-/**
- * @file ed448goldilocks/decaf.c
- * @author Mike Hamburg
+/*
+ * Copyright 2017-2018 The OpenSSL Project Authors. All Rights Reserved.
+ * Copyright 2015-2016 Cryptography Research, Inc.
*
- * @copyright
- * Copyright (c) 2015-2016 Cryptography Research, Inc. \n
- * Released under the MIT License. See LICENSE.txt for license information.
+ * 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
*
- * @brief Decaf high-level functions.
- *
- * @warning This file was automatically generated in Python.
- * Please do not edit it.
+ * Originally written by Mike Hamburg
*/
#include <openssl/crypto.h>
#include "word.h"
#define COMBS_N 5
#define COMBS_T 5
#define COMBS_S 18
-#define DECAF_WINDOW_BITS 5
-#define DECAF_WNAF_FIXED_TABLE_BITS 5
-#define DECAF_WNAF_VAR_TABLE_BITS 3
+#define C448_WNAF_FIXED_TABLE_BITS 5
+#define C448_WNAF_VAR_TABLE_BITS 3
static const int EDWARDS_D = -39081;
-static const curve448_scalar_t precomputed_scalarmul_adjustment = {{{
- SC_LIMB(0xc873d6d54a7bb0cf), SC_LIMB(0xe933d8d723a70aad), SC_LIMB(0xbb124b65129c96fd), SC_LIMB(0x00000008335dc163)
-}}};
-
-const uint8_t decaf_x448_base_point[DECAF_X448_PUBLIC_BYTES] = { 0x05 };
-
-#define RISTRETTO_FACTOR DECAF_448_RISTRETTO_FACTOR
-const gf RISTRETTO_FACTOR = {{{
- 0x42ef0f45572736, 0x7bf6aa20ce5296, 0xf4fd6eded26033, 0x968c14ba839a66, 0xb8d54b64a2d780, 0x6aa0a1f1a7b8a5, 0x683bf68d722fa2, 0x22d962fbeb24f7
-}}};
-
+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 EFF_D (-(TWISTED_D))
-#define NEG_D 1
-
-/* End of template stuff */
-
-#define WBITS DECAF_WORD_BITS /* NB this may be different from ARCH_WORD_BITS */
+#define WBITS C448_WORD_BITS /* NB this may be different from ARCH_WORD_BITS */
/* Projective Niels coordinates */
-typedef struct { gf a, b, c; } niels_s, niels_t[1];
-typedef struct { niels_t n; gf z; } VECTOR_ALIGNED pniels_s, pniels_t[1];
+typedef struct {
+ gf a, b, c;
+} niels_s, niels_t[1];
+typedef struct {
+ niels_t n;
+ gf z;
+} VECTOR_ALIGNED pniels_t[1];
/* Precomputed base */
-struct curve448_precomputed_s { niels_t table [COMBS_N<<(COMBS_T-1)]; };
+struct curve448_precomputed_s {
+ niels_t table[COMBS_N << (COMBS_T - 1)];
+};
extern const gf curve448_precomputed_base_as_fe[];
const curve448_precomputed_s *curve448_precomputed_base =
- (const curve448_precomputed_s *) &curve448_precomputed_base_as_fe;
+ (const curve448_precomputed_s *)&curve448_precomputed_base_as_fe;
+
+/* Inverse. */
+static void gf_invert(gf y, const gf x, int assert_nonzero)
+{
+ mask_t ret;
-/** Inverse. */
-static void
-gf_invert(gf y, const gf x, int assert_nonzero) {
gf t1, t2;
- gf_sqr(t1, x); // o^2
- mask_t ret = gf_isr(t2, t1); // +-1/sqrt(o^2) = +-1/o
+ gf_sqr(t1, x); /* o^2 */
+ ret = gf_isr(t2, t1); /* +-1/sqrt(o^2) = +-1/o */
(void)ret;
- if (assert_nonzero) assert(ret);
+ if (assert_nonzero)
+ assert(ret);
gf_sqr(t1, t2);
- gf_mul(t2, t1, x); // not direct to y in case of alias.
