security/nss/lib/freebl/ecl/ecp_jac.c

Thu, 22 Jan 2015 13:21:57 +0100

author
Michael Schloh von Bennewitz <michael@schloh.com>
date
Thu, 22 Jan 2015 13:21:57 +0100
branch
TOR_BUG_9701
changeset 15
b8a032363ba2
permissions
-rw-r--r--

Incorporate requested changes from Mozilla in review:
https://bugzilla.mozilla.org/show_bug.cgi?id=1123480#c6

michael@0 1 /* This Source Code Form is subject to the terms of the Mozilla Public
michael@0 2 * License, v. 2.0. If a copy of the MPL was not distributed with this
michael@0 3 * file, You can obtain one at http://mozilla.org/MPL/2.0/. */
michael@0 4
michael@0 5 #include "ecp.h"
michael@0 6 #include "mplogic.h"
michael@0 7 #include <stdlib.h>
michael@0 8 #ifdef ECL_DEBUG
michael@0 9 #include <assert.h>
michael@0 10 #endif
michael@0 11
michael@0 12 /* Converts a point P(px, py) from affine coordinates to Jacobian
michael@0 13 * projective coordinates R(rx, ry, rz). Assumes input is already
michael@0 14 * field-encoded using field_enc, and returns output that is still
michael@0 15 * field-encoded. */
michael@0 16 mp_err
michael@0 17 ec_GFp_pt_aff2jac(const mp_int *px, const mp_int *py, mp_int *rx,
michael@0 18 mp_int *ry, mp_int *rz, const ECGroup *group)
michael@0 19 {
michael@0 20 mp_err res = MP_OKAY;
michael@0 21
michael@0 22 if (ec_GFp_pt_is_inf_aff(px, py) == MP_YES) {
michael@0 23 MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, rz));
michael@0 24 } else {
michael@0 25 MP_CHECKOK(mp_copy(px, rx));
michael@0 26 MP_CHECKOK(mp_copy(py, ry));
michael@0 27 MP_CHECKOK(mp_set_int(rz, 1));
michael@0 28 if (group->meth->field_enc) {
michael@0 29 MP_CHECKOK(group->meth->field_enc(rz, rz, group->meth));
michael@0 30 }
michael@0 31 }
michael@0 32 CLEANUP:
michael@0 33 return res;
michael@0 34 }
michael@0 35
michael@0 36 /* Converts a point P(px, py, pz) from Jacobian projective coordinates to
michael@0 37 * affine coordinates R(rx, ry). P and R can share x and y coordinates.
michael@0 38 * Assumes input is already field-encoded using field_enc, and returns
michael@0 39 * output that is still field-encoded. */
michael@0 40 mp_err
michael@0 41 ec_GFp_pt_jac2aff(const mp_int *px, const mp_int *py, const mp_int *pz,
michael@0 42 mp_int *rx, mp_int *ry, const ECGroup *group)
michael@0 43 {
michael@0 44 mp_err res = MP_OKAY;
michael@0 45 mp_int z1, z2, z3;
michael@0 46
michael@0 47 MP_DIGITS(&z1) = 0;
michael@0 48 MP_DIGITS(&z2) = 0;
michael@0 49 MP_DIGITS(&z3) = 0;
michael@0 50 MP_CHECKOK(mp_init(&z1));
michael@0 51 MP_CHECKOK(mp_init(&z2));
michael@0 52 MP_CHECKOK(mp_init(&z3));
michael@0 53
michael@0 54 /* if point at infinity, then set point at infinity and exit */
michael@0 55 if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {
michael@0 56 MP_CHECKOK(ec_GFp_pt_set_inf_aff(rx, ry));
michael@0 57 goto CLEANUP;
