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linuxdebug/lib/mpi/ec.c

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/* ec.c - Elliptic Curve functions
* Copyright (C) 2007 Free Software Foundation, Inc.
* Copyright (C) 2013 g10 Code GmbH
*
* This file is part of Libgcrypt.
*
* Libgcrypt is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as
* published by the Free Software Foundation; either version 2.1 of
* the License, or (at your option) any later version.
*
* Libgcrypt is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this program; if not, see <http://www.gnu.org/licenses/>.
*/
#include "mpi-internal.h"
#include "longlong.h"
#define point_init(a) mpi_point_init((a))
#define point_free(a) mpi_point_free_parts((a))
#define log_error(fmt, ...) pr_err(fmt, ##__VA_ARGS__)
#define log_fatal(fmt, ...) pr_err(fmt, ##__VA_ARGS__)
#define DIM(v) (sizeof(v)/sizeof((v)[0]))
/* Create a new point option. NBITS gives the size in bits of one
* coordinate; it is only used to pre-allocate some resources and
* might also be passed as 0 to use a default value.
*/
MPI_POINT mpi_point_new(unsigned int nbits)
{
MPI_POINT p;
(void)nbits; /* Currently not used. */
p = kmalloc(sizeof(*p), GFP_KERNEL);
if (p)
mpi_point_init(p);
return p;
}
EXPORT_SYMBOL_GPL(mpi_point_new);
/* Release the point object P. P may be NULL. */
void mpi_point_release(MPI_POINT p)
{
if (p) {
mpi_point_free_parts(p);
kfree(p);
}
}
EXPORT_SYMBOL_GPL(mpi_point_release);
/* Initialize the fields of a point object. gcry_mpi_point_free_parts
* may be used to release the fields.
*/
void mpi_point_init(MPI_POINT p)
{
p->x = mpi_new(0);
p->y = mpi_new(0);
p->z = mpi_new(0);
}
EXPORT_SYMBOL_GPL(mpi_point_init);
/* Release the parts of a point object. */
void mpi_point_free_parts(MPI_POINT p)
{
mpi_free(p->x); p->x = NULL;
mpi_free(p->y); p->y = NULL;
mpi_free(p->z); p->z = NULL;
}
EXPORT_SYMBOL_GPL(mpi_point_free_parts);
/* Set the value from S into D. */
static void point_set(MPI_POINT d, MPI_POINT s)
{
mpi_set(d->x, s->x);
mpi_set(d->y, s->y);
mpi_set(d->z, s->z);
}
static void point_resize(MPI_POINT p, struct mpi_ec_ctx *ctx)
{
size_t nlimbs = ctx->p->nlimbs;
mpi_resize(p->x, nlimbs);
p->x->nlimbs = nlimbs;
mpi_resize(p->z, nlimbs);
p->z->nlimbs = nlimbs;
if (ctx->model != MPI_EC_MONTGOMERY) {
mpi_resize(p->y, nlimbs);
p->y->nlimbs = nlimbs;
}
}
static void point_swap_cond(MPI_POINT d, MPI_POINT s, unsigned long swap,
struct mpi_ec_ctx *ctx)
{
mpi_swap_cond(d->x, s->x, swap);
if (ctx->model != MPI_EC_MONTGOMERY)
mpi_swap_cond(d->y, s->y, swap);
mpi_swap_cond(d->z, s->z, swap);
}
/* W = W mod P. */
static void ec_mod(MPI w, struct mpi_ec_ctx *ec)
{
if (ec->t.p_barrett)
mpi_mod_barrett(w, w, ec->t.p_barrett);
else
mpi_mod(w, w, ec->p);
}
static void ec_addm(MPI w, MPI u, MPI v, struct mpi_ec_ctx *ctx)
{
mpi_add(w, u, v);
ec_mod(w, ctx);
}
static void ec_subm(MPI w, MPI u, MPI v, struct mpi_ec_ctx *ec)
{
mpi_sub(w, u, v);
while (w->sign)
mpi_add(w, w, ec->p);
/*ec_mod(w, ec);*/
}
static void ec_mulm(MPI w, MPI u, MPI v, struct mpi_ec_ctx *ctx)
{
mpi_mul(w, u, v);
ec_mod(w, ctx);
}
/* W = 2 * U mod P. */
static void ec_mul2(MPI w, MPI u, struct mpi_ec_ctx *ctx)
{
mpi_lshift(w, u, 1);
ec_mod(w, ctx);
}
static void ec_powm(MPI w, const MPI b, const MPI e,
struct mpi_ec_ctx *ctx)
{
mpi_powm(w, b, e, ctx->p);
/* mpi_abs(w); */
}
/* Shortcut for
* ec_powm(B, B, mpi_const(MPI_C_TWO), ctx);
* for easier optimization.
*/
static void ec_pow2(MPI w, const MPI b, struct mpi_ec_ctx *ctx)
{
/* Using mpi_mul is slightly faster (at least on amd64). */
/* mpi_powm(w, b, mpi_const(MPI_C_TWO), ctx->p); */
ec_mulm(w, b, b, ctx);
}
/* Shortcut for
* ec_powm(B, B, mpi_const(MPI_C_THREE), ctx);
* for easier optimization.
