctx, EVP_shake256(), NULL) + || !EVP_DigestUpdate(hashctx, dom_s, strlen(dom_s)) + || !EVP_DigestUpdate(hashctx, dom, sizeof(dom)) + || !EVP_DigestUpdate(hashctx, context, context_len)) + return C448_FAILURE; + + return C448_SUCCESS; +} + +/* In this file because it uses the hash */ +c448_error_t c448_ed448_convert_private_key_to_x448( + uint8_t x[X448_PRIVATE_BYTES], + const uint8_t ed [EDDSA_448_PRIVATE_BYTES]) +{ + /* pass the private key through oneshot_hash function */ + /* and keep the first X448_PRIVATE_BYTES bytes */ + return oneshot_hash(x, X448_PRIVATE_BYTES, ed, + EDDSA_448_PRIVATE_BYTES); +} + +c448_error_t c448_ed448_derive_public_key( + uint8_t pubkey[EDDSA_448_PUBLIC_BYTES], + const uint8_t privkey[EDDSA_448_PRIVATE_BYTES]) +{ + /* only this much used for keygen */ + uint8_t secret_scalar_ser[EDDSA_448_PRIVATE_BYTES]; + curve448_scalar_t secret_scalar; + unsigned int c; + curve448_point_t p; + + if (!oneshot_hash(secret_scalar_ser, sizeof(secret_scalar_ser), privkey, + EDDSA_448_PRIVATE_BYTES)) + return C448_FAILURE; + + clamp(secret_scalar_ser); + + curve448_scalar_decode_long(secret_scalar, secret_scalar_ser, + sizeof(secret_scalar_ser)); + + /* + * Since we are going to mul_by_cofactor during encoding, divide by it + * here. However, the EdDSA base point is not the same as the decaf base + * point if the sigma isogeny is in use: the EdDSA base point is on + * Etwist_d/(1-d) and the decaf base point is on Etwist_d, and when + * converted it effectively picks up a factor of 2 from the isogenies. So + * we might start at 2 instead of 1. + */ + for (c = 1; c < C448_EDDSA_ENCODE_RATIO; c <<= 1) + curve448_scalar_halve(secret_scalar, secret_scalar); + + curve448_precomputed_scalarmul(p, curve448_precomputed_base, secret_scalar); + + curve448_point_mul_by_ratio_and_encode_like_eddsa(pubkey, p); + + /* Cleanup */ + curve448_scalar_destroy(secret_scalar); + curve448_point_destroy(p); + OPENSSL_cleanse(secret_scalar_ser, sizeof(secret_scalar_ser)); + + return C448_SUCCESS; +} + +c448_error_t c448_ed448_sign( + uint8_t signature[EDDSA_448_SIGNATURE_BYTES], + const uint8_t privkey[EDDSA_448_PRIVATE_BYTES], + const uint8_t pubkey[EDDSA_448_PUBLIC_BYTES], + const uint8_t *message, size_t message_len, + uint8_t prehashed, const uint8_t *context, + size_t context_len) +{ + curve448_scalar_t secret_scalar; + EVP_MD_CTX *hashctx = EVP_MD_CTX_new(); + c448_error_t ret = C448_FAILURE; + curve448_scalar_t nonce_scalar; + uint8_t nonce_point[EDDSA_448_PUBLIC_BYTES] = { 0 }; + unsigned int c; + curve448_scalar_t challenge_scalar; + + if (hashctx == NULL) + return C448_FAILURE; + + { + /* + * Schedule the secret key, First EDDSA_448_PRIVATE_BYTES is serialised + * secret scalar,next EDDSA_448_PRIVATE_BYTES bytes is the seed. + */ + uint8_t expanded[EDDSA_448_PRIVATE_BYTES * 2]; + + if (!oneshot_hash(expanded, sizeof(expanded), privkey, + EDDSA_448_PRIVATE_BYTES)) + goto err; + clamp(expanded); + curve448_scalar_decode_long(secret_scalar, expanded, + EDDSA_448_PRIVATE_BYTES); + + /* Hash to create the nonce */ + if (!hash_init_with_dom(hashctx, prehashed, 0, context, context_len) + || !EVP_DigestUpdate(hashctx, + expanded + EDDSA_448_PRIVATE_BYTES, + EDDSA_448_PRIVATE_BYTES) + || !EVP_DigestUpdate(hashctx, message, message_len)) { + OPENSSL_cleanse(expanded, sizeof(expanded)); + goto err; + } + OPENSSL_cleanse(expanded, sizeof(expanded)); + } + + /* Decode the nonce */ + { + uint8_t nonce[2 * EDDSA_448_PRIVATE_BYTES]; + + if (!EVP_DigestFinalXOF(hashctx, nonce, sizeof(nonce))) + goto err; + curve448_scalar_decode_long(nonce_scalar, nonce, sizeof(nonce)); + OPENSSL_cleanse(nonce, sizeof(nonce)); + } + + { + /* Scalarmul to create the nonce-point */ + curve448_scalar_t nonce_scalar_2; + curve448_point_t p; + + curve448_scalar_halve(nonce_scalar_2, nonce_scalar); + for (c = 2; c < C448_EDDSA_ENCODE_RATIO; c <<= 1) + curve448_scalar_halve(nonce_scalar_2, nonce_scalar_2); + + curve448_precomputed_scalarmul(p, curve448_precomputed_base, + nonce_scalar_2); + curve448_point_mul_by_ratio_and_encode_like_eddsa(nonce_point, p); + curve448_point_destroy(p); + curve448_scalar_destroy(nonce_scalar_2); + } + + { + uint8_t challenge[2 * EDDSA_448_PRIVATE_BYTES]; + + /* Compute the challenge */ + if (!hash_init_with_dom(hashctx, prehashed, 0, context, context_len) + || !EVP_DigestUpdate(hashctx, nonce_point, sizeof(nonce_point)) + || !EVP_DigestUpdate(hashctx, pubkey, EDDSA_448_PUBLIC_BYTES) + || !EVP_DigestUpdate(hashctx, message, message_len) + || !EVP_DigestFinalXOF(hashctx, challenge, sizeof(challenge))) + goto