diff options
Diffstat (limited to 'lib/mpi')
| -rw-r--r-- | lib/mpi/Makefile | 6 | ||||
| -rw-r--r-- | lib/mpi/ec.c | 1506 | ||||
| -rw-r--r-- | lib/mpi/mpi-add.c | 155 | ||||
| -rw-r--r-- | lib/mpi/mpi-bit.c | 253 | ||||
| -rw-r--r-- | lib/mpi/mpi-cmp.c | 46 | ||||
| -rw-r--r-- | lib/mpi/mpi-div.c | 234 | ||||
| -rw-r--r-- | lib/mpi/mpi-internal.h | 53 | ||||
| -rw-r--r-- | lib/mpi/mpi-inv.c | 143 | ||||
| -rw-r--r-- | lib/mpi/mpi-mod.c | 155 | ||||
| -rw-r--r-- | lib/mpi/mpi-mul.c | 91 | ||||
| -rw-r--r-- | lib/mpi/mpicoder.c | 336 | ||||
| -rw-r--r-- | lib/mpi/mpih-div.c | 294 | ||||
| -rw-r--r-- | lib/mpi/mpih-mul.c | 25 | ||||
| -rw-r--r-- | lib/mpi/mpiutil.c | 204 |
14 files changed, 3490 insertions, 11 deletions
diff --git a/lib/mpi/Makefile b/lib/mpi/Makefile index 43b8fce14079..6e6ef9a34fe1 100644 --- a/lib/mpi/Makefile +++ b/lib/mpi/Makefile @@ -13,10 +13,16 @@ mpi-y = \ generic_mpih-rshift.o \ generic_mpih-sub1.o \ generic_mpih-add1.o \ + ec.o \ mpicoder.o \ + mpi-add.o \ mpi-bit.o \ mpi-cmp.o \ mpi-sub-ui.o \ + mpi-div.o \ + mpi-inv.o \ + mpi-mod.o \ + mpi-mul.o \ mpih-cmp.o \ mpih-div.o \ mpih-mul.o \ diff --git a/lib/mpi/ec.c b/lib/mpi/ec.c new file mode 100644 index 000000000000..40f5908e57a4 --- /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); diff --git a/lib/mpi/mpi-add.c b/lib/mpi/mpi-add.c new file mode 100644 index 000000000000..2cdae54c1bd0 --- /dev/null +++ b/lib/mpi/mpi-add.c @@ -0,0 +1,155 @@ +/* mpi-add.c - MPI functions + * Copyright (C) 1994, 1996, 1998, 2001, 2002, + * 2003 Free Software Foundation, Inc. + * + * This file is part of Libgcrypt. + * + * Note: This code is heavily based on the GNU MP Library. + * Actually it's the same code with only minor changes in the + * way the data is stored; this is to support the abstraction + * of an optional secure memory allocation which may be used + * to avoid revealing of sensitive data due to paging etc. + */ + +#include "mpi-internal.h" + +/**************** + * Add the unsigned integer V to the mpi-integer U and store the + * result in W. U and V may be the same. + */ +void mpi_add_ui(MPI w, MPI u, unsigned long v) +{ + mpi_ptr_t wp, up; + mpi_size_t usize, wsize; + int usign, wsign; + + usize = u->nlimbs; + usign = u->sign; + wsign = 0; + + /* If not space for W (and possible carry), increase space. */ + wsize = usize + 1; + if (w->alloced < wsize) + mpi_resize(w, wsize); + + /* These must be after realloc (U may be the same as W). */ + up = u->d; + wp = w->d; + + if (!usize) { /* simple */ + wp[0] = v; + wsize = v ? 1:0; + } else if (!usign) { /* mpi is not negative */ + mpi_limb_t cy; + cy = mpihelp_add_1(wp, up, usize, v); + wp[usize] = cy; + wsize = usize + cy; + } else { + /* The signs are different. Need exact comparison to determine + * which operand to subtract from which. + */ + if (usize == 1 && up[0] < v) { + wp[0] = v - up[0]; + wsize = 1; + } else { + mpihelp_sub_1(wp, up, usize, v); + /* Size can decrease with at most one limb. */ + wsize = usize - (wp[usize-1] == 0); + wsign = 1; + } + } + + w->nlimbs = wsize; + w->sign = wsign; +} + + +void mpi_add(MPI w, MPI u, MPI v) +{ + mpi_ptr_t wp, up, vp; + mpi_size_t usize, vsize, wsize; + int usign, vsign, wsign; + + if (u->nlimbs < v->nlimbs) { /* Swap U and V. */ + usize = v->nlimbs; + usign = v->sign; + vsize = u->nlimbs; + vsign = u->sign; + wsize = usize + 1; + RESIZE_IF_NEEDED(w, wsize); + /* These must be after realloc (u or v may be the same as w). */ + up = v->d; + vp = u->d; + } else { + usize = u->nlimbs; + usign = u->sign; + vsize = v->nlimbs; + vsign = v->sign; + wsize = usize + 1; + RESIZE_IF_NEEDED(w, wsize); + /* These must be after realloc (u or v may be the same as w). */ + up = u->d; + vp = v->d; + } + wp = w->d; + wsign = 0; + + if (!vsize) { /* simple */ + MPN_COPY(wp, up, usize); + wsize = usize; + wsign = usign; + } else if (usign != vsign) { /* different sign */ + /* This test is right since USIZE >= VSIZE */ + if (usize != vsize) { + mpihelp_sub(wp, up, usize, vp, vsize); + wsize = usize; + MPN_NORMALIZE(wp, wsize); + wsign = usign; + } else if (mpihelp_cmp(up, vp, usize) < 0) { + mpihelp_sub_n(wp, vp, up, usize); + wsize = usize; + MPN_NORMALIZE(wp, wsize); + if (!usign) + wsign = 1; + } else { + mpihelp_sub_n(wp, up, vp, usize); + wsize = usize; + MPN_NORMALIZE(wp, wsize); + if (usign) + wsign = 1; + } + } else { /* U and V have same sign. Add them. */ + mpi_limb_t cy = mpihelp_add(wp, up, usize, vp, vsize); + wp[usize] = cy; + wsize = usize + cy; + if (usign) + wsign = 1; + } + + w->nlimbs = wsize; + w->sign = wsign; +} +EXPORT_SYMBOL_GPL(mpi_add); + +void mpi_sub(MPI w, MPI u, MPI v) +{ + MPI vv = mpi_copy(v); + vv->sign = !vv->sign; + mpi_add(w, u, vv); + mpi_free(vv); +} + + +void mpi_addm(MPI w, MPI u, MPI v, MPI m) +{ + mpi_add(w, u, v); + mpi_mod(w, w, m); +} +EXPORT_SYMBOL_GPL(mpi_addm); + +void mpi_subm(MPI w, MPI u, MPI v, MPI m) +{ + mpi_sub(w, u, v); + mpi_mod(w, w, m); +} +EXPORT_SYMBOL_GPL(mpi_subm); diff --git a/lib/mpi/mpi-bit.c b/lib/mpi/mpi-bit.c index 503537e08436..142b680835df 100644 --- a/lib/mpi/mpi-bit.c +++ b/lib/mpi/mpi-bit.c @@ -1,4 +1,4 @@ -/* mpi-bit.c - MPI bit level fucntions +/* mpi-bit.c - MPI bit level functions * Copyright (C) 1998, 1999 Free Software Foundation, Inc. * * This file is part of GnuPG. @@ -32,6 +32,7 @@ void mpi_normalize(MPI a) for (; a->nlimbs && !a->d[a->nlimbs - 1]; a->nlimbs--) ; } +EXPORT_SYMBOL_GPL(mpi_normalize); /**************** * Return the number of bits in A. @@ -54,3 +55,253 @@ unsigned mpi_get_nbits(MPI a) return n; } EXPORT_SYMBOL_GPL(mpi_get_nbits); + +/**************** + * Test whether bit N is set. + */ +int mpi_test_bit(MPI a, unsigned int n) +{ + unsigned int limbno, bitno; + mpi_limb_t limb; + + limbno = n / BITS_PER_MPI_LIMB; + bitno = n % BITS_PER_MPI_LIMB; + + if (limbno >= a->nlimbs) + return 0; /* too far left: this is a 0 */ + limb = a->d[limbno]; + return (limb & (A_LIMB_1 << bitno)) ? 