| /* |
| * Copyright 2017-2022 The OpenSSL Project Authors. All Rights Reserved. |
| * Copyright 2015-2016 Cryptography Research, Inc. |
| * |
| * Licensed under the Apache License 2.0 (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 "crypto/ecx.h" |
| #include "curve448_local.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(0xc873d6d54a7bb0cfULL), SC_LIMB(0xe933d8d723a70aadULL), |
| SC_LIMB(0xbb124b65129c96fdULL), SC_LIMB(0x00000008335dc163ULL) |
| } |
| } |
| }; |
| |
| #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 ossl_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 ossl_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 |
| ossl_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 |
| ossl_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 |
| ossl_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; |
| |
| ossl_curve448_scalar_add(scalar1x, scalar, precomputed_scalarmul_adjustment); |
| ossl_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 |
| ossl_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)); |
| ossl_curve448_point_destroy(q); |
| } |
| |
| c448_error_t |
| ossl_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(ossl_curve448_point_valid(p) || ~succ); |
| |
| return c448_succeed_if(mask_to_bool(succ)); |
| } |
| |
| c448_error_t |
| ossl_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 |
| ossl_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); |
| ossl_curve448_point_destroy(q); |
| } |
| |
| void ossl_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); |
| |
| ossl_curve448_scalar_decode_long(the_scalar, scalar2, sizeof(scalar2)); |
| |
| /* Compensate for the encoding ratio */ |
| for (i = 1; i < X448_ENCODE_RATIO; i <<= 1) |
| ossl_curve448_scalar_halve(the_scalar, the_scalar); |
| |
| ossl_curve448_precomputed_scalarmul(p, ossl_curve448_precomputed_base, |
| the_scalar); |
| ossl_curve448_point_mul_by_ratio_and_encode_like_x448(out, p); |
| ossl_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)); |
| /* |
| * Coverity gets confused by the value of pos, thinking it might be |
| * 32. This would require current & 0xFFFF to be zero which isn't |
| * possible. Suppress this false positive, since adding a check |
| * isn't desirable. |
| */ |
| /* coverity[overflow_before_widen] */ |
| 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; |
| |
| ossl_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); |
| } |
| |
| ossl_curve448_point_destroy(tmp); |
| OPENSSL_cleanse(twop, sizeof(twop)); |
| } |
| |
| void |
| ossl_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, ossl_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, |
| ossl_curve448_wnaf_base[control_pre[0].addend >> 1], |
| i); |
| contv++; |
| contp++; |
| } else { |
| i = control_pre[0].power; |
| niels_to_pt(combo, ossl_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, |
| ossl_curve448_wnaf_base[control_pre[contp].addend |
| >> 1], i); |
| else |
| sub_niels_from_pt(combo, |
| ossl_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 ossl_curve448_point_destroy(curve448_point_t point) |
| { |
| OPENSSL_cleanse(point, sizeof(curve448_point_t)); |
| } |
| |
| int ossl_x448(uint8_t out_shared_key[56], const uint8_t private_key[56], |
| const uint8_t peer_public_value[56]) |
| { |
| return ossl_x448_int(out_shared_key, peer_public_value, private_key) |
| == C448_SUCCESS; |
| } |
| |
| void ossl_x448_public_from_private(uint8_t out_public_value[56], |
| const uint8_t private_key[56]) |
| { |
| ossl_x448_derive_public_key(out_public_value, private_key); |
| } |