*/
static void ec_pow3(MPI w, const MPI b, struct mpi_ec_ctx *ctx)
{
mpi_powm(w, b, mpi_const(MPI_C_THREE), ctx->p);
}
static void ec_invm(MPI x, MPI a, struct mpi_ec_ctx *ctx)
{
if (!mpi_invm(x, a, ctx->p))
log_error("ec_invm: inverse does not exist:\n");
}
static void mpih_set_cond(mpi_ptr_t wp, mpi_ptr_t up,
mpi_size_t usize, unsigned long set)
{
mpi_size_t i;
mpi_limb_t mask = ((mpi_limb_t)0) - set;
mpi_limb_t x;
for (i = 0; i < usize; i++) {
x = mask & (wp[i] ^ up[i]);
wp[i] = wp[i] ^ x;
}
}
/* Routines for 2^255 - 19. */
#define LIMB_SIZE_25519 ((256+BITS_PER_MPI_LIMB-1)/BITS_PER_MPI_LIMB)
static void ec_addm_25519(MPI w, MPI u, MPI v, struct mpi_ec_ctx *ctx)
{
mpi_ptr_t wp, up, vp;
mpi_size_t wsize = LIMB_SIZE_25519;
mpi_limb_t n[LIMB_SIZE_25519];
mpi_limb_t borrow;
if (w->nlimbs != wsize || u->nlimbs != wsize || v->nlimbs != wsize)
log_bug("addm_25519: different sizes\n");
memset(n, 0, sizeof(n));
up = u->d;
vp = v->d;
wp = w->d;
mpihelp_add_n(wp, up, vp, wsize);
borrow = mpihelp_sub_n(wp, wp, ctx->p->d, wsize);
mpih_set_cond(n, ctx->p->d, wsize, (borrow != 0UL));
mpihelp_add_n(wp, wp, n, wsize);
wp[LIMB_SIZE_25519-1] &= ~((mpi_limb_t)1 << (255 % BITS_PER_MPI_LIMB));
}
static void ec_subm_25519(MPI w, MPI u, MPI v, struct mpi_ec_ctx *ctx)
{
mpi_ptr_t wp, up, vp;
mpi_size_t wsize = LIMB_SIZE_25519;
mpi_limb_t n[LIMB_SIZE_25519];
mpi_limb_t borrow;
if (w->nlimbs != wsize || u->nlimbs != wsize || v->nlimbs != wsize)
log_bug("subm_25519: different sizes\n");
memset(n, 0, sizeof(n));
up = u->d;
vp = v->d;
wp = w->d;
borrow = mpihelp_sub_n(wp, up, vp, wsize);
mpih_set_cond(n, ctx->p->d, wsize, (borrow != 0UL));
mpihelp_add_n(wp, wp, n, wsize);
wp[LIMB_SIZE_25519-1] &= ~((mpi_limb_t)1 << (255 % BITS_PER_MPI_LIMB));
}
static void ec_mulm_25519(MPI w, MPI u, MPI v, struct mpi_ec_ctx *ctx)
{
mpi_ptr_t wp, up, vp;
mpi_size_t wsize = LIMB_SIZE_25519;
mpi_limb_t n[LIMB_SIZE_25519*2];
mpi_limb_t m[LIMB_SIZE_25519+1];
mpi_limb_t cy;
int msb;
(void)ctx;
if (w->nlimbs != wsize || u->nlimbs != wsize || v->nlimbs != wsize)
log_bug("mulm_25519: different sizes\n");
up = u->d;
vp = v->d;
wp = w->d;
mpihelp_mul_n(n, up, vp, wsize);
memcpy(wp, n, wsize * BYTES_PER_MPI_LIMB);
wp[LIMB_SIZE_25519-1] &= ~((mpi_limb_t)1 << (255 % BITS_PER_MPI_LIMB));
memcpy(m, n+LIMB_SIZE_25519-1, (wsize+1) * BYTES_PER_MPI_LIMB);
mpihelp_rshift(m, m, LIMB_SIZE_25519+1, (255 % BITS_PER_MPI_LIMB));
memcpy(n, m, wsize * BYTES_PER_MPI_LIMB);
cy = mpihelp_lshift(m, m, LIMB_SIZE_25519, 4);
m[LIMB_SIZE_25519] = cy;
cy = mpihelp_add_n(m, m, n, wsize);
m[LIMB_SIZE_25519] += cy;
cy = mpihelp_add_n(m, m, n, wsize);
m[LIMB_SIZE_25519] += cy;
cy = mpihelp_add_n(m, m, n, wsize);
m[LIMB_SIZE_25519] += cy;
cy = mpihelp_add_n(wp, wp, m, wsize);
m[LIMB_SIZE_25519] += cy;
memset(m, 0, wsize * BYTES_PER_MPI_LIMB);
msb = (wp[LIMB_SIZE_25519-1] >> (255 % BITS_PER_MPI_LIMB));
m[0] = (m[LIMB_SIZE_25519] * 2 + msb) * 19;
wp[LIMB_SIZE_25519-1] &= ~((mpi_limb_t)1 << (255 % BITS_PER_MPI_LIMB));
mpihelp_add_n(wp, wp, m, wsize);
m[0] = 0;
cy = mpihelp_sub_n(wp, wp, ctx->p->d, wsize);
mpih_set_cond(m, ctx->p->d, wsize, (cy != 0UL));
mpihelp_add_n(wp, wp, m, wsize);
}
static void ec_mul2_25519(MPI w, MPI u, struct mpi_ec_ctx *ctx)
{
ec_addm_25519(w, u, u, ctx);
}
static void ec_pow2_25519(MPI w, const MPI b, struct mpi_ec_ctx *ctx)
{
ec_mulm_25519(w, b, b, ctx);
}
/* Routines for 2^448 - 2^224 - 1. */
#define LIMB_SIZE_448 ((448+BITS_PER_MPI_LIMB-1)/BITS_PER_MPI_LIMB)
#define LIMB_SIZE_HALF_448 ((LIMB_SIZE_448+1)/2)
static void ec_addm_448(MPI w, MPI u, MPI v, struct mpi_ec_ctx *ctx)
{
mpi_ptr_t wp, up, vp;
mpi_size_t wsize = LIMB_SIZE_448;
mpi_limb_t n[LIMB_SIZE_448];
mpi_limb_t cy;
if (w->nlimbs != wsize || u->nlimbs != wsize || v->nlimbs != wsize)
log_bug("addm_448: different sizes\n");
memset(n, 0, sizeof(n));
up = u->d;
vp = v->d;
wp = w->d;
cy = mpihelp_add_n(wp, up, vp, wsize);
mpih_set_cond(n, ctx->p->d, wsize, (cy != 0UL));
mpihelp_sub_n(wp, wp, n, wsize);
}
static void ec_subm_448(MPI w, MPI u, MPI v, struct mpi_ec_ctx *ctx)
{
mpi_ptr_t wp, up, vp;
mpi_size_t wsize = LIMB_SIZE_448;
mpi_limb_t n[LIMB_SIZE_448];
mpi_limb_t borrow;
if (w->nlimbs != wsize || u->nlimbs != wsize || v->nlimbs != wsize)
log_bug("subm_448: different sizes\n");
memset(n, 0, sizeof(n));
up = u->d;
vp = v->d;
wp = w->d;
borrow = mpihelp_sub_n(wp, up, vp, wsize);
mpih_set_cond(n, ctx->p->d, wsize, (borrow != 0UL));
mpihelp_add_n(wp, wp, n, wsize);
}
static void ec_mulm_448(MPI w, MPI u, MPI v, struct mpi_ec_ctx *ctx)
{
mpi_ptr_t wp, up, vp;
mpi_size_t wsize = LIMB_SIZE_448;
mpi_limb_t n[LIMB_SIZE_448*2];
mpi_limb_t a2[LIMB_SIZE_HALF_448];
mpi_limb_t a3[LIMB_SIZE_HALF_448];
mpi_limb_t b0[LIMB_SIZE_HALF_448];
mpi_limb_t b1[LIMB_SIZE_HALF_448];
mpi_limb_t cy;
int i;
#if (LIMB_SIZE_HALF_448 > LIMB_SIZE_448/2)
mpi_limb_t b1_rest, a3_rest;
#endif
if (w->nlimbs != wsize || u->nlimbs != wsize || v->nlimbs != wsize)
log_bug("mulm_448: different sizes\n");
up = u->d;
vp = v->d;
wp = w->d;
mpihelp_mul_n(n, up, vp, wsize);
for (i = 0; i < (wsize + 1) / 2; i++) {
b0[i] = n[i];
b1[i] = n[i+wsize/2];
a2[i] = n[i+wsize];
a3[i] = n[i+wsize+wsize/2];
}