1 : 0; +} +EXPORT_SYMBOL_GPL(mpi_test_bit); + +/**************** + * Set bit N of A. + */ +void mpi_set_bit(MPI a, unsigned int n) +{ + unsigned int i, limbno, bitno; + + limbno = n / BITS_PER_MPI_LIMB; + bitno = n % BITS_PER_MPI_LIMB; + + if (limbno >= a->nlimbs) { + for (i = a->nlimbs; i < a->alloced; i++) + a->d[i] = 0; + mpi_resize(a, limbno+1); + a->nlimbs = limbno+1; + } + a->d[limbno] |= (A_LIMB_1<<bitno); +} + +/**************** + * Set bit N of A. and clear all bits above + */ +void mpi_set_highbit(MPI a, unsigned int n) +{ + unsigned int i, limbno, bitno; + + limbno = n / BITS_PER_MPI_LIMB; + bitno = n % BITS_PER_MPI_LIMB; + + if (limbno >= a->nlimbs) { + for (i = a->nlimbs; i < a->alloced; i++) + a->d[i] = 0; + mpi_resize(a, limbno+1); + a->nlimbs = limbno+1; + } + a->d[limbno] |= (A_LIMB_1<<bitno); + for (bitno++; bitno < BITS_PER_MPI_LIMB; bitno++) + a->d[limbno] &= ~(A_LIMB_1 << bitno); + a->nlimbs = limbno+1; +} +EXPORT_SYMBOL_GPL(mpi_set_highbit); + +/**************** + * clear bit N of A and all bits above + */ +void mpi_clear_highbit(MPI a, unsigned int n) +{ + unsigned int limbno, bitno; + + limbno = n / BITS_PER_MPI_LIMB; + bitno = n % BITS_PER_MPI_LIMB; + + if (limbno >= a->nlimbs) + return; /* not allocated, therefore no need to clear bits :-) */ + + for ( ; bitno < BITS_PER_MPI_LIMB; bitno++) + a->d[limbno] &= ~(A_LIMB_1 << bitno); + a->nlimbs = limbno+1; +} + +/**************** + * Clear bit N of A. + */ +void mpi_clear_bit(MPI a, unsigned int n) +{ + unsigned int limbno, bitno; + + limbno = n / BITS_PER_MPI_LIMB; + bitno = n % BITS_PER_MPI_LIMB; + + if (limbno >= a->nlimbs) + return; /* Don't need to clear this bit, it's far too left. */ + a->d[limbno] &= ~(A_LIMB_1 << bitno); +} +EXPORT_SYMBOL_GPL(mpi_clear_bit); + + +/**************** + * Shift A by COUNT limbs to the right + * This is used only within the MPI library + */ +void mpi_rshift_limbs(MPI a, unsigned int count) +{ + mpi_ptr_t ap = a->d; + mpi_size_t n = a->nlimbs; + unsigned int i; + + if (count >= n) { + a->nlimbs = 0; + return; + } + + for (i = 0; i < n - count; i++) + ap[i] = ap[i+count]; + ap[i] = 0; + a->nlimbs -= count; +} + +/* + * Shift A by N bits to the right. + */ +void mpi_rshift(MPI x, MPI a, unsigned int n) +{ + mpi_size_t xsize; + unsigned int i; + unsigned int nlimbs = (n/BITS_PER_MPI_LIMB); + unsigned int nbits = (n%BITS_PER_MPI_LIMB); + + if (x == a) { + /* In-place operation. */ + if (nlimbs >= x->nlimbs) { + x->nlimbs = 0; + return; + } + + if (nlimbs) { + for (i = 0; i < x->nlimbs - nlimbs; i++) + x->d[i] = x->d[i+nlimbs]; + x->d[i] = 0; + x->nlimbs -= nlimbs; + } + if (x->nlimbs && nbits) + mpihelp_rshift(x->d, x->d, x->nlimbs, nbits); + } else if (nlimbs) { + /* Copy and shift by more or equal bits than in a limb. */ + xsize = a->nlimbs; + x->sign = a->sign; + RESIZE_IF_NEEDED(x, xsize); + x->nlimbs = xsize; + for (i = 0; i < a->nlimbs; i++) + x->d[i] = a->d[i]; + x->nlimbs = i; + + if (nlimbs >= x->nlimbs) { + x->nlimbs = 0; + return; + } + + if (nlimbs) { + for (i = 0; i < x->nlimbs - nlimbs; i++) + x->d[i] = x->d[i+nlimbs]; + x->d[i] = 0; + x->nlimbs -= nlimbs; + } + + if (x->nlimbs && nbits) + mpihelp_rshift(x->d, x->d, x->nlimbs, nbits); + } else { + /* Copy and shift by less than bits in a limb. */ + xsize = a->nlimbs; + x->sign = a->sign; + RESIZE_IF_NEEDED(x, xsize); + x->nlimbs = xsize; + + if (xsize) { + if (nbits) + mpihelp_rshift(x->d, a->d, x->nlimbs, nbits); + else { + /* The rshift helper function is not specified for + * NBITS==0, thus we do a plain copy here. + */ + for (i = 0; i < x->nlimbs; i++) + x->d[i] = a->d[i]; + } + } + } + MPN_NORMALIZE(x->d, x->nlimbs); +} + +/**************** + * Shift A by COUNT limbs to the left + * This is used only within the MPI library + */ +void mpi_lshift_limbs(MPI a, unsigned int count) +{ + mpi_ptr_t ap; + int n = a->nlimbs; + int i; + + if (!count || !n) + return; + + RESIZE_IF_NEEDED(a, n+count); + + ap = a->d; + for (i = n-1; i >= 0; i--) + ap[i+count] = ap[i]; + for (i = 0; i < count; i++) + ap[i] = 0; + a->nlimbs += count; +} + +/* + * Shift A by N bits to the left. + */ +void mpi_lshift(MPI x, MPI a, unsigned int n) +{ + unsigned int nlimbs = (n/BITS_PER_MPI_LIMB); + unsigned int nbits = (n%BITS_PER_MPI_LIMB); + + if (x == a && !n) + return; /* In-place shift with an amount of zero. */ + + if (x != a) { + /* Copy A to X. */ + unsigned int alimbs = a->nlimbs; + int asign = a->sign; + mpi_ptr_t xp, ap; + + RESIZE_IF_NEEDED(x, alimbs+nlimbs+1); + xp = x->d; + ap = a->d; + MPN_COPY(xp, ap, alimbs); + x->nlimbs = alimbs; + x->flags = a->flags; + x->sign = asign; + } + + if (nlimbs && !nbits) { + /* Shift a full number of limbs. */ + mpi_lshift_limbs(x, nlimbs); + } else if (n) { + /* We use a very dump approach: Shift left by the number of + * limbs plus one and than fix it up by an rshift. + */ + mpi_lshift_limbs(x, nlimbs+1); + mpi_rshift(x, x, BITS_PER_MPI_LIMB - nbits); + } + + MPN_NORMALIZE(x->d, x->nlimbs); +} diff --git a/lib/mpi/mpi-cmp.c b/lib/mpi/mpi-cmp.c index d25e9e96c310..c4cfa3ff0581 100644 --- a/lib/mpi/mpi-cmp.c +++ b/lib/mpi/mpi-cmp.c @@ -41,28 +41,54 @@ int mpi_cmp_ui(MPI u, unsigned long v) } EXPORT_SYMBOL_GPL(mpi_cmp_ui); -int mpi_cmp(MPI u, MPI v) +static int do_mpi_cmp(MPI u, MPI v, int absmode) { - mpi_size_t usize, vsize; + mpi_size_t usize; + mpi_size_t vsize; + int usign; + int vsign; int cmp; mpi_normalize(u); mpi_normalize(v); + usize = u->nlimbs; vsize = v->nlimbs; - if (!u->sign && v->sign) + usign = absmode ? 0 : u->sign; + vsign = absmode ? 0 : v->sign; + + /* Compare sign bits. */ + + if (!usign && vsign) return 1; - if (u->sign && !v->sign) + if (usign && !vsign) return -1; - if (usize != vsize && !u->sign && !v->sign) + + /* U and V are either both positive or both negative. */ + + if (usize != vsize && !usign && !vsign) return usize - vsize; - if (usize != vsize && u->sign && v->sign) - return vsize - usize; + if (usize != vsize && usign && vsign) + return vsize + usize; if (!usize) return 0; cmp = mpihelp_cmp(u->d, v->d, usize); - if (u->sign) - return -cmp; - return cmp; + if (!cmp) + return 0; + if ((cmp < 0?1:0) == (usign?1:0)) + return 1; + + return -1; +} + +int mpi_cmp(MPI u, MPI v) +{ + return do_mpi_cmp(u, v, 0); } EXPORT_SYMBOL_GPL(mpi_cmp); + +int mpi_cmpabs(MPI u, MPI v) +{ + return do_mpi_cmp(u, v, 1); +} +EXPORT_SYMBOL_GPL(mpi_cmpabs); diff --git a/lib/mpi/mpi-div.c b/lib/mpi/mpi-div.c new file mode 100644 index 000000000000..45beab8b9e9e --- /dev/null +++ b/lib/mpi/mpi-div.c @@ -0,0 +1,234 @@ +/* mpi-div.c - MPI functions + * Copyright (C) 1994, 1996, 1998, 2001, 2002, + * 2003 Free Software Foundation, Inc. + * + * This file is part of Libgcrypt. + * + * Note: This code is heavily based on the GNU MP Library. + * Actually it's the same code with only minor changes in the + * way the data is stored; this is to support the abstraction + * of an optional secure memory