err; + + curve448_scalar_decode_long(challenge_scalar, challenge, + sizeof(challenge)); + OPENSSL_cleanse(challenge, sizeof(challenge)); + } + + curve448_scalar_mul(challenge_scalar, challenge_scalar, secret_scalar); + curve448_scalar_add(challenge_scalar, challenge_scalar, nonce_scalar); + + OPENSSL_cleanse(signature, EDDSA_448_SIGNATURE_BYTES); + memcpy(signature, nonce_point, sizeof(nonce_point)); + curve448_scalar_encode(&signature[EDDSA_448_PUBLIC_BYTES], + challenge_scalar); + + curve448_scalar_destroy(secret_scalar); + curve448_scalar_destroy(nonce_scalar); + curve448_scalar_destroy(challenge_scalar); + + ret = C448_SUCCESS; + err: + EVP_MD_CTX_free(hashctx); + return ret; +} + +c448_error_t c448_ed448_sign_prehash( + uint8_t signature[EDDSA_448_SIGNATURE_BYTES], + const uint8_t privkey[EDDSA_448_PRIVATE_BYTES], + const uint8_t pubkey[EDDSA_448_PUBLIC_BYTES], + const uint8_t hash[64], const uint8_t *context, + size_t context_len) +{ + return c448_ed448_sign(signature, privkey, pubkey, hash, 64, 1, context, + context_len); +} + +c448_error_t c448_ed448_verify( + const uint8_t signature[EDDSA_448_SIGNATURE_BYTES], + const uint8_t pubkey[EDDSA_448_PUBLIC_BYTES], + const uint8_t *message, size_t message_len, + uint8_t prehashed, const uint8_t *context, + uint8_t context_len) +{ + curve448_point_t pk_point, r_point; + c448_error_t error = + curve448_point_decode_like_eddsa_and_mul_by_ratio(pk_point, pubkey); + curve448_scalar_t challenge_scalar; + curve448_scalar_t response_scalar; + + if (C448_SUCCESS != error) + return error; + + error = + curve448_point_decode_like_eddsa_and_mul_by_ratio(r_point, signature); + if (C448_SUCCESS != error) + return error; + + { + /* Compute the challenge */ + EVP_MD_CTX *hashctx = EVP_MD_CTX_new(); + uint8_t challenge[2 * EDDSA_448_PRIVATE_BYTES]; + + if (hashctx == NULL + || !hash_init_with_dom(hashctx, prehashed, 0, context, + context_len) + || !EVP_DigestUpdate(hashctx, signature, EDDSA_448_PUBLIC_BYTES) + || !EVP_DigestUpdate(hashctx, pubkey, EDDSA_448_PUBLIC_BYTES) + || !EVP_DigestUpdate(hashctx, message, message_len) + || !EVP_DigestFinalXOF(hashctx, challenge, sizeof(challenge))) { + EVP_MD_CTX_free(hashctx); + return C448_FAILURE; + } + + EVP_MD_CTX_free(hashctx); + curve448_scalar_decode_long(challenge_scalar, challenge, + sizeof(challenge)); + OPENSSL_cleanse(challenge, sizeof(challenge)); + } + curve448_scalar_sub(challenge_scalar, curve448_scalar_zero, + challenge_scalar); + + curve448_scalar_decode_long(response_scalar, + &signature[EDDSA_448_PUBLIC_BYTES], + EDDSA_448_PRIVATE_BYTES); + + /* pk_point = -c(x(P)) + (cx + k)G = kG */ + curve448_base_double_scalarmul_non_secret(pk_point, + response_scalar, + pk_point, challenge_scalar); + return c448_succeed_if(curve448_point_eq(pk_point, r_point)); +} + +c448_error_t c448_ed448_verify_prehash( + const uint8_t signature[EDDSA_448_SIGNATURE_BYTES], + const uint8_t pubkey[EDDSA_448_PUBLIC_BYTES], + const uint8_t hash[64], const uint8_t *context, + uint8_t context_len) +{ + return c448_ed448_verify(signature, pubkey, hash, 64, 1, context, + context_len); +} + +int ED448_sign(uint8_t *out_sig, const uint8_t *message, size_t message_len, + const uint8_t public_key[57], const uint8_t private_key[57], + const uint8_t *context, size_t context_len) +{ + return c448_ed448_sign(out_sig, private_key, public_key, message, + message_len, 0, context, context_len) + == C448_SUCCESS; +} + +int ED448_verify(const uint8_t *message, size_t message_len, + const uint8_t signature[114], const uint8_t public_key[57], + const uint8_t *context, size_t context_len) +{ + return c448_ed448_verify(signature, public_key, message, message_len, 0, + context, (uint8_t)context_len) == C448_SUCCESS; +} + +int ED448ph_sign(uint8_t *out_sig, const uint8_t hash[64], + const uint8_t public_key[57], const uint8_t private_key[57], + const uint8_t *context, size_t context_len) +{ + return c448_ed448_sign_prehash(out_sig, private_key, public_key, hash, + context, context_len) == C448_SUCCESS; + +} + +int ED448ph_verify(const uint8_t hash[64], const uint8_t signature[114], + const uint8_t public_key[57], const uint8_t *context, + size_t context_len) +{ + return c448_ed448_verify_prehash(signature, public_key, hash, context, + (uint8_t)context_len) == C448_SUCCESS; +} + +int ED448_public_from_private(uint8_t out_public_key[57], + const uint8_t private_key[57]) +{ + return c448_ed448_derive_public_key(out_public_key, private_key) + == C448_SUCCESS; +} diff --git a/deps/openssl/openssl/crypto/ec/curve448/f_generic.c b/deps/openssl/openssl/crypto/ec/curve448/f_generic.c new file mode 100644 index 0000000000..ed8f36d868 --- /dev/null +++ b/deps/openssl/openssl/crypto/ec/curve448/f_generic.c @@ -0,0 +1,204 @@ +/* + * Copyright 2017-2018 The OpenSSL Project Authors. All Rights Reserved. + * Copyright 2015-2016 Cryptography Research, Inc. