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- /*
- * Copyright 2017-2023 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;
- ossl_gf_sqr(t1, x); /* o^2 */
- ret = gf_isr(t2, t1); /* +-1/sqrt(o^2) = +-1/o */
- (void)ret;
- if (assert_nonzero)
- assert(ret);
- ossl_gf_sqr(t1, t2);
- ossl_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;
- ossl_gf_sqr(c, q->x);
- ossl_gf_sqr(a, q->y);
- gf_add_nr(d, c, a); /* 2+e */
- gf_add_nr(p->t, q->y, q->x); /* 2+e */
- ossl_gf_sqr(b, p->t);
- gf_subx_nr(b, b, d, 3); /* 4+e */
- gf_sub_nr(p->t, a, c); /* 3+e */
- ossl_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 */
- ossl_gf_mul(p->x, a, b);
- ossl_gf_mul(p->z, p->t, a);
- ossl_gf_mul(p->y, p->t, d);
- if (!before_double)
- ossl_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);
- ossl_gf_mul(e->t, e->y, eu);
- ossl_gf_mul(e->x, d->z, e->y);
- ossl_gf_mul(e->y, d->z, eu);
- ossl_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);
- ossl_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 */
- ossl_gf_mul(a, e->a, b);
- gf_add_nr(b, d->x, d->y); /* 2+e */
- ossl_gf_mul(d->y, e->b, b);
- ossl_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 */
- ossl_gf_mul(d->z, a, d->y);
- ossl_gf_mul(d->x, d->y, b);
- ossl_gf_mul(d->y, a, c);
- if (!before_double)
- ossl_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 */
- ossl_gf_mul(a, e->b, b);
- gf_add_nr(b, d->x, d->y); /* 2+e */
- ossl_gf_mul(d->y, e->a, b);
- ossl_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 */
- ossl_gf_mul(d->z, a, d->y);
- ossl_gf_mul(d->x, d->y, b);
- ossl_gf_mul(d->y, a, c);
- if (!before_double)
- ossl_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;
- ossl_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;
- ossl_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 */
- ossl_gf_mul(a, p->y, q->x);
- ossl_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;
- ossl_gf_mul(a, p->x, p->y);
- ossl_gf_mul(b, p->z, p->t);
- out = gf_eq(a, b);
- ossl_gf_sqr(a, p->x);
- ossl_gf_sqr(b, p->y);
- gf_sub(a, b, a);
- ossl_gf_sqr(b, p->t);
- gf_mulw(c, b, TWISTED_D);
- ossl_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;
- ossl_gf_sqr(x, q->x);
- ossl_gf_sqr(t, q->y);
- gf_add(u, x, t);
- gf_add(z, q->y, q->x);
- ossl_gf_sqr(y, z);
- gf_sub(y, y, u);
- gf_sub(z, t, x);
- ossl_gf_sqr(x, q->z);
- gf_add(t, x, x);
- gf_sub(t, t, z);
- ossl_gf_mul(x, t, y);
- ossl_gf_mul(y, z, u);
- ossl_gf_mul(z, u, t);
- OPENSSL_cleanse(u, sizeof(u));
- }
- /* Affinize */
- gf_invert(z, z, 1);
- ossl_gf_mul(t, x, z);
- ossl_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]);
- ossl_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 */
- ossl_gf_mul(p->x, p->z, p->t);
- succ &= gf_isr(p->t, p->x); /* 1/sqrt(num * denom) */
- ossl_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) */
- ossl_gf_sqr(c, p->x);
- ossl_gf_sqr(a, p->y);
- gf_add(d, c, a);
- gf_add(p->t, p->y, p->x);
- ossl_gf_sqr(b, p->t);
- gf_sub(b, b, d);
- gf_sub(p->t, a, c);
- ossl_gf_sqr(p->x, p->z);
- gf_add(p->z, p->x, p->x);
- gf_sub(a, p->z, d);
- ossl_gf_mul(p->x, a, b);
- ossl_gf_mul(p->z, p->t, a);
- ossl_gf_mul(p->y, p->t, d);
- ossl_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 */
- ossl_gf_mul(x2, t1, z2); /* DA */
- gf_add_nr(z2, z3, x3); /* C = x3 + z3 */ /* 2+e */
- ossl_gf_mul(x3, t2, z2); /* CB */
- gf_sub_nr(z3, x2, x3); /* DA-CB */ /* 3+e */
- ossl_gf_sqr(z2, z3); /* (DA-CB)^2 */
- ossl_gf_mul(z3, x1, z2); /* z3 = x1(DA-CB)^2 */
- gf_add_nr(z2, x2, x3); /* (DA+CB) */ /* 2+e */
- ossl_gf_sqr(x3, z2); /* x3 = (DA+CB)^2 */
- ossl_gf_sqr(z2, t1); /* AA = A^2 */
- ossl_gf_sqr(t1, t2); /* BB = B^2 */
- ossl_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 */
- ossl_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);
- ossl_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 */
- ossl_gf_mul(q->z, q->t, q->y); /* y/x */
- ossl_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);
- }
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