allocation which may be used + * to avoid revealing of sensitive data due to paging etc. + */ + +#include "mpi-internal.h" +#include "longlong.h" + +void mpi_tdiv_qr(MPI quot, MPI rem, MPI num, MPI den); +void mpi_fdiv_qr(MPI quot, MPI rem, MPI dividend, MPI divisor); + +void mpi_fdiv_r(MPI rem, MPI dividend, MPI divisor) +{ + int divisor_sign = divisor->sign; + MPI temp_divisor = NULL; + + /* We need the original value of the divisor after the remainder has been + * preliminary calculated. We have to copy it to temporary space if it's + * the same variable as REM. + */ + if (rem == divisor) { + temp_divisor = mpi_copy(divisor); + divisor = temp_divisor; + } + + mpi_tdiv_r(rem, dividend, divisor); + + if (((divisor_sign?1:0) ^ (dividend->sign?1:0)) && rem->nlimbs) + mpi_add(rem, rem, divisor); + + if (temp_divisor) + mpi_free(temp_divisor); +} + +void mpi_fdiv_q(MPI quot, MPI dividend, MPI divisor) +{ + MPI tmp = mpi_alloc(mpi_get_nlimbs(quot)); + mpi_fdiv_qr(quot, tmp, dividend, divisor); + mpi_free(tmp); +} + +void mpi_fdiv_qr(MPI quot, MPI rem, MPI dividend, MPI divisor) +{ + int divisor_sign = divisor->sign; + MPI temp_divisor = NULL; + + if (quot == divisor || rem == divisor) { + temp_divisor = mpi_copy(divisor); + divisor = temp_divisor; + } + + mpi_tdiv_qr(quot, rem, dividend, divisor); + + if ((divisor_sign ^ dividend->sign) && rem->nlimbs) { + mpi_sub_ui(quot, quot, 1); + mpi_add(rem, rem, divisor); + } + + if (temp_divisor) + mpi_free(temp_divisor); +} + +/* If den == quot, den needs temporary storage. + * If den == rem, den needs temporary storage. + * If num == quot, num needs temporary storage. + * If den has temporary storage, it can be normalized while being copied, + * i.e no extra storage should be allocated. + */ + +void mpi_tdiv_r(MPI rem, MPI num, MPI den) +{ + mpi_tdiv_qr(NULL, rem, num, den); +} + +void mpi_tdiv_qr(MPI quot, MPI rem, MPI num, MPI den) +{ + mpi_ptr_t np, dp; + mpi_ptr_t qp, rp; + mpi_size_t nsize = num->nlimbs; + mpi_size_t dsize = den->nlimbs; + mpi_size_t qsize, rsize; + mpi_size_t sign_remainder = num->sign; + mpi_size_t sign_quotient = num->sign ^ den->sign; + unsigned int normalization_steps; + mpi_limb_t q_limb; + mpi_ptr_t marker[5]; + int markidx = 0; + + /* Ensure space is enough for quotient and remainder. + * We need space for an extra limb in the remainder, because it's + * up-shifted (normalized) below. + */ + rsize = nsize + 1; + mpi_resize(rem, rsize); + + qsize = rsize - dsize; /* qsize cannot be bigger than this. */ + if (qsize <= 0) { + if (num != rem) { + rem->nlimbs = num->nlimbs; + rem->sign = num->sign; + MPN_COPY(rem->d, num->d, nsize); + } + if (quot) { + /* This needs to follow the assignment to rem, in case the + * numerator and quotient are the same. + */ + quot->nlimbs = 0; + quot->sign = 0; + } + return; + } + + if (quot) + mpi_resize(quot, qsize); + + /* Read pointers here, when reallocation is finished. */ + np = num->d; + dp = den->d; + rp = rem->d; + + /* Optimize division by a single-limb divisor. */ + if (dsize == 1) { + mpi_limb_t rlimb; + if (quot) { + qp = quot->d; + rlimb = mpihelp_divmod_1(qp, np, nsize, dp[0]); + qsize -= qp[qsize - 1] == 0; + quot->nlimbs = qsize; + quot->sign = sign_quotient; + } else + rlimb = mpihelp_mod_1(np, nsize, dp[0]); + rp[0] = rlimb; + rsize = rlimb != 0?1:0; + rem->nlimbs = rsize; + rem->sign = sign_remainder; + return; + } + + + if (quot) { + qp = quot->d; + /* Make sure QP and NP point to different objects. Otherwise the + * numerator would be gradually overwritten by the quotient limbs. + */ + if (qp == np) { /* Copy NP object to temporary space. */ + np = marker[markidx++] = mpi_alloc_limb_space(nsize); + MPN_COPY(np, qp, nsize); + } + } else /* Put quotient at top of remainder. */ + qp = rp + dsize; + + normalization_steps = count_leading_zeros(dp[dsize - 1]); + + /* Normalize the denominator, i.e. make its most significant bit set by + * shifting it NORMALIZATION_STEPS bits to the left. Also shift the + * numerator the same number of steps (to keep the quotient the same!). + */ + if (normalization_steps) { + mpi_ptr_t tp; + mpi_limb_t nlimb; + + /* Shift up the denominator setting the most significant bit of + * the most significant word. Use temporary storage not to clobber + * the original contents of the denominator. + */ + tp = marker[markidx++] = mpi_alloc_limb_space(dsize); + mpihelp_lshift(tp, dp, dsize, normalization_steps); + dp = tp; + + /* Shift up the numerator, possibly introducing a new most + * significant word. Move the shifted numerator in the remainder + * meanwhile. + */ + nlimb = mpihelp_lshift(rp, np, nsize, normalization_steps); + if (nlimb) { + rp[nsize] = nlimb; + rsize = nsize + 1; + } else + rsize = nsize; + } else { + /* The denominator is already normalized, as required. Copy it to + * temporary space if it overlaps with the quotient or remainder. + */ + if (dp == rp || (quot && (dp == qp))) { + mpi_ptr_t tp; + + tp = marker[markidx++] = mpi_alloc_limb_space(dsize); + MPN_COPY(tp, dp, dsize); + dp = tp; + } + + /* Move the numerator to the remainder. */ + if (rp != np) + MPN_COPY(rp, np, nsize); + + rsize = nsize; + } + + q_limb = mpihelp_divrem(qp, 0, rp, rsize, dp, dsize); + + if (quot) { + qsize = rsize - dsize; + if (q_limb) { + qp[qsize] = q_limb; + qsize += 1; + } + + quot->nlimbs = qsize; + quot->sign = sign_quotient; + } + + rsize = dsize; + MPN_NORMALIZE(rp, rsize); + + if (normalization_steps && rsize) { + mpihelp_rshift(rp, rp, rsize, normalization_steps); + rsize -= rp[rsize - 1] == 0?1:0; + } + + rem->nlimbs = rsize; + rem->sign = sign_remainder; + while (markidx) { + markidx--; + mpi_free_limb_space(marker[markidx]); + } +} diff --git a/lib/mpi/mpi-internal.h b/lib/mpi/mpi-internal.h index 91df5f0b70f2..554002182db1 100644 --- a/lib/mpi/mpi-internal.h +++ b/lib/mpi/mpi-internal.h @@ -52,6 +52,12 @@ typedef mpi_limb_t *mpi_ptr_t; /* pointer to a limb */ typedef int mpi_size_t; /* (must be a signed type) */ +#define RESIZE_IF_NEEDED(a, b) \ + do { \ + if ((a)->alloced < (b)) \ + mpi_resize((a), (b)); \ + } while (0) + /* Copy N limbs from S to D. */ #define MPN_COPY(d, s, n) \ do { \ @@ -60,6 +66,14 @@ typedef int mpi_size_t; /* (must be a signed type) */ (d)[_i] = (s)[_i]; \ } while (0) +#define MPN_COPY_INCR(d, s, n) \ + do { \ + mpi_size_t _i; \ + for (_i = 0; _i < (n); _i++) \ + (d)[_i] = (s)[_i]; \ + } while (0) + + #define MPN_COPY_DECR(d, s, n) \ do { \ mpi_size_t _i; \ @@ -92,6 +106,38 @@ typedef int mpi_size_t; /* (must be a signed type) */ mul_n(prodp, up, vp, size, tspace); \ } while (0); +/* Divide the two-limb number in (NH,,NL) by D, with DI being the largest + * limb not larger than (2**(2*BITS_PER_MP_LIMB))/D - (2**BITS_PER_MP_LIMB). + * If this would yield overflow, DI should be the largest possible number + * (i.e., only ones). For correct operation, the most significant bit of D + * has to be set. Put the quotient in Q and the remainder in R. + */ +#define UDIV_QRNND_PREINV(q, r, nh, nl, d, di) \ + do { \ + mpi_limb_t _ql __maybe_unused; \ + mpi_limb_t _q, _r; \ + mpi_limb_t _xh, _xl; \ + umul_ppmm(_q, _ql, (nh), (di)); \ + _q += (nh); /* DI is 2**BITS_PER_MPI_LIMB too small */ \ + umul_ppmm(_xh, _xl, _q, (d)); \ + sub_ddmmss(_xh, _r, (nh), (nl), _xh, _xl); \ + if (_xh) { \ + sub_ddmmss(_xh, _r, _xh, _r, 0, (d)); \ + _q++; \ + if (_xh) { \ + sub_ddmmss(_xh, _r, _xh, _r, 0, (d)); \ + _q++; \ + } \ + } \ + if (_r >= (d)) { \ + _r -= (d); \ + _q++; \ + } \ + (r) = _r; \ + (q) = _q; \ + } while (0) + + /*-- mpiutil.c --*/ mpi_ptr_t mpi_alloc_limb_space(unsigned nlimbs); void mpi_free_limb_space(mpi_ptr_t a); @@ -135,6 +181,8 @@ int mpihelp_mul(mpi_ptr_t prodp, mpi_ptr_t up, mpi_size_t usize, void mpih_sqr_n_basecase(mpi_ptr_t prodp, mpi_ptr_t up, mpi_size_t size); void mpih_sqr_n(mpi_ptr_t prodp, mpi_ptr_t up, mpi_size_t size, mpi_ptr_t tspace); +void mpihelp_mul_n(mpi_ptr_t prodp, + mpi_ptr_t up, mpi_ptr_t vp, mpi_size_t size); int mpihelp_mul_karatsuba_case(mpi_ptr_t prodp, mpi_ptr_t up, mpi_size_t usize, @@ -146,9 +194,14 @@ mpi_limb_t mpihelp_mul_1(mpi_ptr_t res_ptr, mpi_ptr_t s1_ptr, mpi_size_t s1_size, mpi_limb_t s2_limb); /*-- mpih-div.c --*/ +mpi_limb_t mpihelp_mod_1(mpi_ptr_t dividend_ptr, mpi_size_t dividend_size, + mpi_limb_t divisor_limb); mpi_limb_t mpihelp_divrem(mpi_ptr_t qp, mpi_size_t qextra_limbs, mpi_ptr_t np, mpi_size_t nsize, mpi_ptr_t dp, mpi_size_t dsize); +mpi_limb_t mpihelp_divmod_1(mpi_ptr_t quot_ptr, + mpi_ptr_t dividend_ptr, mpi_size_t dividend_size, + mpi_limb_t divisor_limb); /*-- generic_mpih-[lr]shift.c --*/ mpi_limb_t mpihelp_lshift(mpi_ptr_t wp, mpi_ptr_t up, mpi_size_t usize, diff --git a/lib/mpi/mpi-inv.c b/lib/mpi/mpi-inv.c new file mode 100644 index 000000000000..61e37d18f793 --- /dev/null +++ b/lib/mpi/mpi-inv.c @@ -0,0 +1,143 @@ +/* mpi-inv.c - MPI functions + * Copyright (C) 1998, 2001, 2002, 2003 Free Software Foundation, Inc. + * + * 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" + +/**************** + * Calculate the multiplicative inverse X of A mod N + * That is: Find the solution x for + * 1 = (a*x) mod n + */ +int mpi_invm(MPI x, MPI a, MPI n) +{ + /* Extended Euclid's algorithm (See TAOCP Vol II, 4.5.2, Alg X) + * modified according to Michael Penk's solution for Exercise 35 + * with further enhancement + */ + MPI u, v, u1, u2 = NULL, u3, v1, v2 = NULL, v3, t1, t2 = NULL, t3; + unsigned int k; + int sign; + int odd; + + if (!mpi_cmp_ui(a, 0)) + return 0; /* Inverse does not exists. */ + if (!mpi_cmp_ui(n, 1)) + return 0; /* Inverse does not exists. */ + + u = mpi_copy(a); + v = mpi_copy(n); + + for (k = 0; !mpi_test_bit(u, 0) && !mpi_test_bit(v, 0); k++) { + mpi_rshift(u, u, 1); + mpi_rshift(v, v, 1); + } + odd = mpi_test_bit(v, 0); + + u1 = mpi_alloc_set_ui(1); + if (!odd) + u2 = mpi_alloc_set_ui(0); + u3 = mpi_copy(u); + v1 = mpi_copy(v); + if (!odd) { + v2 = mpi_alloc(mpi_get_nlimbs(u)); + mpi_sub(v2, u1, u); /* U is used as const 1 */ + } + v3 = mpi_copy(v); + if (mpi_test_bit(u, 0)) { /* u is odd */ + t1 = mpi_alloc_set_ui(0); + if (!odd) { + t2 = mpi_alloc_set_ui(1); + t2->sign = 1; + } + t3 = mpi_copy(v); + t3->sign = !t3->sign; + goto Y4; + } else { + t1 = mpi_alloc_set_ui(1); + if (!odd) + t2 = mpi_alloc_set_ui(0); + t3 = mpi_copy(u); + } + + do { + do { + if (!odd) { + if (mpi_test_bit(t1, 0) || mpi_test_bit(t2, 0)) { + /* one is odd */ + mpi_add(t1, t1, v); + mpi_sub(t2, t2, u); + } + mpi_rshift(t1, t1, 1); + mpi_rshift(t2, t2, 1); + mpi_rshift(t3, t3, 1); + } else { + if (mpi_test_bit(t1, 0)) + mpi_add(t1, t1, v); + mpi_rshift(t1, t1, 1); + mpi_rshift(t3, t3, 1); + } +Y4: + ; + } while (!mpi_test_bit(t3, 0)); /* while t3 is even */ + + if (!t3->sign) { + mpi_set(u1, t1); + if (!odd) + mpi_set(u2, t2); + mpi_set(u3, t3); + } else { + mpi_sub(v1, v, t1); + sign = u->sign; u->sign = !u->sign; + if (!odd) + mpi_sub(v2, u, t2); + u->sign = sign; + sign = t3->sign; t3->sign = !t3->sign; + mpi_set(v3, t3); + t3->sign = sign; + } + mpi_sub(t1, u1, v1); + if (!odd) + mpi_sub(t2, u2, v2); + mpi_sub(t3, u3, v3); + if (t1->sign) { + mpi_add(t1, t1, v); + if (!odd) + mpi_sub(t2, t2, u); + } + } while (mpi_cmp_ui(t3, 0)); /* while t3 != 0 */ + /* mpi_lshift( u3, k ); */ + mpi_set(x, u1); + + mpi_free(u1); + mpi_free(v1); + mpi_free(t1); + if (!odd) { + mpi_free(u2); + mpi_free(v2); + mpi_free(t2); + } + mpi_free(u3); + mpi_free(v3); + mpi_free(t3); + + mpi_free(u); + mpi_free(v); + return 1; +} +EXPORT_SYMBOL_GPL(mpi_invm); diff --git a/lib/mpi/mpi-mod.c b/lib/mpi/mpi-mod.c new file mode 100644 index 000000000000..47bc59edd4ff --- /dev/null +++ b/lib/mpi/mpi-mod.c @@ -0,0 +1,155 @@ +/* mpi-mod.c - Modular reduction + * Copyright (C) 1998, 1999, 2001, 2002, 2003, + * 2007 Free Software Foundation, Inc. + * + * This file is part of Libgcrypt. + */ + + +#include "mpi-internal.h" +#include "longlong.h" + +/* Context used with Barrett reduction. */ +struct barrett_ctx_s { + MPI m; /* The modulus - may not be modified. */ + int m_copied; /* If true, M needs to be released. */ + int k; + MPI y; + MPI r1; /* Helper MPI. */ + MPI r2; /* Helper MPI. */ + MPI r3; /* Helper MPI allocated on demand. */ +}; + + + +void mpi_mod(MPI rem, MPI dividend, MPI divisor) +{ + mpi_fdiv_r(rem, dividend, divisor); +} + +/* This function returns a new context for Barrett based operations on + * the modulus M. This context needs to be released using + * _gcry_mpi_barrett_free. If COPY is true M will be transferred to + * the context and the user may change M. If COPY is false, M may not + * be changed until gcry_mpi_barrett_free has been called. + */ +mpi_barrett_t mpi_barrett_init(MPI m, int copy) +{ + mpi_barrett_t ctx; + MPI tmp; + + mpi_normalize(m); + ctx = kcalloc(1, sizeof(*ctx), GFP_KERNEL); + + if (copy) { + ctx->m = mpi_copy(m); + ctx->m_copied = 1; + } else + ctx->m = m; + + ctx->k = mpi_get_nlimbs(m); + tmp = mpi_alloc(ctx->k + 1); + + /* Barrett precalculation: y = floor(b^(2k) / m). */ + mpi_set_ui(tmp, 1); + mpi_lshift_limbs(tmp, 2 * ctx->k); + mpi_fdiv_q(tmp, tmp, m); + + ctx->y = tmp; + ctx->r1 = mpi_alloc(2 * ctx->k + 1); + ctx->r2 = mpi_alloc(2 * ctx->k + 1); + + return ctx; +} + +void mpi_barrett_free(mpi_barrett_t ctx) +{ + if (ctx) { + mpi_free(ctx->y); + mpi_free(ctx->r1); + mpi_free(ctx->r2); + if (ctx->r3) + mpi_free(ctx->r3); + if (ctx->m_copied) + mpi_free(ctx->m); + kfree(ctx); + } +} + + +/* R = X mod M + * + * Using Barrett reduction. Before using this function + * _gcry_mpi_barrett_init must have been called to do the + * precalculations. CTX is the context created by this precalculation + * and also conveys M. If the Barret reduction could no be done a + * straightforward reduction method is used. + * + * We assume that these conditions are met: + * Input: x =(x_2k-1 ...x_0)_b + * m =(m_k-1 ....m_0)_b with m_k-1 != 0 + * Output: r = x mod m + */ +void mpi_mod_barrett(MPI r, MPI x, mpi_barrett_t ctx) +{ + MPI m = ctx->m; + int k = ctx->k; + MPI y = ctx->y; + MPI r1 = ctx->r1; + MPI r2 = ctx->r2; + int sign; + + mpi_normalize(x); + if (mpi_get_nlimbs(x) > 2*k) { + mpi_mod(r, x, m); + return; + } + + sign = x->sign; + x->sign = 0; + + /* 1. q1 = floor( x / b^k-1) + * q2 = q1 * y + * q3 = floor( q2 / b^k+1 ) + * Actually, we don't need qx, we can work direct on r2 + */ + mpi_set(r2, x); + mpi_rshift_limbs(r2, k-1); + mpi_mul(r2, r2, y); + mpi_rshift_limbs(r2, k+1); + + /* 2. r1 = x mod b^k+1 + * r2 = q3 * m mod b^k+1 + * r = r1 - r2 + * 3. if r < 0 then r = r + b^k+1 + */ + mpi_set(r1, x); + if (r1->nlimbs > k+1) /* Quick modulo operation. */ + r1->nlimbs = k+1; + mpi_mul(r2, r2, m); + if (r2->nlimbs > k+1) /* Quick modulo operation. */ + r2->nlimbs = k+1; + mpi_sub(r, r1, r2); + + if (mpi_has_sign(r)) { + if (!ctx->r3) { + ctx->r3 = mpi_alloc(k + 2); + mpi_set_ui(ctx->r3, 1); + mpi_lshift_limbs(ctx->r3, k + 1); + } + mpi_add(r, r, ctx->r3); + } + + /* 4. while r >= m do r = r - m */ + while (mpi_cmp(r, m) >= 0) + mpi_sub(r, r, m); + + x->sign = sign; +} + + +void mpi_mul_barrett(MPI w, MPI u, MPI v, mpi_barrett_t ctx) +{ + mpi_mul(w, u, v); + mpi_mod_barrett(w, w, ctx); +} diff --git a/lib/mpi/mpi-mul.c b/lib/mpi/mpi-mul.c new file mode 100644 index 000000000000..8f5fa200f297 --- /dev/null +++ b/lib/mpi/mpi-mul.c @@ -0,0 +1,91 @@ +/* mpi-mul.c - MPI functions + * Copyright (C) 1994, 1996, 1998, 2001, 2002, + * 2003 Free Software Foundation, Inc. + * + * This file is part of Libgcrypt. + * + * Note: This code is heavily based on the GNU MP Library. + * Actually it's the same code with only minor changes in the + * way the data is stored; this is to support the abstraction + * of an optional secure memory allocation which may be used + * to avoid revealing of sensitive data due to paging etc. + */ + +#include "mpi-internal.h" + +void mpi_mul(MPI w, MPI u, MPI v) +{ + mpi_size_t usize, vsize, wsize; + mpi_ptr_t up, vp, wp; + mpi_limb_t cy; + int usign, vsign, sign_product; + int assign_wp = 0; + mpi_ptr_t tmp_limb = NULL; + + if (u->nlimbs < v->nlimbs) { + /* Swap U and V. */ + usize = v->nlimbs; + usign = v->sign; + up = v->d; + vsize = u->nlimbs; + vsign = u->sign; + vp = u->d; + } else { + usize = u->nlimbs; + usign = u->sign; + up = u->d; + vsize = v->nlimbs; + vsign = v->sign; + vp = v->d; + } + sign_product = usign ^ vsign; + wp = w->d; + + /* Ensure W has space enough to store the result. */ + wsize = usize + vsize; + if (w->alloced < wsize) { + if (wp == up || wp == vp) { + wp = mpi_alloc_limb_space(wsize); + assign_wp = 1; + } else { + mpi_resize(w, wsize); + wp = w->d; + } + } else { /* Make U and V not overlap with W. */ + if (wp == up) { + /* W and U are identical. Allocate temporary space for U. */ + up = tmp_limb = mpi_alloc_limb_space(usize); + /* Is V identical too? Keep it identical with U. */ + if (wp == vp) + vp = up; + /* Copy to the temporary space. */ + MPN_COPY(up, wp, usize); + } else if (wp == vp) { + /* W and V are identical. Allocate temporary space for V. */ + vp = tmp_limb = mpi_alloc_limb_space(vsize); + /* Copy to the temporary space. */ + MPN_COPY(vp, wp, vsize); + } + } + + if (!vsize) + wsize = 0; + else { + mpihelp_mul(wp, up, usize, vp, vsize, &cy); + wsize -= cy ? 0:1; + } + + if (assign_wp) + mpi_assign_limb_space(w, wp, wsize); + w->nlimbs = wsize; + w->sign = sign_product; + if (tmp_limb) + mpi_free_limb_space(tmp_limb); +} + +void mpi_mulm(MPI w, MPI u, MPI v, MPI m) +{ + mpi_mul(w, u, v); + mpi_tdiv_r(w, w, m); +} +EXPORT_SYMBOL_GPL(mpi_mulm); diff --git a/lib/mpi/mpicoder.c b/lib/mpi/mpicoder.c index eead4b339466..7ea225b2204f 100644 --- a/lib/mpi/mpicoder.c +++ b/lib/mpi/mpicoder.c @@ -25,6 +25,7 @@ #include <linux/string.h> #include "mpi-internal.h" +#define MAX_EXTERN_SCAN_BYTES (16*1024*1024) #define MAX_EXTERN_MPI_BITS 16384 /** @@ -109,6 +110,112 @@ MPI mpi_read_from_buffer(const void *xbuffer, unsigned *ret_nread) } EXPORT_SYMBOL_GPL(mpi_read_from_buffer); +/**************** + * Fill the mpi VAL from the hex string in STR. + */ +int mpi_fromstr(MPI val, const char *str) +{ + int sign = 0; + int prepend_zero = 0; + int i, j, c, c1, c2; + unsigned int nbits, nbytes, nlimbs; + mpi_limb_t a; + + if (*str == '-') { + sign = 1; + str++; + } + + /* Skip optional hex prefix. */ + if (*str == '0' && str[1] == 'x') + str += 2; + + nbits = strlen(str); + if (nbits > MAX_EXTERN_SCAN_BYTES) { + mpi_clear(val); + return -EINVAL; + } + nbits *= 4; + if ((nbits % 8)) + prepend_zero = 1; + + nbytes = (nbits+7) / 8; + nlimbs = (nbytes+BYTES_PER_MPI_LIMB-1) / BYTES_PER_MPI_LIMB; + + if (val->alloced < nlimbs) + mpi_resize(val, nlimbs); + + i = BYTES_PER_MPI_LIMB - (nbytes % BYTES_PER_MPI_LIMB); + i %= BYTES_PER_MPI_LIMB; + j = val->nlimbs = nlimbs; + val->sign = sign; + for (; j > 0; j--) { + a = 0; + for (; i < BYTES_PER_MPI_LIMB; i++) { + if (prepend_zero) { + c1 = '0'; + prepend_zero = 0; + } else + c1 = *str++; + + if (!c1) { + mpi_clear(val); + return -EINVAL; + } + c2 = *str++; + if (!c2) { + mpi_clear(val); + return -EINVAL; + } + if (c1 >= '0' && c1 <= '9') + c = c1 - '0'; + else if (c1 >= 'a' && c1 <= 'f') + c = c1 - 'a' + 10; + else if (c1 >= 'A' && c1 <= 'F') + c = c1 - 'A' + 10; + else { + mpi_clear(val); + return -EINVAL; + } + c <<= 4; + if (c2 >= '0' && c2 <= '9') + c |= c2 - '0'; + else if (c2 >= 'a' && c2 <= 'f') + c |= c2 - 'a' + 10; + else