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + * + * Originally written by Mike Hamburg + */ +#include "field.h" + +static const gf MODULUS = { + FIELD_LITERAL(0xffffffffffffff, 0xffffffffffffff, 0xffffffffffffff, + 0xffffffffffffff, 0xfffffffffffffe, 0xffffffffffffff, + 0xffffffffffffff, 0xffffffffffffff) +}; + +/* Serialize to wire format. */ +void gf_serialize(uint8_t serial[SER_BYTES], const gf x, int with_hibit) +{ + unsigned int j = 0, fill = 0; + dword_t buffer = 0; + int i; + gf red; + + gf_copy(red, x); + gf_strong_reduce(red); + if (!with_hibit) + assert(gf_hibit(red) == 0); + + for (i = 0; i < (with_hibit ? X_SER_BYTES : SER_BYTES); i++) { + if (fill < 8 && j < NLIMBS) { + buffer |= ((dword_t) red->limb[LIMBPERM(j)]) << fill; + fill += LIMB_PLACE_VALUE(LIMBPERM(j)); + j++; + } + serial[i] = (uint8_t)buffer; + fill -= 8; + buffer >>= 8; + } +} + +/* Return high bit of x = low bit of 2x mod p */ +mask_t gf_hibit(const gf x) +{ + gf y; + + gf_add(y, x, x); + gf_strong_reduce(y); + return 0 - (y->limb[0] & 1); +} + +/* Return high bit of x = low bit of 2x mod p */ +mask_t gf_lobit(const gf x) +{ + gf y; + + gf_copy(y, x); + gf_strong_reduce(y); + return 0 - (y->limb[0] & 1); +} + +/* Deserialize from wire format; return -1 on success and 0 on failure. */ +mask_t gf_deserialize(gf x, const uint8_t serial[SER_BYTES], int with_hibit, + uint8_t hi_nmask) +{ + unsigned int j = 0, fill = 0; + dword_t buffer = 0; + dsword_t scarry = 0; + const unsigned nbytes = with_hibit ? X_SER_BYTES : SER_BYTES; + unsigned int i; + mask_t succ; + + for (i = 0; i < NLIMBS; i++) { + while (fill < LIMB_PLACE_VALUE(LIMBPERM(i)) && j < nbytes) { + uint8_t sj; + + sj = serial[j]; + if (j == nbytes - 1) + sj &= ~hi_nmask; + buffer |= ((dword_t) sj) << fill; + fill += 8; + j++; + } + x->limb[LIMBPERM(i)] = (word_t) + ((i < NLIMBS - 1) ? buffer & LIMB_MASK(LIMBPERM(i)) : buffer); + fill -= LIMB_PLACE_VALUE(LIMBPERM(i)); + buffer >>= LIMB_PLACE_VALUE(LIMBPERM(i)); + scarry = + (scarry + x->limb[LIMBPERM(i)] - + MODULUS->limb[LIMBPERM(i)]) >> (8 * sizeof(word_t)); + } + succ = with_hibit ? 0 - (mask_t) 1 : ~gf_hibit(x); + return succ & word_is_zero((word_t)buffer) & ~word_is_zero((word_t)scarry); +} + +/* Reduce to canonical form. */ +void gf_strong_reduce(gf a) +{ + dsword_t scarry; + word_t scarry_0; + dword_t carry = 0; + unsigned int i; + + /* first, clear high */ + gf_weak_reduce(a); /* Determined to have negligible perf impact. */ + + /* now the total is less than 2p */ + + /* compute total_value - p. No need to reduce mod p. */ + scarry = 0; + for (i = 0; i < NLIMBS; i++) { + scarry = scarry + a->limb[LIMBPERM(i)] - MODULUS->limb[LIMBPERM(i)]; + a->limb[LIMBPERM(i)] = scarry & LIMB_MASK(LIMBPERM(i)); + scarry >>= LIMB_PLACE_VALUE(LIMBPERM(i)); + } + + /* + * uncommon case: it was >= p, so now scarry = 0 and this = x common case: + * it was < p, so now scarry = -1 and this = x - p + 2^255 so let's add + * back in p. will carry back off the top for 2^255. + */ + assert(scarry == 0 || scarry == -1); + + scarry_0 = (word_t)scarry; + + /* add it back */ + for (i = 0; i < NLIMBS; i++) { + carry = + carry + a->limb[LIMBPERM(i)] + + (scarry_0 & MODULUS->limb[LIMBPERM(i)]); + a->limb[LIMBPERM(i)] = carry & LIMB_MASK(LIMBPERM(i)); + carry >>= LIMB_PLACE_VALUE(LIMBPERM(i)); + } + + assert(carry < 2 && ((word_t)carry + scarry_0) == 0); +} + +/* Subtract two gf elements d=a-b */ +void gf_sub(gf d, const gf a, const gf b) +{ + gf_sub_RAW(d, a, b); + gf_bias(d, 2); + gf_weak_reduce(d); +} + +/* Add two field elements d = a+b */ +void gf_add(gf d, const gf a, const gf b) +{ + gf_add_RAW(d, a, b); + gf_weak_reduce(d); +} + +/* Compare a==b */ +mask_t gf_eq(const gf a, const gf b) +{ + gf c; + mask_t ret = 0; + unsigned int i; + + gf_sub(c, a, b); + gf_strong_reduce(c); + + for (i = 0; i < NLIMBS; i++) + ret |= c->limb[LIMBPERM(i)]; + + return word_is_zero(ret); +} + +mask_t gf_isr(gf a, const gf x) +{ + gf L0, L1, L2; + + gf_sqr(L1, x); + gf_mul(L2, x, L1); + gf_sqr(L1, L2); + gf_mul(L2, x, L1); + gf_sqrn(L1, L2, 