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1506 lines
36 KiB
1506 lines
36 KiB
/* ec.c - Elliptic Curve functions |
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* Copyright (C) 2007 Free Software Foundation, Inc. |
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* Copyright (C) 2013 g10 Code GmbH |
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* |
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* This file is part of Libgcrypt. |
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* |
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* Libgcrypt is free software; you can redistribute it and/or modify |
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* it under the terms of the GNU Lesser General Public License as |
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* published by the Free Software Foundation; either version 2.1 of |
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* the License, or (at your option) any later version. |
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* |
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* Libgcrypt is distributed in the hope that it will be useful, |
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* but WITHOUT ANY WARRANTY; without even the implied warranty of |
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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* GNU Lesser General Public License for more details. |
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* |
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* You should have received a copy of the GNU Lesser General Public |
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* License along with this program; if not, see <http://www.gnu.org/licenses/>. |
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*/ |
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#include "mpi-internal.h" |
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#include "longlong.h" |
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#define point_init(a) mpi_point_init((a)) |
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#define point_free(a) mpi_point_free_parts((a)) |
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#define log_error(fmt, ...) pr_err(fmt, ##__VA_ARGS__) |
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#define log_fatal(fmt, ...) pr_err(fmt, ##__VA_ARGS__) |
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#define DIM(v) (sizeof(v)/sizeof((v)[0])) |
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/* Create a new point option. NBITS gives the size in bits of one |
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* coordinate; it is only used to pre-allocate some resources and |
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* might also be passed as 0 to use a default value. |
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*/ |
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MPI_POINT mpi_point_new(unsigned int nbits) |
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{ |
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MPI_POINT p; |
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(void)nbits; /* Currently not used. */ |
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p = kmalloc(sizeof(*p), GFP_KERNEL); |
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if (p) |
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mpi_point_init(p); |
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return p; |
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} |
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EXPORT_SYMBOL_GPL(mpi_point_new); |
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/* Release the point object P. P may be NULL. */ |
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void mpi_point_release(MPI_POINT p) |
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{ |
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if (p) { |
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mpi_point_free_parts(p); |
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kfree(p); |
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} |
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} |
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EXPORT_SYMBOL_GPL(mpi_point_release); |
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/* Initialize the fields of a point object. gcry_mpi_point_free_parts |
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* may be used to release the fields. |
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*/ |
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void mpi_point_init(MPI_POINT p) |
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{ |
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p->x = mpi_new(0); |
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p->y = mpi_new(0); |
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p->z = mpi_new(0); |
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} |
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EXPORT_SYMBOL_GPL(mpi_point_init); |
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/* Release the parts of a point object. */ |
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void mpi_point_free_parts(MPI_POINT p) |
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{ |
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mpi_free(p->x); p->x = NULL; |
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mpi_free(p->y); p->y = NULL; |
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mpi_free(p->z); p->z = NULL; |
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} |
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EXPORT_SYMBOL_GPL(mpi_point_free_parts); |
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/* Set the value from S into D. */ |
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static void point_set(MPI_POINT d, MPI_POINT s) |
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{ |
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mpi_set(d->x, s->x); |
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mpi_set(d->y, s->y); |
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mpi_set(d->z, s->z); |
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} |
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static void point_resize(MPI_POINT p, struct mpi_ec_ctx *ctx) |
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{ |
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size_t nlimbs = ctx->p->nlimbs; |
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mpi_resize(p->x, nlimbs); |
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p->x->nlimbs = nlimbs; |
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mpi_resize(p->z, nlimbs); |