#if (LIMB_SIZE_HALF_448 > LIMB_SIZE_448/2)
b0[LIMB_SIZE_HALF_448-1] &= ((mpi_limb_t)1UL << 32)-1;
a2[LIMB_SIZE_HALF_448-1] &= ((mpi_limb_t)1UL << 32)-1;
b1_rest = 0;
a3_rest = 0;
for (i = (wsize + 1) / 2 - 1; i >= 0; i--) {
mpi_limb_t b1v, a3v;
b1v = b1[i];
a3v = a3[i];
b1[i] = (b1_rest << 32) | (b1v >> 32);
a3[i] = (a3_rest << 32) | (a3v >> 32);
b1_rest = b1v & (((mpi_limb_t)1UL << 32)-1);
a3_rest = a3v & (((mpi_limb_t)1UL << 32)-1);
}
#endif
cy = mpihelp_add_n(b0, b0, a2, LIMB_SIZE_HALF_448);
cy += mpihelp_add_n(b0, b0, a3, LIMB_SIZE_HALF_448);
for (i = 0; i < (wsize + 1) / 2; i++)
wp[i] = b0[i];
#if (LIMB_SIZE_HALF_448 > LIMB_SIZE_448/2)
wp[LIMB_SIZE_HALF_448-1] &= (((mpi_limb_t)1UL << 32)-1);
#endif
#if (LIMB_SIZE_HALF_448 > LIMB_SIZE_448/2)
cy = b0[LIMB_SIZE_HALF_448-1] >> 32;
#endif
cy = mpihelp_add_1(b1, b1, LIMB_SIZE_HALF_448, cy);
cy += mpihelp_add_n(b1, b1, a2, LIMB_SIZE_HALF_448);
cy += mpihelp_add_n(b1, b1, a3, LIMB_SIZE_HALF_448);
cy += mpihelp_add_n(b1, b1, a3, LIMB_SIZE_HALF_448);
#if (LIMB_SIZE_HALF_448 > LIMB_SIZE_448/2)
b1_rest = 0;
for (i = (wsize + 1) / 2 - 1; i >= 0; i--) {
mpi_limb_t b1v = b1[i];
b1[i] = (b1_rest << 32) | (b1v >> 32);
b1_rest = b1v & (((mpi_limb_t)1UL << 32)-1);
}
wp[LIMB_SIZE_HALF_448-1] |= (b1_rest << 32);
#endif
for (i = 0; i < wsize / 2; i++)
wp[i+(wsize + 1) / 2] = b1[i];
#if (LIMB_SIZE_HALF_448 > LIMB_SIZE_448/2)
cy = b1[LIMB_SIZE_HALF_448-1];
#endif
memset(n, 0, wsize * BYTES_PER_MPI_LIMB);
#if (LIMB_SIZE_HALF_448 > LIMB_SIZE_448/2)
n[LIMB_SIZE_HALF_448-1] = cy << 32;
#else
n[LIMB_SIZE_HALF_448] = cy;
#endif
n[0] = cy;
mpihelp_add_n(wp, wp, n, wsize);
memset(n, 0, wsize * BYTES_PER_MPI_LIMB);
cy = mpihelp_sub_n(wp, wp, ctx->p->d, wsize);
mpih_set_cond(n, ctx->p->d, wsize, (cy != 0UL));
mpihelp_add_n(wp, wp, n, wsize);
}
static void ec_mul2_448(MPI w, MPI u, struct mpi_ec_ctx *ctx)
{
ec_addm_448(w, u, u, ctx);
}
static void ec_pow2_448(MPI w, const MPI b, struct mpi_ec_ctx *ctx)
{
ec_mulm_448(w, b, b, ctx);
}
struct field_table {
const char *p;
/* computation routines for the field. */
void (*addm)(MPI w, MPI u, MPI v, struct mpi_ec_ctx *ctx);
void (*subm)(MPI w, MPI u, MPI v, struct mpi_ec_ctx *ctx);
void (*mulm)(MPI w, MPI u, MPI v, struct mpi_ec_ctx *ctx);
void (*mul2)(MPI w, MPI u, struct mpi_ec_ctx *ctx);
void (*pow2)(MPI w, const MPI b, struct mpi_ec_ctx *ctx);
};
static const struct field_table field_table[] = {
{
"0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFED",
ec_addm_25519,
ec_subm_25519,
ec_mulm_25519,
ec_mul2_25519,
ec_pow2_25519
},
{
"0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE"
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
ec_addm_448,
ec_subm_448,
ec_mulm_448,
ec_mul2_448,
ec_pow2_448
},
{ NULL, NULL, NULL, NULL, NULL, NULL },
};
/* Force recomputation of all helper variables. */
static void mpi_ec_get_reset(struct mpi_ec_ctx *ec)
{
ec->t.valid.a_is_pminus3 = 0;
ec->t.valid.two_inv_p = 0;
}
/* Accessor for helper variable. */
static int ec_get_a_is_pminus3(struct mpi_ec_ctx *ec)
{
MPI tmp;
if (!ec->t.valid.a_is_pminus3) {
ec->t.valid.a_is_pminus3 = 1;
tmp = mpi_alloc_like(ec->p);
mpi_sub_ui(tmp, ec->p, 3);
ec->t.a_is_pminus3 = !mpi_cmp(ec->a, tmp);
mpi_free(tmp);
}
return ec->t.a_is_pminus3;
}
/* Accessor for helper variable. */
static MPI ec_get_two_inv_p(struct mpi_ec_ctx *ec)
{
if (!ec->t.valid.two_inv_p) {
ec->t.valid.two_inv_p = 1;
if (!ec->t.two_inv_p)
ec->t.two_inv_p = mpi_alloc(0);
ec_invm(ec->t.two_inv_p, mpi_const(MPI_C_TWO), ec);
}
return ec->t.two_inv_p;
}
static const char *const curve25519_bad_points[] = {
"0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed",
"0x0000000000000000000000000000000000000000000000000000000000000000",
"0x0000000000000000000000000000000000000000000000000000000000000001",
"0x00b8495f16056286fdb1329ceb8d09da6ac49ff1fae35616aeb8413b7c7aebe0",
"0x57119fd0dd4e22d8868e1c58c45c44045bef839c55b1d0b1248c50a3bc959c5f",
"0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffec",
"0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffee",
NULL
};
static const char *const curve448_bad_points[] = {
"0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffe"
"ffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
"0x00000000000000000000000000000000000000000000000000000000"
"00000000000000000000000000000000000000000000000000000000",
"0x00000000000000000000000000000000000000000000000000000000"
"00000000000000000000000000000000000000000000000000000001",
"0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffe"
"fffffffffffffffffffffffffffffffffffffffffffffffffffffffe",
"0xffffffffffffffffffffffffffffffffffffffffffffffffffffffff"
"00000000000000000000000000000000000000000000000000000000",
NULL
};
static const char *const *bad_points_table[] = {
curve25519_bad_points,
curve448_bad_points,
};
static void mpi_ec_coefficient_normalize(MPI a, MPI p)
{
if (a->sign) {
mpi_resize(a, p->nlimbs);
mpihelp_sub_n(a->d, p->d, a->d, p->nlimbs);
a->nlimbs = p->nlimbs;
a->sign = 0;
}
}
/* This function initialized a context for elliptic curve based on the
* field GF(p). P is the prime specifying this field, A is the first
* coefficient. CTX is expected to be zeroized.