3); + gf_mul(L0, L2, L1); + gf_sqrn(L1, L0, 3); + gf_mul(L0, L2, L1); + gf_sqrn(L2, L0, 9); + gf_mul(L1, L0, L2); + gf_sqr(L0, L1); + gf_mul(L2, x, L0); + gf_sqrn(L0, L2, 18); + gf_mul(L2, L1, L0); + gf_sqrn(L0, L2, 37); + gf_mul(L1, L2, L0); + gf_sqrn(L0, L1, 37); + gf_mul(L1, L2, L0); + gf_sqrn(L0, L1, 111); + gf_mul(L2, L1, L0); + gf_sqr(L0, L2); + gf_mul(L1, x, L0); + gf_sqrn(L0, L1, 223); + gf_mul(L1, L2, L0); + gf_sqr(L2, L1); + gf_mul(L0, L2, x); + gf_copy(a, L1); + return gf_eq(L0, ONE); +} diff --git a/deps/openssl/openssl/crypto/ec/curve448/field.h b/deps/openssl/openssl/crypto/ec/curve448/field.h new file mode 100644 index 0000000000..d96d4c023d --- /dev/null +++ b/deps/openssl/openssl/crypto/ec/curve448/field.h @@ -0,0 +1,168 @@ +/* + * Copyright 2017-2018 The OpenSSL Project Authors. All Rights Reserved. + * Copyright 2014 Cryptography Research, Inc. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + * + * Originally written by Mike Hamburg + */ + +#ifndef HEADER_FIELD_H +# define HEADER_FIELD_H + +# include "internal/constant_time_locl.h" +# include <string.h> +# include <assert.h> +# include "word.h" + +# define NLIMBS (64/sizeof(word_t)) +# define X_SER_BYTES 56 +# define SER_BYTES 56 + +# if defined(__GNUC__) || defined(__clang__) +# define INLINE_UNUSED __inline__ __attribute__((__unused__,__always_inline__)) +# define RESTRICT __restrict__ +# define ALIGNED __attribute__((__aligned__(16))) +# else +# define INLINE_UNUSED ossl_inline +# define RESTRICT +# define ALIGNED +# endif + +typedef struct gf_s { + word_t limb[NLIMBS]; +} ALIGNED gf_s, gf[1]; + +/* RFC 7748 support */ +# define X_PUBLIC_BYTES X_SER_BYTES +# define X_PRIVATE_BYTES X_PUBLIC_BYTES +# define X_PRIVATE_BITS 448 + +static INLINE_UNUSED void gf_copy(gf out, const gf a) +{ + *out = *a; +} + +static INLINE_UNUSED void gf_add_RAW(gf out, const gf a, const gf b); +static INLINE_UNUSED void gf_sub_RAW(gf out, const gf a, const gf b); +static INLINE_UNUSED void gf_bias(gf inout, int amount); +static INLINE_UNUSED void gf_weak_reduce(gf inout); + +void gf_strong_reduce(gf inout); +void gf_add(gf out, const gf a, const gf b); +void gf_sub(gf out, const gf a, const gf b); +void gf_mul(gf_s * RESTRICT out, const gf a, const gf b); +void gf_mulw_unsigned(gf_s * RESTRICT out, const gf a, uint32_t b); +void gf_sqr(gf_s * RESTRICT out, const gf a); +mask_t gf_isr(gf a, const gf x); /** a^2 x = 1, QNR, or 0 if x=0. Return true if successful */ +mask_t gf_eq(const gf x, const gf y); +mask_t gf_lobit(const gf x); +mask_t gf_hibit(const gf x); + +void gf_serialize(uint8_t *serial, const gf x, int with_highbit); +mask_t gf_deserialize(gf x, const uint8_t serial[SER_BYTES], int with_hibit, + uint8_t hi_nmask); + +# include "f_impl.h" /* Bring in the inline implementations */ + +# define LIMBPERM(i) (i) +# define LIMB_MASK(i) (((1)<<LIMB_PLACE_VALUE(i))-1) + +static const gf ZERO = {{{0}}}, ONE = {{{1}}}; + +/* Square x, n times. */ +static ossl_inline void gf_sqrn(gf_s * RESTRICT y, const gf x, int n) +{ + gf tmp; + + assert(n > 0); + if (n & 1) { + gf_sqr(y, x); + n--; + } else { + gf_sqr(tmp, x); + gf_sqr(y, tmp); + n -= 2; + } + for (; n; n -= 2) { + gf_sqr(tmp, y); + gf_sqr(y, tmp); + } +} + +# define gf_add_nr gf_add_RAW + +/* Subtract mod p. Bias by 2 and don't reduce */ +static ossl_inline void gf_sub_nr(gf c, const gf a, const gf b) +{ + gf_sub_RAW(c, a, b); + gf_bias(c, 2); + if (GF_HEADROOM < 3) + gf_weak_reduce(c); +} + +/* Subtract mod p. Bias by amt but don't reduce. */ +static ossl_inline void gf_subx_nr(gf c, const gf a, const gf b, int amt) +{ + gf_sub_RAW(c, a, b); + gf_bias(c, amt); + if (GF_HEADROOM < amt + 1) + gf_weak_reduce(c); +} + +/* Mul by signed int. Not constant-time WRT the sign of that int. */ +static ossl_inline void gf_mulw(gf c, const gf a, int32_t w) +{ + if (w > 0) { + gf_mulw_unsigned(c, a, w); + } else { + gf_mulw_unsigned(c, a, -w); + gf_sub(c, ZERO, c); + } +} + +/* Constant time, x = is_z ? z : y */ +static ossl_inline void gf_cond_sel(gf x, const gf y, const gf z, mask_t is_z) +{ + size_t i; + + for (i = 0; i < NLIMBS; i++) { +#if ARCH_WORD_BITS == 32 + x[0].limb[i] = constant_time_select_32(is_z, z[0].limb[i], + y[0].limb[i]); +#else + /* Must be 64 bit */ + x[0].limb[i] = constant_time_select_64(is_z, z[0].limb[i], + y[0].limb[i]); +#endif + } +} + +/* Constant time, if (neg) x=-x; */ +static ossl_inline void gf_cond_neg(gf x, mask_t neg) +{ + gf