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p->z->nlimbs = nlimbs; |
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if (ctx->model != MPI_EC_MONTGOMERY) { |
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mpi_resize(p->y, nlimbs); |
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p->y->nlimbs = nlimbs; |
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} |
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} |
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static void point_swap_cond(MPI_POINT d, MPI_POINT s, unsigned long swap, |
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struct mpi_ec_ctx *ctx) |
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{ |
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mpi_swap_cond(d->x, s->x, swap); |
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if (ctx->model != MPI_EC_MONTGOMERY) |
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mpi_swap_cond(d->y, s->y, swap); |
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mpi_swap_cond(d->z, s->z, swap); |
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} |
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/* W = W mod P. */ |
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static void ec_mod(MPI w, struct mpi_ec_ctx *ec) |
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{ |
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if (ec->t.p_barrett) |
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mpi_mod_barrett(w, w, ec->t.p_barrett); |
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else |
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mpi_mod(w, w, ec->p); |
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} |
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static void ec_addm(MPI w, MPI u, MPI v, struct mpi_ec_ctx *ctx) |
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{ |
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mpi_add(w, u, v); |
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ec_mod(w, ctx); |
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} |
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static void ec_subm(MPI w, MPI u, MPI v, struct mpi_ec_ctx *ec) |
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{ |
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mpi_sub(w, u, v); |
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while (w->sign) |
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mpi_add(w, w, ec->p); |
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/*ec_mod(w, ec);*/ |
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} |
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static void ec_mulm(MPI w, MPI u, MPI v, struct mpi_ec_ctx *ctx) |
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{ |
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mpi_mul(w, u, v); |
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ec_mod(w, ctx); |
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} |
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/* W = 2 * U mod P. */ |
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static void ec_mul2(MPI w, MPI u, struct mpi_ec_ctx *ctx) |
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{ |
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mpi_lshift(w, u, 1); |
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ec_mod(w, ctx); |
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} |
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static void ec_powm(MPI w, const MPI b, const MPI e, |
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struct mpi_ec_ctx *ctx) |
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{ |
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mpi_powm(w, b, e, ctx->p); |
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/* mpi_abs(w); */ |
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} |
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/* Shortcut for |
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* ec_powm(B, B, mpi_const(MPI_C_TWO), ctx); |
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* for easier optimization. |
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*/ |
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static void ec_pow2(MPI w, const MPI b, struct mpi_ec_ctx *ctx) |
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{ |
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/* Using mpi_mul is slightly faster (at least on amd64). */ |
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/* mpi_powm(w, b, mpi_const(MPI_C_TWO), ctx->p); */ |
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ec_mulm(w, b, b, ctx); |
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} |
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/* Shortcut for |
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* ec_powm(B, B, mpi_const(MPI_C_THREE), ctx); |
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* for easier optimization. |
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*/ |
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static void ec_pow3(MPI w, const MPI b, struct mpi_ec_ctx *ctx) |
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{ |
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mpi_powm(w, b, mpi_const(MPI_C_THREE), ctx->p); |
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} |
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static void ec_invm(MPI x, MPI a, struct mpi_ec_ctx *ctx) |
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{ |
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if (!mpi_invm(x, a, ctx->p)) |
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log_error("ec_invm: inverse does not exist:\n"); |
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} |
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static void mpih_set_cond(mpi_ptr_t wp, mpi_ptr_t up, |
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mpi_size_t usize, unsigned long set) |
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{ |
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mpi_size_t i; |
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mpi_limb_t mask = ((mpi_limb_t)0) - set; |
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mpi_limb_t x; |
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for (i = 0; i < usize; i++) { |
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x = mask & (wp[i] ^ up[i]); |
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wp[i] = wp[i] ^ x; |
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} |
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} |
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/* Routines for 2^255 - 19. */ |
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#define LIMB_SIZE_25519 ((256+BITS_PER_MPI_LIMB-1)/BITS_PER_MPI_LIMB) |
