diff options
Diffstat (limited to 'lib/crypto/mpi/ec.c')
| -rw-r--r-- | lib/crypto/mpi/ec.c | 1507 |
1 files changed, 0 insertions, 1507 deletions
diff --git a/lib/crypto/mpi/ec.c b/lib/crypto/mpi/ec.c deleted file mode 100644 index 4781f00982ef..000000000000 --- a/lib/crypto/mpi/ec.c +++ /dev/null @@ -1,1507 +0,0 @@ -/* 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->d = NULL; - ctx->t.two_inv_p = NULL; - - 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--) { - 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); - swap(q1, prd); - swap(q2, sum); - } - - 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); |