michael@0 58 }
michael@0 59
michael@0 60 /* transform (px, py, pz) into (px / pz^2, py / pz^3) */
michael@0 61 if (mp_cmp_d(pz, 1) == 0) {
michael@0 62 MP_CHECKOK(mp_copy(px, rx));
michael@0 63 MP_CHECKOK(mp_copy(py, ry));
michael@0 64 } else {
michael@0 65 MP_CHECKOK(group->meth->field_div(NULL, pz, &z1, group->meth));
michael@0 66 MP_CHECKOK(group->meth->field_sqr(&z1, &z2, group->meth));
michael@0 67 MP_CHECKOK(group->meth->field_mul(&z1, &z2, &z3, group->meth));
michael@0 68 MP_CHECKOK(group->meth->field_mul(px, &z2, rx, group->meth));
michael@0 69 MP_CHECKOK(group->meth->field_mul(py, &z3, ry, group->meth));
michael@0 70 }
michael@0 71
michael@0 72 CLEANUP:
michael@0 73 mp_clear(&z1);
michael@0 74 mp_clear(&z2);
michael@0 75 mp_clear(&z3);
michael@0 76 return res;
michael@0 77 }
michael@0 78
michael@0 79 /* Checks if point P(px, py, pz) is at infinity. Uses Jacobian
michael@0 80 * coordinates. */
michael@0 81 mp_err
michael@0 82 ec_GFp_pt_is_inf_jac(const mp_int *px, const mp_int *py, const mp_int *pz)
michael@0 83 {
michael@0 84 return mp_cmp_z(pz);
michael@0 85 }
michael@0 86
michael@0 87 /* Sets P(px, py, pz) to be the point at infinity. Uses Jacobian
michael@0 88 * coordinates. */
michael@0 89 mp_err
michael@0 90 ec_GFp_pt_set_inf_jac(mp_int *px, mp_int *py, mp_int *pz)
michael@0 91 {
michael@0 92 mp_zero(pz);
michael@0 93 return MP_OKAY;
michael@0 94 }
michael@0 95
michael@0 96 /* Computes R = P + Q where R is (rx, ry, rz), P is (px, py, pz) and Q is
michael@0 97 * (qx, qy, 1). Elliptic curve points P, Q, and R can all be identical.
michael@0 98 * Uses mixed Jacobian-affine coordinates. Assumes input is already
michael@0 99 * field-encoded using field_enc, and returns output that is still
michael@0 100 * field-encoded. Uses equation (2) from Brown, Hankerson, Lopez, and
michael@0 101 * Menezes. Software Implementation of the NIST Elliptic Curves Over Prime
michael@0 102 * Fields. */
michael@0 103 mp_err
michael@0 104 ec_GFp_pt_add_jac_aff(const mp_int *px, const mp_int *py, const mp_int *pz,
michael@0 105 const mp_int *qx, const mp_int *qy, mp_int *rx,
michael@0 106 mp_int *ry, mp_int *rz, const ECGroup *group)
michael@0 107 {
michael@0 108 mp_err res = MP_OKAY;
michael@0 109 mp_int A, B, C, D, C2, C3;
michael@0 110
michael@0 111 MP_DIGITS(&A) = 0;
michael@0 112 MP_DIGITS(&B) = 0;
michael@0 113 MP_DIGITS(&C) = 0;
michael@0 114 MP_DIGITS(&D) = 0;
michael@0 115 MP_DIGITS(&C2) = 0;
michael@0 116 MP_DIGITS(&C3) = 0;
michael@0 117 MP_CHECKOK(mp_init(&A));
michael@0 118 MP_CHECKOK(mp_init(&B));
michael@0 119 MP_CHECKOK(mp_init(&C));
michael@0 120 MP_CHECKOK(mp_init(&D));
michael@0 121 MP_CHECKOK(mp_init(&C2));
michael@0 122 MP_CHECKOK(mp_init(&C3));
michael@0 123
michael@0 124 /* If either P or Q is the point at infinity, then return the other