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static void ec_addm_25519(MPI w, MPI u, MPI v, struct mpi_ec_ctx *ctx) |
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{ |
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mpi_ptr_t wp, up, vp; |
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mpi_size_t wsize = LIMB_SIZE_25519; |
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mpi_limb_t n[LIMB_SIZE_25519]; |
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mpi_limb_t borrow; |
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if (w->nlimbs != wsize || u->nlimbs != wsize || v->nlimbs != wsize) |
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log_bug("addm_25519: different sizes\n"); |
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memset(n, 0, sizeof(n)); |
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up = u->d; |
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vp = v->d; |
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wp = w->d; |
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mpihelp_add_n(wp, up, vp, wsize); |
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borrow = mpihelp_sub_n(wp, wp, ctx->p->d, wsize); |
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mpih_set_cond(n, ctx->p->d, wsize, (borrow != 0UL)); |
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mpihelp_add_n(wp, wp, n, wsize); |
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wp[LIMB_SIZE_25519-1] &= ~((mpi_limb_t)1 << (255 % BITS_PER_MPI_LIMB)); |
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} |
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static void ec_subm_25519(MPI w, MPI u, MPI v, struct mpi_ec_ctx *ctx) |
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{ |
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mpi_ptr_t wp, up, vp; |
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mpi_size_t wsize = LIMB_SIZE_25519; |
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mpi_limb_t n[LIMB_SIZE_25519]; |
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mpi_limb_t borrow; |
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if (w->nlimbs != wsize || u->nlimbs != wsize || v->nlimbs != wsize) |
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log_bug("subm_25519: different sizes\n"); |
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memset(n, 0, sizeof(n)); |
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up = u->d; |
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vp = v->d; |
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wp = w->d; |
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borrow = mpihelp_sub_n(wp, up, vp, wsize); |
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mpih_set_cond(n, ctx->p->d, wsize, (borrow != 0UL)); |
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mpihelp_add_n(wp, wp, n, wsize); |
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wp[LIMB_SIZE_25519-1] &= ~((mpi_limb_t)1 << (255 % BITS_PER_MPI_LIMB)); |
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} |
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static void ec_mulm_25519(MPI w, MPI u, MPI v, struct mpi_ec_ctx *ctx) |
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{ |
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mpi_ptr_t wp, up, vp; |
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mpi_size_t wsize = LIMB_SIZE_25519; |
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mpi_limb_t n[LIMB_SIZE_25519*2]; |
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mpi_limb_t m[LIMB_SIZE_25519+1]; |
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mpi_limb_t cy; |
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int msb; |
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(void)ctx; |
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if (w->nlimbs != wsize || u->nlimbs != wsize || v->nlimbs != wsize) |
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log_bug("mulm_25519: different sizes\n"); |
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up = u->d; |
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vp = v->d; |
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wp = w->d; |
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mpihelp_mul_n(n, up, vp, wsize); |
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memcpy(wp, n, wsize * BYTES_PER_MPI_LIMB); |
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wp[LIMB_SIZE_25519-1] &= ~((mpi_limb_t)1 << (255 % BITS_PER_MPI_LIMB)); |
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memcpy(m, n+LIMB_SIZE_25519-1, (wsize+1) * BYTES_PER_MPI_LIMB); |
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mpihelp_rshift(m, m, LIMB_SIZE_25519+1, (255 % BITS_PER_MPI_LIMB)); |
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memcpy(n, m, wsize * BYTES_PER_MPI_LIMB); |
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cy = mpihelp_lshift(m, m, LIMB_SIZE_25519, 4); |
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m[LIMB_SIZE_25519] = cy; |
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cy = mpihelp_add_n(m, m, n, wsize); |
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m[LIMB_SIZE_25519] += cy; |
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cy = mpihelp_add_n(m, m, n, wsize); |
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m[LIMB_SIZE_25519] += cy; |
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cy = mpihelp_add_n(m, m, n, wsize); |
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m[LIMB_SIZE_25519] += cy; |
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cy = mpihelp_add_n(wp, wp, m, wsize); |
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m[LIMB_SIZE_25519] += cy; |
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memset(m, 0, wsize * BYTES_PER_MPI_LIMB); |
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msb = (wp[LIMB_SIZE_25519-1] >> (255 % BITS_PER_MPI_LIMB)); |
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m[0] = (m[LIMB_SIZE_25519] * 2 + msb) * 19; |
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wp[LIMB_SIZE_25519-1] &= ~((mpi_limb_t)1 << (255 % BITS_PER_MPI_LIMB)); |
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mpihelp_add_n(wp, wp, m, wsize); |
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m[0] = 0; |
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cy = mpihelp_sub_n(wp, wp, ctx->p->d, wsize); |
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mpih_set_cond(m, ctx->p->d, wsize, (cy != 0UL)); |
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mpihelp_add_n(wp, wp, m, wsize); |
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} |
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static void ec_mul2_25519(MPI w, MPI u, struct mpi_ec_ctx *ctx) |
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{ |