+ 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
-) {
+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 );
+
+ 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);
+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
-) {
+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 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
-) {
+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 );
+
+ 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 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
-) {
+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 );
+
+ 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
-) {
+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 );
+ 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
-) {
+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 );
+
+ 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
-) {
+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 );
+
+ gf_mul(L0, p->z, pn->z);
+ gf_copy(p->z, L0);
+ sub_niels_from_pt(p, pn->n, before_double);
}
-decaf_bool_t curve448_point_eq ( const curve448_point_t p, const curve448_point_t q ) {
+c448_bool_t curve448_point_eq(const curve448_point_t p,
+ const curve448_point_t q)
+{
+ mask_t succ;
+
/* equality mod 2-torsion compares x/y */
gf a, b;
- gf_mul ( a, p->y, q->x );
- gf_mul ( b, q->y, p->x );
- mask_t succ = gf_eq(a,b);
+ gf_mul(a, p->y, q->x);
+ gf_mul(b, q->y, p->x);
+ succ = gf_eq(a, b);
return mask_to_bool(succ);
}
-decaf_bool_t curve448_point_valid (
- const curve448_point_t p
-) {
- gf a,b,c;
- gf_mul(a,p->x,p->y);
- gf_mul(b,p->z,p->t);
- mask_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);
+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
-) {
+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
-) {
+void curve448_precomputed_scalarmul(curve448_point_t out,
+ const curve448_precomputed_s * table,
+ const curve448_scalar_t scalar)
+{
int i;
- unsigned j,k;
+ unsigned 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);
-
- niels_t ni;
-
- for (i=s-1; i>=0; i--) {
- if (i != (int)s-1) point_double_internal(out,out,0);
-
- for (j=0; j<n; j++) {
+ curve448_scalar_halve(scalar1x, scalar1x);
+
+ for (i = s - 1; i >= 0; i--) {
+ if (i != (int)s - 1)
+ point_double_internal(out, out, 0);
+
+ for (j = 0; j < n; j++) {
int tab = 0;
-
- for (k=0; k<t; k++) {
- unsigned int bit = i + s*(k + j*t);
- if (bit < DECAF_448_SCALAR_BITS) {
- tab |= (scalar1x->limb[bit/WBITS] >> (bit%WBITS) & 1) << k;
+ mask_t invert;
+
+ for (k = 0; k < t; k++) {
+ unsigned int bit = i + s * (k + j * t);
+ if (bit < C448_SCALAR_BITS) {
+ tab |=
+ (scalar1x->limb[bit / WBITS] >> (bit % WBITS) & 1) << k;
}
}
-
- mask_t invert = (tab>>(t-1))-1;
+
+ invert = (tab >> (t - 1)) - 1;
tab ^= invert;
- tab &= (1<<(t-1)) - 1;
+ tab &= (1 << (t - 1)) - 1;
- constant_time_lookup_niels(ni, &table->table[j<<(t-1)], 1<<(t-1), tab);
+ constant_time_lookup_niels(ni, &table->table[j << (t - 1)],
+ 1 << (t - 1), tab);
cond_neg_niels(ni, invert);
- if ((i!=(int)s-1)||j) {
- add_niels_to_pt(out, ni, j==n-1 && i);
+ if ((i != (int)s - 1) || j) {
+ add_niels_to_pt(out, ni, j == n - 1 && i);
} else {
niels_to_pt(out, ni);
}
}
}
-
- OPENSSL_cleanse(ni,sizeof(ni));
- OPENSSL_cleanse(scalar1x,sizeof(scalar1x));
+
+ OPENSSL_cleanse(ni, sizeof(ni));
+ OPENSSL_cleanse(scalar1x, sizeof(scalar1x));
}
-void curve448_point_mul_by_ratio_and_encode_like_eddsa (
- uint8_t enc[DECAF_EDDSA_448_PUBLIC_BYTES],
- const curve448_point_t p
-) {
-
+void curve448_point_mul_by_ratio_and_encode_like_eddsa(
+ uint8_t enc[EDDSA_448_PUBLIC_BYTES],
+ const curve448_point_t p)
+{
+
/* The point is now on the twisted curve. Move it to untwisted. */
gf x, y, z, t;
curve448_point_t q;
- curve448_point_copy(q,p);
+ 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));
+
+ 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);
-
+ gf_invert(z, z, 1);
+ gf_mul(t, x, z);
+ gf_mul(x, y, z);
+
/* Encode */
- enc[DECAF_EDDSA_448_PRIVATE_BYTES-1] = 0;
+ enc[EDDSA_448_PRIVATE_BYTES - 1] = 0;
gf_serialize(enc, x, 1);
- enc[DECAF_EDDSA_448_PRIVATE_BYTES-1] |= 0x80 & gf_lobit(t);