if (c2 >= 'A' && c2 <= 'F') + c |= c2 - 'A' + 10; + else { + mpi_clear(val); + return -EINVAL; + } + a <<= 8; + a |= c; + } + i = 0; + val->d[j-1] = a; + } + + return 0; +} +EXPORT_SYMBOL_GPL(mpi_fromstr); + +MPI mpi_scanval(const char *string) +{ + MPI a; + + a = mpi_alloc(0); + if (!a) + return NULL; + + if (mpi_fromstr(a, string)) { + mpi_free(a); + return NULL; + } + mpi_normalize(a); + return a; +} +EXPORT_SYMBOL_GPL(mpi_scanval); + static int count_lzeros(MPI a) { mpi_limb_t alimb; @@ -413,3 +520,232 @@ MPI mpi_read_raw_from_sgl(struct scatterlist *sgl, unsigned int nbytes) return val; } EXPORT_SYMBOL_GPL(mpi_read_raw_from_sgl); + +/* Perform a two's complement operation on buffer P of size N bytes. */ +static void twocompl(unsigned char *p, unsigned int n) +{ + int i; + + for (i = n-1; i >= 0 && !p[i]; i--) + ; + if (i >= 0) { + if ((p[i] & 0x01)) + p[i] = (((p[i] ^ 0xfe) | 0x01) & 0xff); + else if ((p[i] & 0x02)) + p[i] = (((p[i] ^ 0xfc) | 0x02) & 0xfe); + else if ((p[i] & 0x04)) + p[i] = (((p[i] ^ 0xf8) | 0x04) & 0xfc); + else if ((p[i] & 0x08)) + p[i] = (((p[i] ^ 0xf0) | 0x08) & 0xf8); + else if ((p[i] & 0x10)) + p[i] = (((p[i] ^ 0xe0) | 0x10) & 0xf0); + else if ((p[i] & 0x20)) + p[i] = (((p[i] ^ 0xc0) | 0x20) & 0xe0); + else if ((p[i] & 0x40)) + p[i] = (((p[i] ^ 0x80) | 0x40) & 0xc0); + else + p[i] = 0x80; + + for (i--; i >= 0; i--) + p[i] ^= 0xff; + } +} + +int mpi_print(enum gcry_mpi_format format, unsigned char *buffer, + size_t buflen, size_t *nwritten, MPI a) +{ + unsigned int nbits = mpi_get_nbits(a); + size_t len; + size_t dummy_nwritten; + int negative; + + if (!nwritten) + nwritten = &dummy_nwritten; + + /* Libgcrypt does no always care to set clear the sign if the value + * is 0. For printing this is a bit of a surprise, in particular + * because if some of the formats don't support negative numbers but + * should be able to print a zero. Thus we need this extra test + * for a negative number. + */ + if (a->sign && mpi_cmp_ui(a, 0)) + negative = 1; + else + negative = 0; + + len = buflen; + *nwritten = 0; + if (format == GCRYMPI_FMT_STD) { + unsigned char *tmp; + int extra = 0; + unsigned int n; + + tmp = mpi_get_buffer(a, &n, NULL); + if (!tmp) + return -EINVAL; + + if (negative) { + twocompl(tmp, n); + if (!(*tmp & 0x80)) { + /* Need to extend the sign. */ + n++; + extra = 2; + } + } else if (n && (*tmp & 0x80)) { + /* Positive but the high bit of the returned buffer is set. + * Thus we need to print an extra leading 0x00 so that the + * output is interpreted as a positive number. + */ + n++; + extra = 1; + } + + if (buffer && n > len) { + /* The provided buffer is too short. */ + kfree(tmp); + return -E2BIG; + } + if (buffer) { + unsigned char *s = buffer; + + if (extra == 1) + *s++ = 0; + else if (extra) + *s++ = 0xff; + memcpy(s, tmp, n-!!extra); + } + kfree(tmp); + *nwritten = n; + return 0; + } else if (format == GCRYMPI_FMT_USG) { + unsigned int n = (nbits + 7)/8; + + /* Note: We ignore the sign for this format. */ + /* FIXME: for performance reasons we should put this into + * mpi_aprint because we can then use the buffer directly. + */ + + if (buffer && n > len) + return -E2BIG; + if (buffer) { + unsigned char *tmp; + + tmp = mpi_get_buffer(a, &n, NULL); + if (!tmp) + return -EINVAL; + memcpy(buffer, tmp, n); + kfree(tmp); + } + *nwritten = n; + return 0; + } else if (format == GCRYMPI_FMT_PGP) { + unsigned int n = (nbits + 7)/8; + + /* The PGP format can only handle unsigned integers. */ + if (negative) + return -EINVAL; + + if (buffer && n+2 > len) + return -E2BIG; + + if (buffer) { + unsigned char *tmp; + unsigned char *s = buffer; + + s[0] = nbits >> 8; + s[1] = nbits; + + tmp = mpi_get_buffer(a, &n, NULL); + if (!tmp) + return -EINVAL; + memcpy(s+2, tmp, n); + kfree(tmp); + } + *nwritten = n+2; + return 0; + } else if (format == GCRYMPI_FMT_SSH) { + unsigned char *tmp; + int extra = 0; + unsigned int n; + + tmp = mpi_get_buffer(a, &n, NULL); + if (!tmp) + return -EINVAL; + + if (negative) { + twocompl(tmp, n); + if (!(*tmp & 0x80)) { + /* Need to extend the sign. */ + n++; + extra = 2; + } + } else if (n && (*tmp & 0x80)) { + n++; + extra = 1; + } + + if (buffer && n+4 > len) { + kfree(tmp); + return -E2BIG; + } + + if (buffer) { + unsigned char *s = buffer; + + *s++ = n >> 24; + *s++ = n >> 16; + *s++ = n >> 8; + *s++ = n; + if (extra == 1) + *s++ = 0; + else if (extra) + *s++ = 0xff; + memcpy(s, tmp, n-!!extra); + } + kfree(tmp); + *nwritten = 4+n; + return 0; + } else if (format == GCRYMPI_FMT_HEX) { + unsigned char *tmp; + int i; + int extra = 0; + unsigned int n = 0; + + tmp = mpi_get_buffer(a, &n, NULL); + if (!tmp) + return -EINVAL; + if (!n || (*tmp & 0x80)) + extra = 2; + + if (buffer && 2*n + extra + negative + 1 > len) { + kfree(tmp); + return -E2BIG; + } + if (buffer) { + unsigned char *s = buffer; + + if (negative) + *s++ = '-'; + if (extra) { + *s++ = '0'; + *s++ = '0'; + } + + for (i = 0; i < n; i++) { + unsigned int c = tmp[i]; + + *s++ = (c >> 4) < 10 ? '0'+(c>>4) : 'A'+(c>>4)-10; + c &= 15; + *s++ = c < 10 ? '0'+c : 'A'+c-10; + } + *s++ = 0; + *nwritten = s - buffer; + } else { + *nwritten = 2*n + extra + negative + 1; + } + kfree(tmp); + return 0; + } else + return -EINVAL; +} +EXPORT_SYMBOL_GPL(mpi_print); diff --git a/lib/mpi/mpih-div.c b/lib/mpi/mpih-div.c index 913a519eb005..be70ee2e42d3 100644 --- a/lib/mpi/mpih-div.c +++ b/lib/mpi/mpih-div.c @@ -24,6 +24,150 @@ #define UDIV_TIME UMUL_TIME #endif + +mpi_limb_t +mpihelp_mod_1(mpi_ptr_t dividend_ptr, mpi_size_t dividend_size, + mpi_limb_t divisor_limb) +{ + mpi_size_t i; + mpi_limb_t n1, n0, r; + mpi_limb_t dummy __maybe_unused; + + /* Botch: Should this be handled at all? Rely on callers? */ + if (!dividend_size) + return 0; + + /* If multiplication is much faster than division, and the + * dividend is large, pre-invert the divisor, and use + * only multiplications in the inner loop. + * + * This test should be read: + * Does it ever help to use udiv_qrnnd_preinv? + * && Does what we save compensate for the inversion overhead? + */ + if (UDIV_TIME > (2 * UMUL_TIME + 6) + && (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME) { + int normalization_steps; + + normalization_steps = count_leading_zeros(divisor_limb); + if (normalization_steps) { + mpi_limb_t divisor_limb_inverted; + + divisor_limb <<= normalization_steps; + + /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The + * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the + * most significant bit (with weight 2**N) implicit. + * + * Special case for DIVISOR_LIMB == 100...000. + */ + if (!