y; + + gf_sub(y, ZERO, x); + gf_cond_sel(x, x, y, neg); +} + +/* Constant time, if (swap) (x,y) = (y,x); */ +static ossl_inline void gf_cond_swap(gf x, gf_s * RESTRICT y, mask_t swap) +{ + size_t i; + + for (i = 0; i < NLIMBS; i++) { +#if ARCH_WORD_BITS == 32 + constant_time_cond_swap_32(swap, &(x[0].limb[i]), &(y->limb[i])); +#else + /* Must be 64 bit */ + constant_time_cond_swap_64(swap, &(x[0].limb[i]), &(y->limb[i])); +#endif + } +} + +#endif /* HEADER_FIELD_H */ diff --git a/deps/openssl/openssl/crypto/ec/curve448/point_448.h b/deps/openssl/openssl/crypto/ec/curve448/point_448.h new file mode 100644 index 0000000000..0ef3b8714e --- /dev/null +++ b/deps/openssl/openssl/crypto/ec/curve448/point_448.h @@ -0,0 +1,301 @@ +/* + * Copyright 2017-2018 The OpenSSL Project Authors. All Rights Reserved. + * Copyright 2015-2016 Cryptography Research, Inc. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + * + * Originally written by Mike Hamburg + */ + +#ifndef HEADER_POINT_448_H +# define HEADER_POINT_448_H + +# include "curve448utils.h" +# include "field.h" + +/* Comb config: number of combs, n, t, s. */ +#define COMBS_N 5 +#define COMBS_T 5 +#define COMBS_S 18 + +/* Projective Niels coordinates */ +typedef struct { + gf a, b, c; +} niels_s, niels_t[1]; +typedef struct { + niels_t n; + gf z; +} pniels_t[1]; + +/* Precomputed base */ +struct curve448_precomputed_s { + niels_t table[COMBS_N << (COMBS_T - 1)]; +}; + +# define C448_SCALAR_LIMBS ((446-1)/C448_WORD_BITS+1) + +/* The number of bits in a scalar */ +# define C448_SCALAR_BITS 446 + +/* Number of bytes in a serialized scalar. */ +# define C448_SCALAR_BYTES 56 + +/* X448 encoding ratio. */ +# define X448_ENCODE_RATIO 2 + +/* Number of bytes in an x448 public key */ +# define X448_PUBLIC_BYTES 56 + +/* Number of bytes in an x448 private key */ +# define X448_PRIVATE_BYTES 56 + +/* Twisted Edwards extended homogeneous coordinates */ +typedef struct curve448_point_s { + gf x, y, z, t; +} curve448_point_t[1]; + +/* Precomputed table based on a point. Can be trivial implementation. */ +struct curve448_precomputed_s; + +/* Precomputed table based on a point. Can be trivial implementation. */ +typedef struct curve448_precomputed_s curve448_precomputed_s; + +/* Scalar is stored packed, because we don't need the speed. */ +typedef struct curve448_scalar_s { + c448_word_t limb[C448_SCALAR_LIMBS]; +} curve448_scalar_t[1]; + +/* A scalar equal to 1. */ +extern const curve448_scalar_t curve448_scalar_one; + +/* A scalar equal to 0. */ +extern const curve448_scalar_t curve448_scalar_zero; + +/* The identity point on the curve. */ +extern const curve448_point_t curve448_point_identity; + +/* Precomputed table for the base point on the curve. */ +extern const struct curve448_precomputed_s *curve448_precomputed_base; +extern const niels_t *curve448_wnaf_base; + +/* + * Read a scalar from wire format or from bytes. + * + * ser (in): Serialized form of a scalar. + * out (out): Deserialized form. + * + * Returns: + * C448_SUCCESS: The scalar was correctly encoded. + * C448_FAILURE: The scalar was greater than the modulus, and has been reduced + * modulo that modulus. + */ +c448_error_t curve448_scalar_decode(curve448_scalar_t out, + const unsigned char ser[C448_SCALAR_BYTES]); + +/* + * Read a scalar from wire format or from bytes. Reduces mod scalar prime. + * + * ser (in): Serialized form of a scalar. + * ser_len (in): Length of serialized form. + * out (out): Deserialized form. + */ +void curve448_scalar_decode_long(curve448_scalar_t out, + const unsigned char *ser, size_t ser_len); + +/* + * Serialize a scalar to wire format. + * + * ser (out): Serialized form of a scalar. + * s (in): Deserialized scalar. + */ +void curve448_scalar_encode(unsigned char ser[C448_SCALAR_BYTES], + const curve448_scalar_t s); + +/* + * Add two scalars. |a|, |b| and |out| may alias each other. + * + * a (in): One scalar. + * b (in): Another scalar. + * out (out): a+b. + */ +void curve448_scalar_add(curve448_scalar_t out, + const curve448_scalar_t a, const curve448_scalar_t b); + +/* + * Subtract two scalars. |a|, |b| and |out| may alias each other. + * a (in): One scalar. + * b (in): Another scalar. + * out (out): a-b. + */ +void curve448_scalar_sub(curve448_scalar_t out, + const curve448_scalar_t a, const curve448_scalar_t b); + +/* + * Multiply two scalars. |a|, |b| and |out| may alias each other. + * + * a (in): One scalar. + * b (in): Another scalar. + * out (out): a*b. + */ +void