+ 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));
+ 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));
-decaf_error_t curve448_point_decode_like_eddsa_and_mul_by_ratio (
- curve448_point_t p,
- const uint8_t enc[DECAF_EDDSA_448_PUBLIC_BYTES]
-) {
- uint8_t enc2[DECAF_EDDSA_448_PUBLIC_BYTES];
- memcpy(enc2,enc,sizeof(enc2));
+ low = ~word_is_zero(enc2[EDDSA_448_PRIVATE_BYTES - 1] & 0x80);
+ enc2[EDDSA_448_PRIVATE_BYTES - 1] &= ~0x80;
- mask_t low = ~word_is_zero(enc2[DECAF_EDDSA_448_PRIVATE_BYTES-1] & 0x80);
- enc2[DECAF_EDDSA_448_PRIVATE_BYTES-1] &= ~0x80;
-
- mask_t succ = gf_deserialize(p->y, enc2, 1, 0);
+ succ = gf_deserialize(p->y, enc2, 1, 0);
#if 0 == 0
- succ &= word_is_zero(enc2[DECAF_EDDSA_448_PRIVATE_BYTES-1]);
+ succ &= word_is_zero(enc2[EDDSA_448_PRIVATE_BYTES - 1]);
#endif
- 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_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);
+
{
/* 4-isogeny 2xy/(y^2-ax^2), (y^2+ax^2)/(2-y^2-ax^2) */
gf a, b, c, d;
- 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));
+ 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));
+
+ OPENSSL_cleanse(enc2, sizeof(enc2));
assert(curve448_point_valid(p) || ~succ);
-
- return decaf_succeed_if(mask_to_bool(succ));
+
+ return c448_succeed_if(mask_to_bool(succ));
}
-decaf_error_t decaf_x448 (
- uint8_t out[X_PUBLIC_BYTES],
- const uint8_t base[X_PUBLIC_BYTES],
- const uint8_t scalar[X_PRIVATE_BYTES]
-) {
+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;
- ignore_result(gf_deserialize(x1,base,1,0));
- gf_copy(x2,ONE);
- gf_copy(z2,ZERO);
- gf_copy(x3,x1);
- gf_copy(z3,ONE);
-
int t;
mask_t swap = 0;
-
- for (t = X_PRIVATE_BITS-1; t>=0; t--) {
- uint8_t sb = scalar[t/8];
-
+ mask_t nz;
+
+ ignore_result(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;
-
- mask_t k_t = (sb>>(t%8)) & 1;
- k_t = -k_t; /* set to all 0s or all 1s */
-
+ 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);
+ gf_cond_swap(x2, x3, swap);
+ gf_cond_swap(z2, z3, swap);
swap = k_t;
-
- 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);
- mask_t 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 decaf_succeed_if(mask_to_bool(nz));
-}
-/* Thanks Johan Pascal */
-void decaf_ed448_convert_public_key_to_x448 (
- uint8_t x[DECAF_X448_PUBLIC_BYTES],
- const uint8_t ed[DECAF_EDDSA_448_PUBLIC_BYTES]
-) {
- gf y;
- const uint8_t mask = (uint8_t)(0xFE<<(7));
- ignore_result(gf_deserialize(y, ed, 1, mask));
-
- {
- gf n,d;
-
- /* u = y^2 * (1-dy^2) / (1-y^2) */
- gf_sqr(n,y); /* y^2*/
- gf_sub(d,ONE,n); /* 1-y^2*/
- gf_invert(d,d,0); /* 1/(1-y^2)*/
- gf_mul(y,n,d); /* y^2 / (1-y^2) */
- gf_mulw(d,n,EDWARDS_D); /* dy^2*/
- gf_sub(d, ONE, d); /* 1-dy^2*/
- gf_mul(n, y, d); /* y^2 * (1-dy^2) / (1-y^2) */
- gf_serialize(x,n,1);
-
- OPENSSL_cleanse(y,sizeof(y));
- OPENSSL_cleanse(n,sizeof(n));
- OPENSSL_cleanse(d,sizeof(d));
+ 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
-) {
+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_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 decaf_x448_derive_public_key (
- uint8_t out[X_PUBLIC_BYTES],
- const uint8_t scalar[X_PRIVATE_BYTES]
-) {
+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];
- memcpy(scalar2,scalar,sizeof(scalar2));
- scalar2[0] &= -(uint8_t)COFACTOR;
-
- scalar2[X_PRIVATE_BYTES-1] &= ~(-1u<<((X_PRIVATE_BITS+7)%8));
- scalar2[X_PRIVATE_BYTES-1] |= 1<<((X_PRIVATE_BITS+7)%8);
-
curve448_scalar_t the_scalar;
- curve448_scalar_decode_long(the_scalar,scalar2,sizeof(scalar2));
-
+ 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 (unsigned i=1; i<DECAF_X448_ENCODE_RATIO; i<<=1) {
- curve448_scalar_halve(the_scalar,the_scalar);
+ for (i = 1; i < X448_ENCODE_RATIO; i <<= 1) {
+ curve448_scalar_halve(the_scalar, the_scalar);
}
- curve448_point_t p;
- curve448_precomputed_scalarmul(p,curve448_precomputed_base,the_scalar);
- curve448_point_mul_by_ratio_and_encode_like_x448(out,p);
+ curve448_precomputed_scalarmul(p, curve448_precomputed_base, the_scalar);
+ curve448_point_mul_by_ratio_and_encode_like_x448(out, p);
curve448_point_destroy(p);
}
-/**
- * @cond internal
- * Control for variable-time scalar multiply algorithms.