*/
void mpi_ec_init(struct mpi_ec_ctx *ctx, enum gcry_mpi_ec_models model,
enum ecc_dialects dialect,
int flags, MPI p, MPI a, MPI b)
{
int i;
static int use_barrett = -1 /* TODO: 1 or -1 */;
mpi_ec_coefficient_normalize(a, p);
mpi_ec_coefficient_normalize(b, p);
/* Fixme: Do we want to check some constraints? e.g. a < p */
ctx->model = model;
ctx->dialect = dialect;
ctx->flags = flags;
if (dialect == ECC_DIALECT_ED25519)
ctx->nbits = 256;
else
ctx->nbits = mpi_get_nbits(p);
ctx->p = mpi_copy(p);
ctx->a = mpi_copy(a);
ctx->b = mpi_copy(b);
ctx->t.p_barrett = use_barrett > 0 ? mpi_barrett_init(ctx->p, 0) : NULL;
mpi_ec_get_reset(ctx);
if (model == MPI_EC_MONTGOMERY) {
for (i = 0; i < DIM(bad_points_table); i++) {
MPI p_candidate = mpi_scanval(bad_points_table[i][0]);
int match_p = !mpi_cmp(ctx->p, p_candidate);
int j;
mpi_free(p_candidate);
if (!match_p)
continue;
for (j = 0; i < DIM(ctx->t.scratch) && bad_points_table[i][j]; j++)
ctx->t.scratch[j] = mpi_scanval(bad_points_table[i][j]);
}
} else {
/* Allocate scratch variables. */
for (i = 0; i < DIM(ctx->t.scratch); i++)
ctx->t.scratch[i] = mpi_alloc_like(ctx->p);
}
ctx->addm = ec_addm;
ctx->subm = ec_subm;
ctx->mulm = ec_mulm;
ctx->mul2 = ec_mul2;
ctx->pow2 = ec_pow2;
for (i = 0; field_table[i].p; i++) {
MPI f_p;
f_p = mpi_scanval(field_table[i].p);
if (!f_p)
break;
if (!mpi_cmp(p, f_p)) {
ctx->addm = field_table[i].addm;
ctx->subm = field_table[i].subm;
ctx->mulm = field_table[i].mulm;
ctx->mul2 = field_table[i].mul2;
ctx->pow2 = field_table[i].pow2;
mpi_free(f_p);
mpi_resize(ctx->a, ctx->p->nlimbs);
ctx->a->nlimbs = ctx->p->nlimbs;
mpi_resize(ctx->b, ctx->p->nlimbs);
ctx->b->nlimbs = ctx->p->nlimbs;
for (i = 0; i < DIM(ctx->t.scratch) && ctx->t.scratch[i]; i++)
ctx->t.scratch[i]->nlimbs = ctx->p->nlimbs;
break;
}
mpi_free(f_p);
}
}
EXPORT_SYMBOL_GPL(mpi_ec_init);
void mpi_ec_deinit(struct mpi_ec_ctx *ctx)
{
int i;
mpi_barrett_free(ctx->t.p_barrett);
/* Domain parameter. */
mpi_free(ctx->p);
mpi_free(ctx->a);
mpi_free(ctx->b);
mpi_point_release(ctx->G);
mpi_free(ctx->n);
/* The key. */
mpi_point_release(ctx->Q);
mpi_free(ctx->d);
/* Private data of ec.c. */
mpi_free(ctx->t.two_inv_p);
for (i = 0; i < DIM(ctx->t.scratch); i++)
mpi_free(ctx->t.scratch[i]);
}
EXPORT_SYMBOL_GPL(mpi_ec_deinit);
/* Compute the affine coordinates from the projective coordinates in
* POINT. Set them into X and Y. If one coordinate is not required,
* X or Y may be passed as NULL. CTX is the usual context. Returns: 0
* on success or !0 if POINT is at infinity.