michael@0 125 * point */
michael@0 126 if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {
michael@0 127 MP_CHECKOK(ec_GFp_pt_aff2jac(qx, qy, rx, ry, rz, group));
michael@0 128 goto CLEANUP;
michael@0 129 }
michael@0 130 if (ec_GFp_pt_is_inf_aff(qx, qy) == MP_YES) {
michael@0 131 MP_CHECKOK(mp_copy(px, rx));
michael@0 132 MP_CHECKOK(mp_copy(py, ry));
michael@0 133 MP_CHECKOK(mp_copy(pz, rz));
michael@0 134 goto CLEANUP;
michael@0 135 }
michael@0 136
michael@0 137 /* A = qx * pz^2, B = qy * pz^3 */
michael@0 138 MP_CHECKOK(group->meth->field_sqr(pz, &A, group->meth));
michael@0 139 MP_CHECKOK(group->meth->field_mul(&A, pz, &B, group->meth));
michael@0 140 MP_CHECKOK(group->meth->field_mul(&A, qx, &A, group->meth));
michael@0 141 MP_CHECKOK(group->meth->field_mul(&B, qy, &B, group->meth));
michael@0 142
michael@0 143 /* C = A - px, D = B - py */
michael@0 144 MP_CHECKOK(group->meth->field_sub(&A, px, &C, group->meth));
michael@0 145 MP_CHECKOK(group->meth->field_sub(&B, py, &D, group->meth));
michael@0 146
michael@0 147 /* C2 = C^2, C3 = C^3 */
michael@0 148 MP_CHECKOK(group->meth->field_sqr(&C, &C2, group->meth));
michael@0 149 MP_CHECKOK(group->meth->field_mul(&C, &C2, &C3, group->meth));
michael@0 150
michael@0 151 /* rz = pz * C */
michael@0 152 MP_CHECKOK(group->meth->field_mul(pz, &C, rz, group->meth));
michael@0 153
michael@0 154 /* C = px * C^2 */
michael@0 155 MP_CHECKOK(group->meth->field_mul(px, &C2, &C, group->meth));
michael@0 156 /* A = D^2 */
michael@0 157 MP_CHECKOK(group->meth->field_sqr(&D, &A, group->meth));
michael@0 158
michael@0 159 /* rx = D^2 - (C^3 + 2 * (px * C^2)) */
michael@0 160 MP_CHECKOK(group->meth->field_add(&C, &C, rx, group->meth));
michael@0 161 MP_CHECKOK(group->meth->field_add(&C3, rx, rx, group->meth));
michael@0 162 MP_CHECKOK(group->meth->field_sub(&A, rx, rx, group->meth));
michael@0 163
michael@0 164 /* C3 = py * C^3 */
michael@0 165 MP_CHECKOK(group->meth->field_mul(py, &C3, &C3, group->meth));
michael@0 166
michael@0 167 /* ry = D * (px * C^2 - rx) - py * C^3 */
michael@0 168 MP_CHECKOK(group->meth->field_sub(&C, rx, ry, group->meth));
michael@0 169 MP_CHECKOK(group->meth->field_mul(&D, ry, ry, group->meth));
michael@0 170 MP_CHECKOK(group->meth->field_sub(ry, &C3, ry, group->meth));
michael@0 171
michael@0 172 CLEANUP:
michael@0 173 mp_clear(&A);
michael@0 174 mp_clear(&B);
michael@0 175 mp_clear(&C);
michael@0 176 mp_clear(&D);
michael@0 177 mp_clear(&C2);
michael@0 178 mp_clear(&C3);
michael@0 179 return res;
michael@0 180 }
michael@0 181
michael@0 182 /* Computes R = 2P. Elliptic curve points P and R can be identical. Uses
michael@0 183 * Jacobian coordinates.
michael@0 184 *
michael@0 185 * Assumes input is already field-encoded using field_enc, and returns
michael@0 186 * output that is still field-encoded.
