+++ /dev/null
-/* 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);
projects / linux-2.6-block.git / blobdiff