*/
int mpi_ec_get_affine(MPI x, MPI y, MPI_POINT point, struct mpi_ec_ctx *ctx)
{
if (!mpi_cmp_ui(point->z, 0))
return -1;
switch (ctx->model) {
case MPI_EC_WEIERSTRASS: /* Using Jacobian coordinates. */
{
MPI z1, z2, z3;
z1 = mpi_new(0);
z2 = mpi_new(0);
ec_invm(z1, point->z, ctx); /* z1 = z^(-1) mod p */
ec_mulm(z2, z1, z1, ctx); /* z2 = z^(-2) mod p */
if (x)
ec_mulm(x, point->x, z2, ctx);
if (y) {
z3 = mpi_new(0);
ec_mulm(z3, z2, z1, ctx); /* z3 = z^(-3) mod p */
ec_mulm(y, point->y, z3, ctx);
mpi_free(z3);
}
mpi_free(z2);
mpi_free(z1);
}
return 0;
case MPI_EC_MONTGOMERY:
{
if (x)
mpi_set(x, point->x);
if (y) {
log_fatal("%s: Getting Y-coordinate on %s is not supported\n",
"mpi_ec_get_affine", "Montgomery");
return -1;
}
}
return 0;
case MPI_EC_EDWARDS:
{
MPI z;
z = mpi_new(0);
ec_invm(z, point->z, ctx);
mpi_resize(z, ctx->p->nlimbs);
z->nlimbs = ctx->p->nlimbs;
if (x) {
mpi_resize(x, ctx->p->nlimbs);
x->nlimbs = ctx->p->nlimbs;
ctx->mulm(x, point->x, z, ctx);
}
if (y) {
mpi_resize(y, ctx->p->nlimbs);
y->nlimbs = ctx->p->nlimbs;
ctx->mulm(y, point->y, z, ctx);
}
mpi_free(z);
}
return 0;
default:
return -1;
}
}
EXPORT_SYMBOL_GPL(mpi_ec_get_affine);
/* RESULT = 2 * POINT (Weierstrass version). */
static void dup_point_weierstrass(MPI_POINT result,
MPI_POINT point, struct mpi_ec_ctx *ctx)
{
#define x3 (result->x)
#define y3 (result->y)
#define z3 (result->z)
#define t1 (ctx->t.scratch[0])
#define t2 (ctx->t.scratch[1])
#define t3 (ctx->t.scratch[2])
#define l1 (ctx->t.scratch[3])
#define l2 (ctx->t.scratch[4])
#define l3 (ctx->t.scratch[5])
if (!mpi_cmp_ui(point->y, 0) || !mpi_cmp_ui(point->z, 0)) {
/* P_y == 0 || P_z == 0 => [1:1:0] */
mpi_set_ui(x3, 1);
mpi_set_ui(y3, 1);
mpi_set_ui(z3, 0);
} else {
if (ec_get_a_is_pminus3(ctx)) {
/* Use the faster case. */
/* L1 = 3(X - Z^2)(X + Z^2) */
/* T1: used for Z^2. */
/* T2: used for the right term. */
ec_pow2(t1, point->z, ctx);
ec_subm(l1, point->x, t1, ctx);
ec_mulm(l1, l1, mpi_const(MPI_C_THREE), ctx);
ec_addm(t2, point->x, t1, ctx);
ec_mulm(l1, l1, t2, ctx);
} else {
/* Standard case. */
/* L1 = 3X^2 + aZ^4 */
/* T1: used for aZ^4. */
ec_pow2(l1, point->x, ctx);
ec_mulm(l1, l1, mpi_const(MPI_C_THREE), ctx);
ec_powm(t1, point->z, mpi_const(MPI_C_FOUR), ctx);
ec_mulm(t1, t1, ctx->a, ctx);
ec_addm(l1, l1, t1, ctx);
}
/* Z3 = 2YZ */
ec_mulm(z3, point->y, point->z, ctx);
ec_mul2(z3, z3, ctx);
/* L2 = 4XY^2 */
/* T2: used for Y2; required later. */
ec_pow2(t2, point->y, ctx);
ec_mulm(l2, t2, point->x, ctx);
ec_mulm(l2, l2, mpi_const(MPI_C_FOUR), ctx);
/* X3 = L1^2 - 2L2 */
/* T1: used for L2^2. */
ec_pow2(x3, l1, ctx);
ec_mul2(t1, l2, ctx);
ec_subm(x3, x3, t1, ctx);
/* L3 = 8Y^4 */
/* T2: taken from above. */
ec_pow2(t2, t2, ctx);
ec_mulm(l3, t2, mpi_const(MPI_C_EIGHT), ctx);
/* Y3 = L1(L2 - X3) - L3 */
ec_subm(y3, l2, x3, ctx);
ec_mulm(y3, y3, l1, ctx);
ec_subm(y3, y3, l3, ctx);
}
#undef x3
#undef y3
#undef z3
#undef t1
#undef t2
#undef t3
#undef l1
#undef l2
#undef l3
}
/* RESULT = 2 * POINT (Montgomery version). */
static void dup_point_montgomery(MPI_POINT result,
MPI_POINT point, struct mpi_ec_ctx *ctx)
{
(void)result;
(void)point;
(void)ctx;
log_fatal("%s: %s not yet supported\n",
"mpi_ec_dup_point", "Montgomery");
}
/* RESULT = 2 * POINT (Twisted Edwards version). */
static void dup_point_edwards(MPI_POINT result,
MPI_POINT point, struct mpi_ec_ctx *ctx)
{
#define X1 (point->x)
#define Y1 (point->y)
#define Z1 (point->z)
#define X3 (result->x)
#define Y3 (result->y)
#define Z3 (result->z)
#define B (ctx->t.scratch[0])
#define C (ctx->t.scratch[1])
#define D (ctx->t.scratch[2])
#define E (ctx->t.scratch[3])
#define F (ctx->t.scratch[4])
#define H (ctx->t.scratch[5])
#define J (ctx->t.scratch[6])
/* Compute: (X_3 : Y_3 : Z_3) = 2( X_1 : Y_1 : Z_1 ) */
/* B = (X_1 + Y_1)^2 */
ctx->addm(B, X1, Y1, ctx);
ctx->pow2(B, B, ctx);
/* C = X_1^2 */
/* D = Y_1^2 */
ctx->pow2(C, X1, ctx);
ctx->pow2(D, Y1, ctx);
/* E = aC */
if (ctx->dialect == ECC_DIALECT_ED25519)
ctx->subm(E, ctx->p, C, ctx);
else
ctx->mulm(E, ctx->a, C, ctx);
/* F = E + D */
ctx->addm(F, E, D, ctx);
/* H = Z_1^2 */
ctx->pow2(H, Z1, ctx);
/* J = F - 2H */
ctx->mul2(J, H, ctx);
ctx->subm(J, F, J, ctx);
/* X_3 = (B - C - D) · J */
ctx->subm(X3, B, C, ctx);
ctx->subm(X3, X3, D, ctx);
ctx->mulm(X3, X3, J, ctx);
/* Y_3 = F · (E - D) */
ctx->subm(Y3, E, D, ctx);
ctx->mulm(Y3, Y3, F, ctx);
/* Z_3 = F · J */
ctx->mulm(Z3, F, J, ctx);
#undef X1
#undef Y1
#undef Z1
#undef X3
#undef Y3
#undef Z3
#undef B
#undef C
#undef D
#undef E
#undef F
#undef H
#undef J
}
/* RESULT = 2 * POINT */
static void
mpi_ec_dup_point(MPI_POINT result, MPI_POINT point, struct mpi_ec_ctx *ctx)
{
switch (ctx->model) {
case MPI_EC_WEIERSTRASS:
dup_point_weierstrass(result, point, ctx);
break;
case MPI_EC_MONTGOMERY:
dup_point_montgomery(result, point, ctx);