curve448_scalar_mul(curve448_scalar_t out, + const curve448_scalar_t a, const curve448_scalar_t b); + +/* +* Halve a scalar. |a| and |out| may alias each other. +* +* a (in): A scalar. +* out (out): a/2. +*/ +void curve448_scalar_halve(curve448_scalar_t out, const curve448_scalar_t a); + +/* + * Copy a scalar. The scalars may alias each other, in which case this + * function does nothing. + * + * a (in): A scalar. + * out (out): Will become a copy of a. + */ +static ossl_inline void curve448_scalar_copy(curve448_scalar_t out, + const curve448_scalar_t a) +{ + *out = *a; +} + +/* + * Copy a point. The input and output may alias, in which case this function + * does nothing. + * + * a (out): A copy of the point. + * b (in): Any point. + */ +static ossl_inline void curve448_point_copy(curve448_point_t a, + const curve448_point_t b) +{ + *a = *b; +} + +/* + * Test whether two points are equal. If yes, return C448_TRUE, else return + * C448_FALSE. + * + * a (in): A point. + * b (in): Another point. + * + * Returns: + * C448_TRUE: The points are equal. + * C448_FALSE: The points are not equal. + */ +__owur c448_bool_t curve448_point_eq(const curve448_point_t a, + const curve448_point_t b); + +/* + * Double a point. Equivalent to curve448_point_add(two_a,a,a), but potentially + * faster. + * + * two_a (out): The sum a+a. + * a (in): A point. + */ +void curve448_point_double(curve448_point_t two_a, const curve448_point_t a); + +/* + * RFC 7748 Diffie-Hellman scalarmul. This function uses a different + * (non-Decaf) encoding. + * + * out (out): The scaled point base*scalar + * base (in): The point to be scaled. + * scalar (in): The scalar to multiply by. + * + * Returns: + * C448_SUCCESS: The scalarmul succeeded. + * C448_FAILURE: The scalarmul didn't succeed, because the base point is in a + * small subgroup. + */ +__owur c448_error_t x448_int(uint8_t out[X448_PUBLIC_BYTES], + const uint8_t base[X448_PUBLIC_BYTES], + const uint8_t scalar[X448_PRIVATE_BYTES]); + +/* + * Multiply a point by X448_ENCODE_RATIO, then encode it like RFC 7748. + * + * This function is mainly used internally, but is exported in case + * it will be useful. + * + * The ratio is necessary because the internal representation doesn't + * track the cofactor information, so on output we must clear the cofactor. + * This would multiply by the cofactor, but in fact internally points are always + * even, so it multiplies by half the cofactor instead. + * + * As it happens, this aligns with the base point definitions; that is, + * if you pass the Decaf/Ristretto base point to this function, the result + * will be X448_ENCODE_RATIO times the X448 + * base point. + * + * out (out): The scaled and encoded point. + * p (in): The point to be scaled and encoded. + */ +void curve448_point_mul_by_ratio_and_encode_like_x448( + uint8_t out[X448_PUBLIC_BYTES], + const curve448_point_t p); + +/* + * RFC 7748 Diffie-Hellman base point scalarmul. This function uses a different + * (non-Decaf) encoding. + * + * out (out): The scaled point base*scalar + * scalar (in): The scalar to multiply by. + */ +void x448_derive_public_key(uint8_t out[X448_PUBLIC_BYTES], + const uint8_t scalar[X448_PRIVATE_BYTES]); + +/* + * Multiply a precomputed base point by a scalar: out = scalar*base. + * + * scaled (out): The scaled point base*scalar + * base (in): The point to be scaled. + * scalar (in): The scalar to multiply by. + */ +void curve448_precomputed_scalarmul(curve448_point_t scaled, + const curve448_precomputed_s * base, + const curve448_scalar_t scalar); + +/* + * Multiply two base points by two scalars: + * combo = scalar1*curve448_point_base + scalar2*base2. + * + * Otherwise equivalent to curve448_point_double_scalarmul, but may be + * faster at the expense of being variable time. + * + * combo (out): The linear combination scalar1*base + scalar2*base2. + * scalar1 (in): A first scalar to multiply by. + * base2 (in): A second point to be scaled. + * scalar2 (in) A second scalar to multiply by. + * + * Warning: This function takes variable time, and may leak the scalars used. + * It is designed for signature verification. + */ +void curve448_base_double_scalarmul_non_secret(curve448_point_t combo, + const curve448_scalar_t scalar1, + const curve448_point_t base2, + const curve448_scalar_t scalar2); + +/* + * Test that a point is valid, for debugging purposes. + * + * to_test (in): The point to test. + * + * Returns: + * C448_TRUE The point is valid. + * C448_FALSE The