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ec_addm_25519(w, u, u, ctx); |
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} |
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static void ec_pow2_25519(MPI w, const MPI b, struct mpi_ec_ctx *ctx) |
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{ |
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ec_mulm_25519(w, b, b, ctx); |
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} |
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/* Routines for 2^448 - 2^224 - 1. */ |
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#define LIMB_SIZE_448 ((448+BITS_PER_MPI_LIMB-1)/BITS_PER_MPI_LIMB) |
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#define LIMB_SIZE_HALF_448 ((LIMB_SIZE_448+1)/2) |
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static void ec_addm_448(MPI w, MPI u, MPI v, struct mpi_ec_ctx *ctx) |
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{ |
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mpi_ptr_t wp, up, vp; |
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mpi_size_t wsize = LIMB_SIZE_448; |
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mpi_limb_t n[LIMB_SIZE_448]; |
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mpi_limb_t cy; |
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if (w->nlimbs != wsize || u->nlimbs != wsize || v->nlimbs != wsize) |
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log_bug("addm_448: different sizes\n"); |
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memset(n, 0, sizeof(n)); |
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up = u->d; |
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vp = v->d; |
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wp = w->d; |
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cy = mpihelp_add_n(wp, up, vp, wsize); |
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mpih_set_cond(n, ctx->p->d, wsize, (cy != 0UL)); |
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mpihelp_sub_n(wp, wp, n, wsize); |
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} |
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static void ec_subm_448(MPI w, MPI u, MPI v, struct mpi_ec_ctx *ctx) |
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{ |
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mpi_ptr_t wp, up, vp; |
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mpi_size_t wsize = LIMB_SIZE_448; |
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mpi_limb_t n[LIMB_SIZE_448]; |
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mpi_limb_t borrow; |
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if (w->nlimbs != wsize || u->nlimbs != wsize || v->nlimbs != wsize) |
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log_bug("subm_448: different sizes\n"); |
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memset(n, 0, sizeof(n)); |
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up = u->d; |
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vp = v->d; |
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wp = w->d; |
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borrow = mpihelp_sub_n(wp, up, vp, wsize); |
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mpih_set_cond(n, ctx->p->d, wsize, (borrow != 0UL)); |
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mpihelp_add_n(wp, wp, n, wsize); |
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} |
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static void ec_mulm_448(MPI w, MPI u, MPI v, struct mpi_ec_ctx *ctx) |
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{ |
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mpi_ptr_t wp, up, vp; |
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mpi_size_t wsize = LIMB_SIZE_448; |
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mpi_limb_t n[LIMB_SIZE_448*2]; |
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mpi_limb_t a2[LIMB_SIZE_HALF_448]; |
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mpi_limb_t a3[LIMB_SIZE_HALF_448]; |
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mpi_limb_t b0[LIMB_SIZE_HALF_448]; |
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mpi_limb_t b1[LIMB_SIZE_HALF_448]; |
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mpi_limb_t cy; |
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int i; |
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#if (LIMB_SIZE_HALF_448 > LIMB_SIZE_448/2) |
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mpi_limb_t b1_rest, a3_rest; |
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#endif |
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if (w->nlimbs != wsize || u->nlimbs != wsize || v->nlimbs != wsize) |
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log_bug("mulm_448: different sizes\n"); |
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up = u->d; |
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vp = v->d; |
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wp = w->d; |
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mpihelp_mul_n(n, up, vp, wsize); |
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for (i = 0; i < (wsize + 1) / 2; i++) { |
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b0[i] = n[i]; |
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b1[i] = n[i+wsize/2]; |
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a2[i] = n[i+wsize]; |
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a3[i] = n[i+wsize+wsize/2]; |
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} |
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#if (LIMB_SIZE_HALF_448 > LIMB_SIZE_448/2) |
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b0[LIMB_SIZE_HALF_448-1] &= ((mpi_limb_t)1UL << 32)-1; |
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a2[LIMB_SIZE_HALF_448-1] &= ((mpi_limb_t)1UL << 32)-1; |
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b1_rest = 0; |
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a3_rest = 0; |
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for (i = (wsize + 1) / 2 - 1; i >= 0; i--) { |
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mpi_limb_t b1v, a3v; |
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b1v = b1[i]; |
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a3v = a3[i]; |
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b1[i] = (b1_rest << 32) | (b1v >> 32); |
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a3[i] = (a3_rest << 32) | (a3v >> 32); |
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b1_rest = b1v & (((mpi_limb_t)1UL << 32)-1); |
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a3_rest = a3v & (((mpi_limb_t)1UL << 32)-1); |
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} |