michael@0 187 *
michael@0 188 * This routine implements Point Doubling in the Jacobian Projective
michael@0 189 * space as described in the paper "Efficient elliptic curve exponentiation
michael@0 190 * using mixed coordinates", by H. Cohen, A Miyaji, T. Ono.
michael@0 191 */
michael@0 192 mp_err
michael@0 193 ec_GFp_pt_dbl_jac(const mp_int *px, const mp_int *py, const mp_int *pz,
michael@0 194 mp_int *rx, mp_int *ry, mp_int *rz, const ECGroup *group)
michael@0 195 {
michael@0 196 mp_err res = MP_OKAY;
michael@0 197 mp_int t0, t1, M, S;
michael@0 198
michael@0 199 MP_DIGITS(&t0) = 0;
michael@0 200 MP_DIGITS(&t1) = 0;
michael@0 201 MP_DIGITS(&M) = 0;
michael@0 202 MP_DIGITS(&S) = 0;
michael@0 203 MP_CHECKOK(mp_init(&t0));
michael@0 204 MP_CHECKOK(mp_init(&t1));
michael@0 205 MP_CHECKOK(mp_init(&M));
michael@0 206 MP_CHECKOK(mp_init(&S));
michael@0 207
michael@0 208 if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {
michael@0 209 MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, rz));
michael@0 210 goto CLEANUP;
michael@0 211 }
michael@0 212
michael@0 213 if (mp_cmp_d(pz, 1) == 0) {
michael@0 214 /* M = 3 * px^2 + a */
michael@0 215 MP_CHECKOK(group->meth->field_sqr(px, &t0, group->meth));
michael@0 216 MP_CHECKOK(group->meth->field_add(&t0, &t0, &M, group->meth));
michael@0 217 MP_CHECKOK(group->meth->field_add(&t0, &M, &t0, group->meth));
michael@0 218 MP_CHECKOK(group->meth->
michael@0 219 field_add(&t0, &group->curvea, &M, group->meth));
michael@0 220 } else if (mp_cmp_int(&group->curvea, -3) == 0) {
michael@0 221 /* M = 3 * (px + pz^2) * (px - pz^2) */
michael@0 222 MP_CHECKOK(group->meth->field_sqr(pz, &M, group->meth));
michael@0 223 MP_CHECKOK(group->meth->field_add(px, &M, &t0, group->meth));
michael@0 224 MP_CHECKOK(group->meth->field_sub(px, &M, &t1, group->meth));
michael@0 225 MP_CHECKOK(group->meth->field_mul(&t0, &t1, &M, group->meth));
michael@0 226 MP_CHECKOK(group->meth->field_add(&M, &M, &t0, group->meth));
michael@0 227 MP_CHECKOK(group->meth->field_add(&t0, &M, &M, group->meth));
michael@0 228 } else {
michael@0 229 /* M = 3 * (px^2) + a * (pz^4) */
michael@0 230 MP_CHECKOK(group->meth->field_sqr(px, &t0, group->meth));
michael@0 231 MP_CHECKOK(group->meth->field_add(&t0, &t0, &M, group->meth));
michael@0 232 MP_CHECKOK(group->meth->field_add(&t0, &M, &t0, group->meth));
michael@0 233 MP_CHECKOK(group->meth->field_sqr(pz, &M, group->meth));
michael@0 234 MP_CHECKOK(group->meth->field_sqr(&M, &M, group->meth));
michael@0 235 MP_CHECKOK(group->meth->
michael@0 236 field_mul(&M, &group->curvea, &M, group->meth));
michael@0 237 MP_CHECKOK(group->meth->field_add(&M, &t0, &M, group->meth));
michael@0 238 }
michael@0 239
michael@0 240 /* rz = 2 * py * pz */
michael@0 241 /* t0 = 4 * py^2 */
michael@0 242 if (mp_cmp_d(pz, 1) == 0) {
michael@0 243 MP_CHECKOK(group->meth->field_add(py, py, rz, group->meth));