point is invalid. + */ +__owur c448_bool_t curve448_point_valid(const curve448_point_t to_test); + +/* Overwrite scalar with zeros. */ +void curve448_scalar_destroy(curve448_scalar_t scalar); + +/* Overwrite point with zeros. */ +void curve448_point_destroy(curve448_point_t point); + +#endif /* HEADER_POINT_448_H */ diff --git a/deps/openssl/openssl/crypto/ec/curve448/scalar.c b/deps/openssl/openssl/crypto/ec/curve448/scalar.c new file mode 100644 index 0000000000..b5702c0255 --- /dev/null +++ b/deps/openssl/openssl/crypto/ec/curve448/scalar.c @@ -0,0 +1,235 @@ +/* + * Copyright 2017-2018 The OpenSSL Project Authors. All Rights Reserved. + * Copyright 2015-2016 Cryptography Research, Inc. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + * + * Originally written by Mike Hamburg + */ +#include <openssl/crypto.h> + +#include "word.h" +#include "point_448.h" + +static const c448_word_t MONTGOMERY_FACTOR = (c448_word_t) 0x3bd440fae918bc5; +static const curve448_scalar_t sc_p = { + { + { + SC_LIMB(0x2378c292ab5844f3), SC_LIMB(0x216cc2728dc58f55), + SC_LIMB(0xc44edb49aed63690), SC_LIMB(0xffffffff7cca23e9), + SC_LIMB(0xffffffffffffffff), SC_LIMB(0xffffffffffffffff), + SC_LIMB(0x3fffffffffffffff) + } + } +}, sc_r2 = { + { + { + + SC_LIMB(0xe3539257049b9b60), SC_LIMB(0x7af32c4bc1b195d9), + SC_LIMB(0x0d66de2388ea1859), SC_LIMB(0xae17cf725ee4d838), + SC_LIMB(0x1a9cc14ba3c47c44), SC_LIMB(0x2052bcb7e4d070af), + SC_LIMB(0x3402a939f823b729) + } + } +}; + +#define WBITS C448_WORD_BITS /* NB this may be different from ARCH_WORD_BITS */ + +const curve448_scalar_t curve448_scalar_one = {{{1}}}; +const curve448_scalar_t curve448_scalar_zero = {{{0}}}; + +/* + * {extra,accum} - sub +? p + * Must have extra <= 1 + */ +static void sc_subx(curve448_scalar_t out, + const c448_word_t accum[C448_SCALAR_LIMBS], + const curve448_scalar_t sub, + const curve448_scalar_t p, c448_word_t extra) +{ + c448_dsword_t chain = 0; + unsigned int i; + c448_word_t borrow; + + for (i = 0; i < C448_SCALAR_LIMBS; i++) { + chain = (chain + accum[i]) - sub->limb[i]; + out->limb[i] = (c448_word_t)chain; + chain >>= WBITS; + } + borrow = (c448_word_t)chain + extra; /* = 0 or -1 */ + + chain = 0; + for (i = 0; i < C448_SCALAR_LIMBS; i++) { + chain = (chain + out->limb[i]) + (p->limb[i] & borrow); + out->limb[i] = (c448_word_t)chain; + chain >>= WBITS; + } +} + +static void sc_montmul(curve448_scalar_t out, const curve448_scalar_t a, + const curve448_scalar_t b) +{ + unsigned int i, j; + c448_word_t accum[C448_SCALAR_LIMBS + 1] = { 0 }; + c448_word_t hi_carry = 0; + + for (i = 0; i < C448_SCALAR_LIMBS; i++) { + c448_word_t mand = a->limb[i]; + const c448_word_t *mier = b->limb; + + c448_dword_t chain = 0; + for (j = 0; j < C448_SCALAR_LIMBS; j++) { + chain += ((c448_dword_t) mand) * mier[j] + accum[j]; + accum[j] = (c448_word_t)chain; + chain >>= WBITS; + } + accum[j] = (c448_word_t)chain; + + mand = accum[0] * MONTGOMERY_FACTOR; + chain = 0; + mier = sc_p->limb; + for (j = 0; j < C448_SCALAR_LIMBS; j++) { + chain += (c448_dword_t) mand *mier[j] + accum[j]; + if (j) + accum[j - 1] = (c448_word_t)chain; + chain >>= WBITS; + } + chain += accum[j]; + chain += hi_carry; + accum[j - 1] = (c448_word_t)chain; + hi_carry = chain >> WBITS; + } + + sc_subx(out, accum, sc_p, sc_p, hi_carry); +} + +void curve448_scalar_mul(curve448_scalar_t out, const curve448_scalar_t a, + const curve448_scalar_t b) +{ + sc_montmul(out, a, b); + sc_montmul(out, out, sc_r2); +} + +void curve448_scalar_sub(curve448_scalar_t out, const curve448_scalar_t a, + const curve448_scalar_t b) +{ + sc_subx(out, a->limb, b, sc_p, 0); +} + +void curve448_scalar_add(curve448_scalar_t out, const curve448_scalar_t a, + const curve448_scalar_t b) +{ + c448_dword_t chain = 0; + unsigned int i; + + for (i = 0; i < C448_SCALAR_LIMBS; i++) { + chain = (chain + a->limb[i]) + b->limb[i]; + out->limb[i] = (c448_word_t)chain; + chain >>= WBITS; + } + sc_subx(out, out->limb, sc_p, sc_p, (c448_word_t)chain); +} + +static ossl_inline void scalar_decode_short(curve448_scalar_t s, + const unsigned char *ser, + size_t nbytes) +{ + size_t i, j, k = 0; + + for (i = 0; i < C448_SCALAR_LIMBS; i++) { + c448_word_t out = 0; + + for (j = 0; j < sizeof(c448_word_t) && k < nbytes; j++, k++) + out |= ((c448_word_t) ser[k]) << (8 * j); + s->limb[i] = out; + } +} + +c448_error_t curve448_scalar_decode( + curve448_scalar_t s, + const unsigned char ser[C448_SCALAR_BYTES]) +{ + unsigned int i; + c448_dsword_t accum = 