break;
case MPI_EC_EDWARDS:
dup_point_edwards(result, point, ctx);
break;
}
}
/* RESULT = P1 + P2 (Weierstrass version).*/
static void add_points_weierstrass(MPI_POINT result,
MPI_POINT p1, MPI_POINT p2,
struct mpi_ec_ctx *ctx)
{
#define x1 (p1->x)
#define y1 (p1->y)
#define z1 (p1->z)
#define x2 (p2->x)
#define y2 (p2->y)
#define z2 (p2->z)
#define x3 (result->x)
#define y3 (result->y)
#define z3 (result->z)
#define l1 (ctx->t.scratch[0])
#define l2 (ctx->t.scratch[1])
#define l3 (ctx->t.scratch[2])
#define l4 (ctx->t.scratch[3])
#define l5 (ctx->t.scratch[4])
#define l6 (ctx->t.scratch[5])
#define l7 (ctx->t.scratch[6])
#define l8 (ctx->t.scratch[7])
#define l9 (ctx->t.scratch[8])
#define t1 (ctx->t.scratch[9])
#define t2 (ctx->t.scratch[10])
if ((!mpi_cmp(x1, x2)) && (!mpi_cmp(y1, y2)) && (!mpi_cmp(z1, z2))) {
/* Same point; need to call the duplicate function. */
mpi_ec_dup_point(result, p1, ctx);
} else if (!mpi_cmp_ui(z1, 0)) {
/* P1 is at infinity. */
mpi_set(x3, p2->x);
mpi_set(y3, p2->y);
mpi_set(z3, p2->z);
} else if (!mpi_cmp_ui(z2, 0)) {
/* P2 is at infinity. */
mpi_set(x3, p1->x);
mpi_set(y3, p1->y);
mpi_set(z3, p1->z);
} else {
int z1_is_one = !mpi_cmp_ui(z1, 1);
int z2_is_one = !mpi_cmp_ui(z2, 1);
/* l1 = x1 z2^2 */
/* l2 = x2 z1^2 */
if (z2_is_one)
mpi_set(l1, x1);
else {
ec_pow2(l1, z2, ctx);
ec_mulm(l1, l1, x1, ctx);
}
if (z1_is_one)
mpi_set(l2, x2);
else {
ec_pow2(l2, z1, ctx);
ec_mulm(l2, l2, x2, ctx);
}
/* l3 = l1 - l2 */
ec_subm(l3, l1, l2, ctx);
/* l4 = y1 z2^3 */
ec_powm(l4, z2, mpi_const(MPI_C_THREE), ctx);
ec_mulm(l4, l4, y1, ctx);
/* l5 = y2 z1^3 */
ec_powm(l5, z1, mpi_const(MPI_C_THREE), ctx);
ec_mulm(l5, l5, y2, ctx);
/* l6 = l4 - l5 */
ec_subm(l6, l4, l5, ctx);
if (!mpi_cmp_ui(l3, 0)) {
if (!mpi_cmp_ui(l6, 0)) {
/* P1 and P2 are the same - use duplicate function. */
mpi_ec_dup_point(result, p1, ctx);
} else {
/* P1 is the inverse of P2. */
mpi_set_ui(x3, 1);
mpi_set_ui(y3, 1);
mpi_set_ui(z3, 0);
}
} else {
/* l7 = l1 + l2 */
ec_addm(l7, l1, l2, ctx);
/* l8 = l4 + l5 */
ec_addm(l8, l4, l5, ctx);
/* z3 = z1 z2 l3 */
ec_mulm(z3, z1, z2, ctx);
ec_mulm(z3, z3, l3, ctx);
/* x3 = l6^2 - l7 l3^2 */
ec_pow2(t1, l6, ctx);
ec_pow2(t2, l3, ctx);
ec_mulm(t2, t2, l7, ctx);
ec_subm(x3, t1, t2, ctx);
/* l9 = l7 l3^2 - 2 x3 */
ec_mul2(t1, x3, ctx);
ec_subm(l9, t2, t1, ctx);
/* y3 = (l9 l6 - l8 l3^3)/2 */
ec_mulm(l9, l9, l6, ctx);
ec_powm(t1, l3, mpi_const(MPI_C_THREE), ctx); /* fixme: Use saved value*/
ec_mulm(t1, t1, l8, ctx);
ec_subm(y3, l9, t1, ctx);
ec_mulm(y3, y3, ec_get_two_inv_p(ctx), ctx);
}
}
#undef x1
#undef y1
#undef z1
#undef x2
#undef y2
#undef z2
#undef x3
#undef y3
#undef z3
#undef l1
#undef l2
#undef l3
#undef l4
#undef l5
#undef l6
#undef l7
#undef l8
#undef l9
#undef t1
#undef t2
}
/* RESULT = P1 + P2 (Montgomery version).*/
static void add_points_montgomery(MPI_POINT result,
MPI_POINT p1, MPI_POINT p2,
struct mpi_ec_ctx *ctx)
{
(void)result;
(void)p1;
(void)p2;
(void)ctx;
log_fatal("%s: %s not yet supported\n",
"mpi_ec_add_points", "Montgomery");
}
/* RESULT = P1 + P2 (Twisted Edwards version).*/
static void add_points_edwards(MPI_POINT result,
MPI_POINT p1, MPI_POINT p2,
struct mpi_ec_ctx *ctx)
{
#define X1 (p1->x)
#define Y1 (p1->y)
#define Z1 (p1->z)
#define X2 (p2->x)
#define Y2 (p2->y)
#define Z2 (p2->z)
#define X3 (result->x)
#define Y3 (result->y)
#define Z3 (result->z)
#define A (ctx->t.scratch[0])
#define B (ctx->t.scratch[1])
#define C (ctx->t.scratch[2])
#define D (ctx->t.scratch[3])
#define E (ctx->t.scratch[4])
#define F (ctx->t.scratch[5])
#define G (ctx->t.scratch[6])
#define tmp (ctx->t.scratch[7])
point_resize(result, ctx);
/* Compute: (X_3 : Y_3 : Z_3) = (X_1 : Y_1 : Z_1) + (X_2 : Y_2 : Z_3) */
/* A = Z1 · Z2 */
ctx->mulm(A, Z1, Z2, ctx);
/* B = A^2 */
ctx->pow2(B, A, ctx);
/* C = X1 · X2 */
ctx->mulm(C, X1, X2, ctx);
/* D = Y1 · Y2 */
ctx->mulm(D, Y1, Y2, ctx);
/* E = d · C · D */
ctx->mulm(E, ctx->b, C, ctx);
ctx->mulm(E, E, D, ctx);
/* F = B - E */
ctx->subm(F, B, E, ctx);
/* G = B + E */
ctx->addm(G, B, E, ctx);
/* X_3 = A · F · ((X_1 + Y_1) · (X_2 + Y_2) - C - D) */
ctx->addm(tmp, X1, Y1, ctx);
ctx->addm(X3, X2, Y2, ctx);
ctx->mulm(X3, X3, tmp, ctx);
ctx->subm(X3, X3, C, ctx);
ctx->subm(X3, X3, D, ctx);
ctx->mulm(X3, X3, F, ctx);
ctx->mulm(X3, X3, A, ctx);
/* Y_3 = A · G · (D - aC) */
if (ctx->dialect == ECC_DIALECT_ED25519) {
ctx->addm(Y3, D, C, ctx);
} else {
ctx->mulm(Y3, ctx->a, C, ctx);
ctx->subm(Y3, D, Y3, ctx);
}
ctx->mulm(Y3, Y3, G, ctx);
ctx->mulm(Y3, Y3, A, ctx);
/* Z_3 = F · G */
ctx->mulm(Z3, F, G, ctx);
#undef X1
#undef Y1
#undef Z1
#undef X2
#undef Y2
#undef Z2
#undef X3
#undef Y3
#undef Z3
#undef A
#undef B
#undef C
#undef D
#undef E
#undef F
#undef G
#undef tmp
}
/* Compute a step of Montgomery Ladder (only use X and Z in the point).