(divisor_limb << 1)) + divisor_limb_inverted = ~(mpi_limb_t)0; + else + udiv_qrnnd(divisor_limb_inverted, dummy, + -divisor_limb, 0, divisor_limb); + + n1 = dividend_ptr[dividend_size - 1]; + r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps); + + /* Possible optimization: + * if (r == 0 + * && divisor_limb > ((n1 << normalization_steps) + * | (dividend_ptr[dividend_size - 2] >> ...))) + * ...one division less... + */ + for (i = dividend_size - 2; i >= 0; i--) { + n0 = dividend_ptr[i]; + UDIV_QRNND_PREINV(dummy, r, r, + ((n1 << normalization_steps) + | (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))), + divisor_limb, divisor_limb_inverted); + n1 = n0; + } + UDIV_QRNND_PREINV(dummy, r, r, + n1 << normalization_steps, + divisor_limb, divisor_limb_inverted); + return r >> normalization_steps; + } else { + mpi_limb_t divisor_limb_inverted; + + /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The + * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the + * most significant bit (with weight 2**N) implicit. + * + * Special case for DIVISOR_LIMB == 100...000. + */ + if (!(divisor_limb << 1)) + divisor_limb_inverted = ~(mpi_limb_t)0; + else + udiv_qrnnd(divisor_limb_inverted, dummy, + -divisor_limb, 0, divisor_limb); + + i = dividend_size - 1; + r = dividend_ptr[i]; + + if (r >= divisor_limb) + r = 0; + else + i--; + + for ( ; i >= 0; i--) { + n0 = dividend_ptr[i]; + UDIV_QRNND_PREINV(dummy, r, r, + n0, divisor_limb, divisor_limb_inverted); + } + return r; + } + } else { + if (UDIV_NEEDS_NORMALIZATION) { + int normalization_steps; + + normalization_steps = count_leading_zeros(divisor_limb); + if (normalization_steps) { + divisor_limb <<= normalization_steps; + + n1 = dividend_ptr[dividend_size - 1]; + r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps); + + /* Possible optimization: + * if (r == 0 + * && divisor_limb > ((n1 << normalization_steps) + * | (dividend_ptr[dividend_size - 2] >> ...))) + * ...one division less... + */ + for (i = dividend_size - 2; i >= 0; i--) { + n0 = dividend_ptr[i]; + udiv_qrnnd(dummy, r, r, + ((n1 << normalization_steps) + | (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))), + divisor_limb); + n1 = n0; + } + udiv_qrnnd(dummy, r, r, + n1 << normalization_steps, + divisor_limb); + return r >> normalization_steps; + } + } + /* No normalization needed, either because udiv_qrnnd doesn't require + * it, or because DIVISOR_LIMB is already normalized. + */ + i = dividend_size - 1; + r = dividend_ptr[i]; + + if (r >= divisor_limb) + r = 0; + else + i--; + + for (; i >= 0; i--) { + n0 = dividend_ptr[i]; + udiv_qrnnd(dummy, r, r, n0, divisor_limb); + } + return r; + } +} + /* Divide num (NP/NSIZE) by den (DP/DSIZE) and write * the NSIZE-DSIZE least significant quotient limbs at QP * and the DSIZE long remainder at NP. If QEXTRA_LIMBS is @@ -221,3 +365,153 @@ q_test: return most_significant_q_limb; } + +/**************** + * Divide (DIVIDEND_PTR,,DIVIDEND_SIZE) by DIVISOR_LIMB. + * Write DIVIDEND_SIZE limbs of quotient at QUOT_PTR. + * Return the single-limb remainder. + * There are no constraints on the value of the divisor. + * + * QUOT_PTR and DIVIDEND_PTR might point to the same limb. + */ + +mpi_limb_t +mpihelp_divmod_1(mpi_ptr_t quot_ptr, + mpi_ptr_t dividend_ptr, mpi_size_t dividend_size, + mpi_limb_t divisor_limb) +{ + mpi_size_t i; + mpi_limb_t n1, n0, r; + mpi_limb_t dummy __maybe_unused; + + if (!dividend_size) + return 0; + + /* If multiplication is much faster than division, and the + * dividend is large, pre-invert the divisor, and use + * only multiplications in the inner loop. + * + * This test should be read: + * Does it ever help to use udiv_qrnnd_preinv? + * && Does what we save compensate for the inversion overhead? + */ + if (UDIV_TIME > (2 * UMUL_TIME + 6) + && (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME) { + int normalization_steps; + + normalization_steps = count_leading_zeros(divisor_limb); + if (normalization_steps) { + mpi_limb_t divisor_limb_inverted; + + divisor_limb <<= normalization_steps; + + /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The + * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the + * most significant bit (with weight 2**N) implicit. + */ + /* Special case for DIVISOR_LIMB == 100...000. */ + if (!(divisor_limb << 1)) + divisor_limb_inverted = ~(mpi_limb_t)0; + else + udiv_qrnnd(divisor_limb_inverted, dummy, + -divisor_limb, 0, divisor_limb); + + n1 = dividend_ptr[dividend_size - 1]; + r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps); + + /* Possible optimization: + * if (r == 0 + * && divisor_limb > ((n1 << normalization_steps) + * | (dividend_ptr[dividend_size - 2] >> ...))) + * ...one division less... + */ + for (i = dividend_size - 2; i >= 0; i--) { + n0 = dividend_ptr[i]; + UDIV_QRNND_PREINV(quot_ptr[i + 1], r, r, + ((n1 << normalization_steps) + | (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))), + divisor_limb, divisor_limb_inverted); + n1 = n0; + } + UDIV_QRNND_PREINV(quot_ptr[0], r, r, + n1 << normalization_steps, + divisor_limb, divisor_limb_inverted); + return r >> normalization_steps; + } else { + mpi_limb_t divisor_limb_inverted; + + /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The + * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the + * most significant bit (with weight 2**N) implicit. + */ + /* Special case for DIVISOR_LIMB == 100...000. */ + if (!