- */
+/* Control for variable-time scalar multiply algorithms. */
struct smvt_control {
- int power, addend;
+ int power, addend;
};
-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 = DECAF_448_SCALAR_BITS/(table_bits+1) + 3;
+#if defined(__GNUC__) || defined(__clang__)
+# define NUMTRAILINGZEROS __builtin_ctz
+#else
+# define NUMTRAILINGZEROS numtrailingzeros
+static uint32_t numtrailingzeros(uint32_t i)
+{
+ unsigned int 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;
+ }
+ if ((i << 1) != 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.
+ /*
+ * 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.
*/
-
- 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;
- for (w = 1; w<(DECAF_448_SCALAR_BITS-1)/16+3; w++) {
- if (w < (DECAF_448_SCALAR_BITS-1)/16+1) {
+ 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);
+ current += (uint32_t)((scalar->limb[w / B_OVER_16]
+ >> (16 * (w % B_OVER_16))) << 16);
}
-
+
while (current & 0xFFFF) {
- assert(position >= 0);
- uint32_t pos = __builtin_ctz((uint32_t)current), odd = (uint32_t)current >> pos;
+ uint32_t pos = NUMTRAILINGZEROS((uint32_t)current);
+ uint32_t odd = (uint32_t)current >> pos;
int32_t delta = odd & mask;
- if (odd & 1<<(table_bits+1)) delta -= (1<<(table_bits+1));
+
+ assert(position >= 0);
+ if (odd & 1 << (table_bits + 1))
+ delta -= (1 << (table_bits + 1));
current -= delta << pos;
- control[position].power = pos + 16*(w-1);
+ control[position].power = pos + 16 * (w - 1);
control[position].addend = delta;
position--;
}
current >>= 16;
}
- assert(current==0);
-
+ assert(current == 0);
+
position++;
- unsigned int n = table_size - position;
- unsigned int i;
- for (i=0; i<n; i++) {
- control[i] = control[i+position];
+ n = table_size - position;
+ for (i = 0; i < n; i++) {
+ control[i] = control[i + position];
}
- return n-1;
+ return n - 1;
}
-static void
-prepare_wnaf_table(
- pniels_t *output,
- const curve448_point_t working,
- unsigned int tbits
-) {
+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;
+ if (tbits == 0)
+ return;
- curve448_point_double(tmp,working);
- pniels_t twop;
+ curve448_point_double(tmp, working);
pt_to_pniels(twop, tmp);
- add_pniels_to_pt(tmp, output[0],0);
+ 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);
+ 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));
+ OPENSSL_cleanse(twop, sizeof(twop));
}
extern const gf curve448_precomputed_wnaf_as_fe[];
-static const niels_t *curve448_wnaf_base = (const niels_t *)curve448_precomputed_wnaf_as_fe;
-
-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 = DECAF_WNAF_VAR_TABLE_BITS,
- table_bits_pre = DECAF_WNAF_FIXED_TABLE_BITS;
- struct smvt_control control_var[DECAF_448_SCALAR_BITS/(table_bits_var+1)+3];
- struct smvt_control control_pre[DECAF_448_SCALAR_BITS/(table_bits_pre+1)+3];
-
+static const niels_t *curve448_wnaf_base =
+ (const niels_t *)curve448_precomputed_wnaf_as_fe;
+
+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,
+ 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<<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);
-
- int contp=0, contv=0, i = control_var[0].power;
+ i = control_var[0].power;
if (i < 0) {
curve448_point_copy(combo, curve448_point_identity);
} else 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 ) {
+ } 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++;
+ 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), cp = (i==control_pre[contp].power);
- point_double_internal(combo,combo,i && !(cv||cp));
+ int cv = (i == control_var[contv].power), 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);
+ 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);
+ sub_pniels_from_pt(combo,
+ precmp_var[(-control_var[contv].addend)
+ >> 1], i && !cp);
}
contv++;
}
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);
+ 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);
+ 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;
+ /* 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
-) {
+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 decaf_x448(out_shared_key, peer_public_value, private_key)
- == DECAF_SUCCESS;
+ 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])
{
- decaf_x448_derive_public_key(out_public_value, private_key);
+ x448_derive_public_key(out_public_value, private_key);
}
projects / openssl.git / blobdiff