* Inputs: P1, P2, and x-coordinate of DIF = P1 - P1.
* Outputs: PRD = 2 * P1 and SUM = P1 + P2.
*/
static void montgomery_ladder(MPI_POINT prd, MPI_POINT sum,
MPI_POINT p1, MPI_POINT p2, MPI dif_x,
struct mpi_ec_ctx *ctx)
{
ctx->addm(sum->x, p2->x, p2->z, ctx);
ctx->subm(p2->z, p2->x, p2->z, ctx);
ctx->addm(prd->x, p1->x, p1->z, ctx);
ctx->subm(p1->z, p1->x, p1->z, ctx);
ctx->mulm(p2->x, p1->z, sum->x, ctx);
ctx->mulm(p2->z, prd->x, p2->z, ctx);
ctx->pow2(p1->x, prd->x, ctx);
ctx->pow2(p1->z, p1->z, ctx);
ctx->addm(sum->x, p2->x, p2->z, ctx);
ctx->subm(p2->z, p2->x, p2->z, ctx);
ctx->mulm(prd->x, p1->x, p1->z, ctx);
ctx->subm(p1->z, p1->x, p1->z, ctx);
ctx->pow2(sum->x, sum->x, ctx);
ctx->pow2(sum->z, p2->z, ctx);
ctx->mulm(prd->z, p1->z, ctx->a, ctx); /* CTX->A: (a-2)/4 */
ctx->mulm(sum->z, sum->z, dif_x, ctx);
ctx->addm(prd->z, p1->x, prd->z, ctx);
ctx->mulm(prd->z, prd->z, p1->z, ctx);
}
/* RESULT = P1 + P2 */
void mpi_ec_add_points(MPI_POINT result,
MPI_POINT p1, MPI_POINT p2,
struct mpi_ec_ctx *ctx)
{
switch (ctx->model) {
case MPI_EC_WEIERSTRASS:
add_points_weierstrass(result, p1, p2, ctx);
break;
case MPI_EC_MONTGOMERY:
add_points_montgomery(result, p1, p2, ctx);
break;
case MPI_EC_EDWARDS:
add_points_edwards(result, p1, p2, ctx);
break;
}
}
EXPORT_SYMBOL_GPL(mpi_ec_add_points);
/* Scalar point multiplication - the main function for ECC. If takes
* an integer SCALAR and a POINT as well as the usual context CTX.
* RESULT will be set to the resulting point.
*/
void mpi_ec_mul_point(MPI_POINT result,
MPI scalar, MPI_POINT point,
struct mpi_ec_ctx *ctx)
{
MPI x1, y1, z1, k, h, yy;
unsigned int i, loops;
struct gcry_mpi_point p1, p2, p1inv;
if (ctx->model == MPI_EC_EDWARDS) {
/* Simple left to right binary method. Algorithm 3.27 from
* {author={Hankerson, Darrel and Menezes, Alfred J. and Vanstone, Scott},
* title = {Guide to Elliptic Curve Cryptography},
* year = {2003}, isbn = {038795273X},
* url = {http://www.cacr.math.uwaterloo.ca/ecc/},
* publisher = {Springer-Verlag New York, Inc.}}
*/
unsigned int nbits;
int j;
if (mpi_cmp(scalar, ctx->p) >= 0)
nbits = mpi_get_nbits(scalar);
else
nbits = mpi_get_nbits(ctx->p);
mpi_set_ui(result->x, 0);
mpi_set_ui(result->y, 1);
mpi_set_ui(result->z, 1);
point_resize(point, ctx);
point_resize(result, ctx);
point_resize(point, ctx);
for (j = nbits-1; j >= 0; j--) {
mpi_ec_dup_point(result, result, ctx);
if (mpi_test_bit(scalar, j))
mpi_ec_add_points(result, result, point, ctx);
}
return;
} else if (ctx->model == MPI_EC_MONTGOMERY) {
unsigned int nbits;
int j;
struct gcry_mpi_point p1_, p2_;
MPI_POINT q1, q2, prd, sum;
unsigned long sw;
mpi_size_t rsize;
/* Compute scalar point multiplication with Montgomery Ladder.
* Note that we don't use Y-coordinate in the points at all.
* RESULT->Y will be filled by zero.