(divisor_limb << 1)) + divisor_limb_inverted = ~(mpi_limb_t) 0; + else + udiv_qrnnd(divisor_limb_inverted, dummy, + -divisor_limb, 0, divisor_limb); + + i = dividend_size - 1; + r = dividend_ptr[i]; + + if (r >= divisor_limb) + r = 0; + else + quot_ptr[i--] = 0; + + for ( ; i >= 0; i--) { + n0 = dividend_ptr[i]; + UDIV_QRNND_PREINV(quot_ptr[i], r, r, + n0, divisor_limb, divisor_limb_inverted); + } + return r; + } + } else { + if (UDIV_NEEDS_NORMALIZATION) { + int normalization_steps; + + normalization_steps = count_leading_zeros(divisor_limb); + if (normalization_steps) { + divisor_limb <<= normalization_steps; + + n1 = dividend_ptr[dividend_size - 1]; + r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps); + + /* Possible optimization: + * if (r == 0 + * && divisor_limb > ((n1 << normalization_steps) + * | (dividend_ptr[dividend_size - 2] >> ...))) + * ...one division less... + */ + for (i = dividend_size - 2; i >= 0; i--) { + n0 = dividend_ptr[i]; + udiv_qrnnd(quot_ptr[i + 1], r, r, + ((n1 << normalization_steps) + | (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))), + divisor_limb); + n1 = n0; + } + udiv_qrnnd(quot_ptr[0], r, r, + n1 << normalization_steps, + divisor_limb); + return r >> normalization_steps; + } + } + /* No normalization needed, either because udiv_qrnnd doesn't require + * it, or because DIVISOR_LIMB is already normalized. + */ + i = dividend_size - 1; + r = dividend_ptr[i]; + + if (r >= divisor_limb) + r = 0; + else + quot_ptr[i--] = 0; + + for (; i >= 0; i--) { + n0 = dividend_ptr[i]; + udiv_qrnnd(quot_ptr[i], r, r, n0, divisor_limb); + } + return r; + } +} diff --git a/lib/mpi/mpih-mul.c b/lib/mpi/mpih-mul.c index a93647564054..e5f1c84e3c48 100644 --- a/lib/mpi/mpih-mul.c +++ b/lib/mpi/mpih-mul.c @@ -317,6 +317,31 @@ mpih_sqr_n(mpi_ptr_t prodp, mpi_ptr_t up, mpi_size_t size, mpi_ptr_t tspace) } } + +void mpihelp_mul_n(mpi_ptr_t prodp, + mpi_ptr_t up, mpi_ptr_t vp, mpi_size_t size) +{ + if (up == vp) { + if (size < KARATSUBA_THRESHOLD) + mpih_sqr_n_basecase(prodp, up, size); + else { + mpi_ptr_t tspace; + tspace = mpi_alloc_limb_space(2 * size); + mpih_sqr_n(prodp, up, size, tspace); + mpi_free_limb_space(tspace); + } + } else { + if (size < KARATSUBA_THRESHOLD) + mul_n_basecase(prodp, up, vp, size); + else { + mpi_ptr_t tspace; + tspace = mpi_alloc_limb_space(2 * size); + mul_n(prodp, up, vp, size, tspace); + mpi_free_limb_space(tspace); + } + } +} + int mpihelp_mul_karatsuba_case(mpi_ptr_t prodp, mpi_ptr_t up, mpi_size_t usize, diff --git a/lib/mpi/mpiutil.c b/lib/mpi/mpiutil.c index 4cd2b335cb7f..3c63710c20c6 100644 --- a/lib/mpi/mpiutil.c +++ b/lib/mpi/mpiutil.c @@ -20,6 +20,63 @@ #include "mpi-internal.h" +/* Constants allocated right away at startup. */ +static MPI constants[MPI_NUMBER_OF_CONSTANTS]; + +/* Initialize the MPI subsystem. This is called early and allows to + * do some initialization without taking care of threading issues. + */ +static int __init mpi_init(void) +{ + int idx; + unsigned long value; + + for (idx = 0; idx < MPI_NUMBER_OF_CONSTANTS; idx++) { + switch (idx) { + case MPI_C_ZERO: + value = 0; + break; + case MPI_C_ONE: + value = 1; + break; + case MPI_C_TWO: + value = 2; + break; + case MPI_C_THREE: + value = 3; + break; + case MPI_C_FOUR: + value = 4; + break; + case MPI_C_EIGHT: + value = 8; + break; + default: + pr_err("MPI: invalid mpi_const selector %d\n", idx); + return -EFAULT; + } + constants[idx] = mpi_alloc_set_ui(value); + constants[idx]->flags = (16|32); + } + + return 0; +} +postcore_initcall(mpi_init); + +/* Return a constant MPI descripbed by NO which is one of the + * MPI_C_xxx macros. There is no need to copy this returned value; it + * may be used directly. + */ +MPI mpi_const(enum gcry_mpi_constants no) +{ + if ((int)no < 0 || no > MPI_NUMBER_OF_CONSTANTS) + pr_err("MPI: invalid mpi_const selector %d\n", no); + if (!constants[no]) + pr_err("MPI: MPI subsystem not initialized\n"); + return constants[no]; +} +EXPORT_SYMBOL_GPL(mpi_const); + /**************** * Note: It was a bad idea to use the number of limbs to allocate * because on a alpha the limbs are large but we normally need @@ -106,6 +163,15 @@ int mpi_resize(MPI a, unsigned nlimbs) return 0; } +void mpi_clear(MPI a) +{ + if (!a) + return; + a->nlimbs = 0; + a->flags = 0; +} +EXPORT_SYMBOL_GPL(mpi_clear); + void mpi_free(MPI a) { if (!a) @@ -122,5 +188,143 @@ void mpi_free(MPI a) } EXPORT_SYMBOL_GPL(mpi_free); +/**************** + * Note: This copy function should not interpret the MPI + * but copy it transparently. + */ +MPI mpi_copy(MPI a) +{ + int i; + MPI b; + + if (a) { + b = mpi_alloc(a->nlimbs); + b->nlimbs = a->nlimbs; + b->sign = a->sign; + b->flags = a->flags; + b->flags &= ~(16|32); /* Reset the immutable and constant flags. */ + for (i = 0; i < b->nlimbs; i++) + b->d[i] = a->d[i]; + } else + b = NULL; + return b; +} + +/**************** + * This function allocates an MPI which is optimized to hold + * a value as large as the one given in the argument and allocates it + * with the same flags as A. + */ +MPI mpi_alloc_like(MPI a) +{ + MPI b; + + if (a) { + b = mpi_alloc(a->nlimbs); + b->nlimbs = 0; + b->sign = 0; + b->flags = a->flags; + } else + b = NULL; + + return b; +} + + +/* Set U into W and release U. If W is NULL only U will be released. */ +void mpi_snatch(MPI w, MPI u) +{ + if (w) { + mpi_assign_limb_space(w, u->d, u->alloced); + w->nlimbs = u->nlimbs; + w->sign = u->sign; + w->flags = u->flags; + u->alloced = 0; + u->nlimbs = 0; + u->d = NULL; + } + mpi_free(u); +} + + +MPI mpi_set(MPI w, MPI u) +{ + mpi_ptr_t wp, up; + mpi_size_t usize = u->nlimbs; + int usign = u->sign; + + if (!w) + w = mpi_alloc(mpi_get_nlimbs(u)); + RESIZE_IF_NEEDED(w, usize); + wp = w->d; + up = u->d; + MPN_COPY(wp, up, usize); + w->nlimbs = usize; + w->flags = u->flags; + w->flags &= ~(16|32); /* Reset the immutable and constant flags. */ + w->sign = usign; + return w; +} +EXPORT_SYMBOL_GPL(mpi_set); + +MPI mpi_set_ui(MPI w, unsigned long u) +{ + if (!w) + w = mpi_alloc(1); + /* FIXME: If U is 0 we have no need to resize and thus possible + * allocating the the limbs. + */ + RESIZE_IF_NEEDED(w, 1); + w->d[0] = u; + w->nlimbs = u ? 1 : 0; + w->sign = 0; + w->flags = 0; + return w; +} +EXPORT_SYMBOL_GPL(mpi_set_ui); + +MPI mpi_alloc_set_ui(unsigned long u) +{ + MPI w = mpi_alloc(1); + w->d[0] = u; + w->nlimbs = u ? 1 : 0; + w->sign = 0; + return w; +} + +/**************** + * Swap the value of A and B, when SWAP is 1. + * Leave the value when SWAP is 0. + * This implementation should be constant-time regardless of SWAP. + */ +void mpi_swap_cond(MPI a, MPI b, unsigned long swap) +{ + mpi_size_t i; + mpi_size_t nlimbs; + mpi_limb_t mask = ((mpi_limb_t)0) - swap; + mpi_limb_t x; + + if (a->alloced > b->alloced) + nlimbs = b->alloced; + else + nlimbs = a->alloced; + if (a->nlimbs > nlimbs || b->nlimbs > nlimbs) + return; + + for (i = 0; i < nlimbs; i++) { + x = mask & (a->d[i] ^ b->d[i]); + a->d[i] = a->d[i] ^ x; + b->d[i] = b->d[i] ^ x; + } + + x = mask & (a->nlimbs ^ b->nlimbs); + a->nlimbs = a->nlimbs ^ x; + b->nlimbs = b->nlimbs ^ x; + + x = mask & (a->sign ^ b->sign); + a->sign = a->sign ^ x; + b->sign = b->sign ^ x; +} + MODULE_DESCRIPTION("Multiprecision maths library"); MODULE_LICENSE("GPL"); |