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#endif |
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cy = mpihelp_add_n(b0, b0, a2, LIMB_SIZE_HALF_448); |
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cy += mpihelp_add_n(b0, b0, a3, LIMB_SIZE_HALF_448); |
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for (i = 0; i < (wsize + 1) / 2; i++) |
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wp[i] = b0[i]; |
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#if (LIMB_SIZE_HALF_448 > LIMB_SIZE_448/2) |
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wp[LIMB_SIZE_HALF_448-1] &= (((mpi_limb_t)1UL << 32)-1); |
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#endif |
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#if (LIMB_SIZE_HALF_448 > LIMB_SIZE_448/2) |
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cy = b0[LIMB_SIZE_HALF_448-1] >> 32; |
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#endif |
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cy = mpihelp_add_1(b1, b1, LIMB_SIZE_HALF_448, cy); |
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cy += mpihelp_add_n(b1, b1, a2, LIMB_SIZE_HALF_448); |
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cy += mpihelp_add_n(b1, b1, a3, LIMB_SIZE_HALF_448); |
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cy += mpihelp_add_n(b1, b1, a3, LIMB_SIZE_HALF_448); |
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#if (LIMB_SIZE_HALF_448 > LIMB_SIZE_448/2) |
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b1_rest = 0; |
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for (i = (wsize + 1) / 2 - 1; i >= 0; i--) { |
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mpi_limb_t b1v = b1[i]; |
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b1[i] = (b1_rest << 32) | (b1v >> 32); |
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b1_rest = b1v & (((mpi_limb_t)1UL << 32)-1); |
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} |
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wp[LIMB_SIZE_HALF_448-1] |= (b1_rest << 32); |
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#endif |
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for (i = 0; i < wsize / 2; i++) |
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wp[i+(wsize + 1) / 2] = b1[i]; |
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#if (LIMB_SIZE_HALF_448 > LIMB_SIZE_448/2) |
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cy = b1[LIMB_SIZE_HALF_448-1]; |
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#endif |
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memset(n, 0, wsize * BYTES_PER_MPI_LIMB); |
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#if (LIMB_SIZE_HALF_448 > LIMB_SIZE_448/2) |
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n[LIMB_SIZE_HALF_448-1] = cy << 32; |
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#else |
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n[LIMB_SIZE_HALF_448] = cy; |
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#endif |
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n[0] = cy; |
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mpihelp_add_n(wp, wp, n, wsize); |
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memset(n, 0, wsize * BYTES_PER_MPI_LIMB); |
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cy = mpihelp_sub_n(wp, wp, ctx->p->d, wsize); |
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mpih_set_cond(n, ctx->p->d, wsize, (cy != 0UL)); |
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mpihelp_add_n(wp, wp, n, wsize); |
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} |
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static void ec_mul2_448(MPI w, MPI u, struct mpi_ec_ctx *ctx) |
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{ |
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ec_addm_448(w, u, u, ctx); |
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} |
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static void ec_pow2_448(MPI w, const MPI b, struct mpi_ec_ctx *ctx) |
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{ |
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ec_mulm_448(w, b, b, ctx); |
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} |
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struct field_table { |
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const char *p; |
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|
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/* computation routines for the field. */ |
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void (*addm)(MPI w, MPI u, MPI v, struct mpi_ec_ctx *ctx); |
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void (*subm)(MPI w, MPI u, MPI v, struct mpi_ec_ctx *ctx); |
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void (*mulm)(MPI w, MPI u, MPI v, struct mpi_ec_ctx *ctx); |
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void (*mul2)(MPI w, MPI u, struct mpi_ec_ctx *ctx); |
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void (*pow2)(MPI w, const MPI b, struct mpi_ec_ctx *ctx); |
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}; |
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|
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static const struct field_table field_table[] = { |
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{ |
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"0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFED", |
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ec_addm_25519, |
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ec_subm_25519, |
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ec_mulm_25519, |
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ec_mul2_25519, |
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ec_pow2_25519 |
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}, |
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{ |
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"0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE" |
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"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", |
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ec_addm_448, |
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ec_subm_448, |
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ec_mulm_448, |
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ec_mul2_448, |
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ec_pow2_448 |
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}, |
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{ NULL, NULL, NULL, NULL, NULL, NULL }, |
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}; |
|
|
|
/* 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);
|
|
|