*/
nbits = mpi_get_nbits(scalar);
point_init(&p1);
point_init(&p2);
point_init(&p1_);
point_init(&p2_);
mpi_set_ui(p1.x, 1);
mpi_free(p2.x);
p2.x = mpi_copy(point->x);
mpi_set_ui(p2.z, 1);
point_resize(&p1, ctx);
point_resize(&p2, ctx);
point_resize(&p1_, ctx);
point_resize(&p2_, ctx);
mpi_resize(point->x, ctx->p->nlimbs);
point->x->nlimbs = ctx->p->nlimbs;
q1 = &p1;
q2 = &p2;
prd = &p1_;
sum = &p2_;
for (j = nbits-1; j >= 0; j--) {
MPI_POINT t;
sw = mpi_test_bit(scalar, j);
point_swap_cond(q1, q2, sw, ctx);
montgomery_ladder(prd, sum, q1, q2, point->x, ctx);
point_swap_cond(prd, sum, sw, ctx);
t = q1; q1 = prd; prd = t;
t = q2; q2 = sum; sum = t;
}
mpi_clear(result->y);
sw = (nbits & 1);
point_swap_cond(&p1, &p1_, sw, ctx);
rsize = p1.z->nlimbs;
MPN_NORMALIZE(p1.z->d, rsize);
if (rsize == 0) {
mpi_set_ui(result->x, 1);
mpi_set_ui(result->z, 0);
} else {
z1 = mpi_new(0);
ec_invm(z1, p1.z, ctx);
ec_mulm(result->x, p1.x, z1, ctx);
mpi_set_ui(result->z, 1);
mpi_free(z1);
}
point_free(&p1);
point_free(&p2);
point_free(&p1_);
point_free(&p2_);
return;
}
x1 = mpi_alloc_like(ctx->p);
y1 = mpi_alloc_like(ctx->p);
h = mpi_alloc_like(ctx->p);
k = mpi_copy(scalar);
yy = mpi_copy(point->y);
if (mpi_has_sign(k)) {
k->sign = 0;
ec_invm(yy, yy, ctx);
}
if (!mpi_cmp_ui(point->z, 1)) {
mpi_set(x1, point->x);
mpi_set(y1, yy);
} else {
MPI z2, z3;
z2 = mpi_alloc_like(ctx->p);
z3 = mpi_alloc_like(ctx->p);
ec_mulm(z2, point->z, point->z, ctx);
ec_mulm(z3, point->z, z2, ctx);
ec_invm(z2, z2, ctx);
ec_mulm(x1, point->x, z2, ctx);
ec_invm(z3, z3, ctx);
ec_mulm(y1, yy, z3, ctx);
mpi_free(z2);
mpi_free(z3);
}
z1 = mpi_copy(mpi_const(MPI_C_ONE));
mpi_mul(h, k, mpi_const(MPI_C_THREE)); /* h = 3k */
loops = mpi_get_nbits(h);
if (loops < 2) {
/* If SCALAR is zero, the above mpi_mul sets H to zero and thus
* LOOPs will be zero. To avoid an underflow of I in the main
* loop we set LOOP to 2 and the result to (0,0,0).
*/
loops = 2;
mpi_clear(result->x);
mpi_clear(result->y);
mpi_clear(result->z);
} else {
mpi_set(result->x, point->x);
mpi_set(result->y, yy);
mpi_set(result->z, point->z);
}
mpi_free(yy); yy = NULL;
p1.x = x1; x1 = NULL;
p1.y = y1; y1 = NULL;
p1.z = z1; z1 = NULL;
point_init(&p2);
point_init(&p1inv);
/* Invert point: y = p - y mod p */
point_set(&p1inv, &p1);
ec_subm(p1inv.y, ctx->p, p1inv.y, ctx);
for (i = loops-2; i > 0; i--) {
mpi_ec_dup_point(result, result, ctx);
if (mpi_test_bit(h, i) == 1 && mpi_test_bit(k, i) == 0) {
point_set(&p2, result);
mpi_ec_add_points(result, &p2, &p1, ctx);
}
if (mpi_test_bit(h, i) == 0 && mpi_test_bit(k, i) == 1) {
point_set(&p2, result);
mpi_ec_add_points(result, &p2, &p1inv, ctx);
}
}
point_free(&p1);
point_free(&p2);
point_free(&p1inv);
mpi_free(h);
mpi_free(k);
}
EXPORT_SYMBOL_GPL(mpi_ec_mul_point);
/* Return true if POINT is on the curve described by CTX. */
int mpi_ec_curve_point(MPI_POINT point, struct mpi_ec_ctx *ctx)
{
int res = 0;
MPI x, y, w;
x = mpi_new(0);
y = mpi_new(0);
w = mpi_new(0);
/* Check that the point is in range. This needs to be done here and
* not after conversion to affine coordinates.
*/
if (mpi_cmpabs(point->x, ctx->p) >= 0)
goto leave;
if (mpi_cmpabs(point->y, ctx->p) >= 0)
goto leave;
if (mpi_cmpabs(point->z, ctx->p) >= 0)
goto leave;
switch (ctx->model) {
case MPI_EC_WEIERSTRASS:
{
MPI xxx;
if (mpi_ec_get_affine(x, y, point, ctx))
goto leave;
xxx = mpi_new(0);
/* y^2 == x^3 + a·x + b */
ec_pow2(y, y, ctx);
ec_pow3(xxx, x, ctx);
ec_mulm(w, ctx->a, x, ctx);
ec_addm(w, w, ctx->b, ctx);
ec_addm(w, w, xxx, ctx);
if (!mpi_cmp(y, w))
res = 1;
mpi_free(xxx);
}
break;
case MPI_EC_MONTGOMERY:
{
#define xx y
/* With Montgomery curve, only X-coordinate is valid. */
if (mpi_ec_get_affine(x, NULL, point, ctx))
goto leave;
/* The equation is: b * y^2 == x^3 + a · x^2 + x */
/* We check if right hand is quadratic residue or not by
* Euler's criterion.
*/
/* CTX->A has (a-2)/4 and CTX->B has b^-1 */
ec_mulm(w, ctx->a, mpi_const(MPI_C_FOUR), ctx);
ec_addm(w, w, mpi_const(MPI_C_TWO), ctx);
ec_mulm(w, w, x, ctx);
ec_pow2(xx, x, ctx);
ec_addm(w, w, xx, ctx);
ec_addm(w, w, mpi_const(MPI_C_ONE), ctx);
ec_mulm(w, w, x, ctx);
ec_mulm(w, w, ctx->b, ctx);
#undef xx
/* Compute Euler's criterion: w^(p-1)/2 */
#define p_minus1 y
ec_subm(p_minus1, ctx->p, mpi_const(MPI_C_ONE), ctx);
mpi_rshift(p_minus1, p_minus1, 1);
ec_powm(w, w, p_minus1, ctx);
res = !mpi_cmp_ui(w, 1);
#undef p_minus1
}
break;
case MPI_EC_EDWARDS:
{
if (mpi_ec_get_affine(x, y, point, ctx))
goto leave;
mpi_resize(w, ctx->p->nlimbs);
w->nlimbs = ctx->p->nlimbs;
/* a · x^2 + y^2 - 1 - b · x^2 · y^2 == 0 */
ctx->pow2(x, x, ctx);
ctx->pow2(y, y, ctx);
if (ctx->dialect == ECC_DIALECT_ED25519)
ctx->subm(w, ctx->p, x, ctx);
else
ctx->mulm(w, ctx->a, x, ctx);
ctx->addm(w, w, y, ctx);
ctx->mulm(x, x, y, ctx);
ctx->mulm(x, x, ctx->b, ctx);
ctx->subm(w, w, x, ctx);
if (!mpi_cmp_ui(w, 1))
res = 1;
}
break;
}
leave:
mpi_free(w);
mpi_free(x);
mpi_free(y);
return res;
}
EXPORT_SYMBOL_GPL(mpi_ec_curve_point);
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