0; + + scalar_decode_short(s, ser, C448_SCALAR_BYTES); + for (i = 0; i < C448_SCALAR_LIMBS; i++) + accum = (accum + s->limb[i] - sc_p->limb[i]) >> WBITS; + /* Here accum == 0 or -1 */ + + curve448_scalar_mul(s, s, curve448_scalar_one); /* ham-handed reduce */ + + return c448_succeed_if(~word_is_zero((uint32_t)accum)); +} + +void curve448_scalar_destroy(curve448_scalar_t scalar) +{ + OPENSSL_cleanse(scalar, sizeof(curve448_scalar_t)); +} + +void curve448_scalar_decode_long(curve448_scalar_t s, + const unsigned char *ser, size_t ser_len) +{ + size_t i; + curve448_scalar_t t1, t2; + + if (ser_len == 0) { + curve448_scalar_copy(s, curve448_scalar_zero); + return; + } + + i = ser_len - (ser_len % C448_SCALAR_BYTES); + if (i == ser_len) + i -= C448_SCALAR_BYTES; + + scalar_decode_short(t1, &ser[i], ser_len - i); + + if (ser_len == sizeof(curve448_scalar_t)) { + assert(i == 0); + /* ham-handed reduce */ + curve448_scalar_mul(s, t1, curve448_scalar_one); + curve448_scalar_destroy(t1); + return; + } + + while (i) { + i -= C448_SCALAR_BYTES; + sc_montmul(t1, t1, sc_r2); + (void)curve448_scalar_decode(t2, ser + i); + curve448_scalar_add(t1, t1, t2); + } + + curve448_scalar_copy(s, t1); + curve448_scalar_destroy(t1); + curve448_scalar_destroy(t2); +} + +void curve448_scalar_encode(unsigned char ser[C448_SCALAR_BYTES], + const curve448_scalar_t s) +{ + unsigned int i, j, k = 0; + + for (i = 0; i < C448_SCALAR_LIMBS; i++) { + for (j = 0; j < sizeof(c448_word_t); j++, k++) + ser[k] = s->limb[i] >> (8 * j); + } +} + +void curve448_scalar_halve(curve448_scalar_t out, const curve448_scalar_t a) +{ + c448_word_t mask = 0 - (a->limb[0] & 1); + c448_dword_t chain = 0; + unsigned int i; + + for (i = 0; i < C448_SCALAR_LIMBS; i++) { + chain = (chain + a->limb[i]) + (sc_p->limb[i] & mask); + out->limb[i] = (c448_word_t)chain; + chain >>= C448_WORD_BITS; + } + for (i = 0; i < C448_SCALAR_LIMBS - 1; i++) + out->limb[i] = out->limb[i] >> 1 | out->limb[i + 1] << (WBITS - 1); + out->limb[i] = out->limb[i] >> 1 | (c448_word_t)(chain << (WBITS - 1)); +} diff --git a/deps/openssl/openssl/crypto/ec/curve448/word.h b/deps/openssl/openssl/crypto/ec/curve448/word.h new file mode 100644 index 0000000000..a48b9e053a --- /dev/null +++ b/deps/openssl/openssl/crypto/ec/curve448/word.h @@ -0,0 +1,81 @@ +/* + * Copyright 2017-2018 The OpenSSL Project Authors. All Rights Reserved. + * Copyright 2014 Cryptography Research, Inc. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + * + * Originally written by Mike Hamburg + */ + +#ifndef HEADER_WORD_H +# define HEADER_WORD_H + +# include <string.h> +# include <assert.h> +# include <stdlib.h> +# include <openssl/e_os2.h> +# include "arch_intrinsics.h" +# include "curve448utils.h" + +# if (ARCH_WORD_BITS == 64) +typedef uint64_t word_t, mask_t; +typedef __uint128_t dword_t; +typedef int32_t hsword_t; +typedef int64_t sword_t; +typedef __int128_t dsword_t; +# elif (ARCH_WORD_BITS == 32) +typedef uint32_t word_t, mask_t; +typedef uint64_t dword_t; +typedef int16_t hsword_t; +typedef int32_t sword_t; +typedef int64_t dsword_t; +# else +# error "For now, we only support 32- and 64-bit architectures." +# endif + +/* + * Scalar limbs are keyed off of the API word size instead of the arch word + * size. + */ +# if C448_WORD_BITS == 64 +# define SC_LIMB(x) (x) +# elif C448_WORD_BITS == 32 +# define SC_LIMB(x) ((uint32_t)(x)),((x) >> 32) +# else +# error "For now we only support 32- and 64-bit architectures." +# endif + +/* + * The plan on booleans: The external interface uses c448_bool_t, but this + * might be a different size than our particular arch's word_t (and thus + * mask_t). Also, the caller isn't guaranteed to pass it as nonzero. So + * bool_to_mask converts word sizes and checks nonzero. On the flip side, + * mask_t is always -1 or 0, but it might be a different size than + * c448_bool_t. On the third hand, we have success vs boolean types, but + * that's handled in common.h: it converts between c448_bool_t and + * c448_error_t. + */ +static ossl_inline c448_bool_t mask_to_bool(mask_t m) +{ + return (c448_sword_t)(sword_t)m; +} + +static ossl_inline mask_t bool_to_mask(c448_bool_t m) +{ + /* On most arches this will be optimized to a simple cast. */ + mask_t ret = 0; + unsigned int i; + unsigned int limit = sizeof(c448_bool_t) / sizeof(mask_t); + + if (limit < 1) + limit = 1; + for (i = 0; i < limit; i++) + ret |= ~word_is_zero(m >> (i * 8 * sizeof(word_t))); + + return ret; +} + +#endif /* HEADER_WORD_H */ |