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Diffstat (limited to '')
| -rw-r--r-- | lib/mpi/ec.c | 1506 |
1 files changed, 1506 insertions, 0 deletions
diff --git a/lib/mpi/ec.c b/lib/mpi/ec.c new file mode 100644 index 000000000..40f5908e5 --- /dev/null +++ b/lib/mpi/ec.c @@ -0,0 +1,1506 @@ +/* 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); |