michael@0 244 MP_CHECKOK(group->meth->field_sqr(rz, &t0, group->meth));
michael@0 245 } else {
michael@0 246 MP_CHECKOK(group->meth->field_add(py, py, &t0, group->meth));
michael@0 247 MP_CHECKOK(group->meth->field_mul(&t0, pz, rz, group->meth));
michael@0 248 MP_CHECKOK(group->meth->field_sqr(&t0, &t0, group->meth));
michael@0 249 }
michael@0 250
michael@0 251 /* S = 4 * px * py^2 = px * (2 * py)^2 */
michael@0 252 MP_CHECKOK(group->meth->field_mul(px, &t0, &S, group->meth));
michael@0 253
michael@0 254 /* rx = M^2 - 2 * S */
michael@0 255 MP_CHECKOK(group->meth->field_add(&S, &S, &t1, group->meth));
michael@0 256 MP_CHECKOK(group->meth->field_sqr(&M, rx, group->meth));
michael@0 257 MP_CHECKOK(group->meth->field_sub(rx, &t1, rx, group->meth));
michael@0 258
michael@0 259 /* ry = M * (S - rx) - 8 * py^4 */
michael@0 260 MP_CHECKOK(group->meth->field_sqr(&t0, &t1, group->meth));
michael@0 261 if (mp_isodd(&t1)) {
michael@0 262 MP_CHECKOK(mp_add(&t1, &group->meth->irr, &t1));
michael@0 263 }
michael@0 264 MP_CHECKOK(mp_div_2(&t1, &t1));
michael@0 265 MP_CHECKOK(group->meth->field_sub(&S, rx, &S, group->meth));
michael@0 266 MP_CHECKOK(group->meth->field_mul(&M, &S, &M, group->meth));
michael@0 267 MP_CHECKOK(group->meth->field_sub(&M, &t1, ry, group->meth));
michael@0 268
michael@0 269 CLEANUP:
michael@0 270 mp_clear(&t0);
michael@0 271 mp_clear(&t1);
michael@0 272 mp_clear(&M);
michael@0 273 mp_clear(&S);
michael@0 274 return res;
michael@0 275 }
michael@0 276
michael@0 277 /* by default, this routine is unused and thus doesn't need to be compiled */
michael@0 278 #ifdef ECL_ENABLE_GFP_PT_MUL_JAC
michael@0 279 /* Computes R = nP where R is (rx, ry) and P is (px, py). The parameters
michael@0 280 * a, b and p are the elliptic curve coefficients and the prime that
michael@0 281 * determines the field GFp. Elliptic curve points P and R can be
michael@0 282 * identical. Uses mixed Jacobian-affine coordinates. Assumes input is
michael@0 283 * already field-encoded using field_enc, and returns output that is still
michael@0 284 * field-encoded. Uses 4-bit window method. */
michael@0 285 mp_err
michael@0 286 ec_GFp_pt_mul_jac(const mp_int *n, const mp_int *px, const mp_int *py,
michael@0 287 mp_int *rx, mp_int *ry, const ECGroup *group)
michael@0 288 {
michael@0 289 mp_err res = MP_OKAY;
michael@0 290 mp_int precomp[16][2], rz;
michael@0 291 int i, ni, d;
michael@0 292
michael@0 293 MP_DIGITS(&rz) = 0;
michael@0 294 for (i = 0; i < 16; i++) {
michael@0 295 MP_DIGITS(&precomp[i][0]) = 0;
michael@0 296 MP_DIGITS(&precomp[i][1]) = 0;
michael@0 297 }
michael@0 298
michael@0 299 ARGCHK(group != NULL, MP_BADARG);
michael@0 300 ARGCHK((n != NULL) && (px != NULL) && (py != NULL), MP_BADARG);
michael@0 301
michael@0 302 /* initialize precomputation table */
michael@0 303 for (i = 0; i < 16; i++) {
michael@0 304 MP_CHECKOK(mp_init(&precomp[i][0]));
michael@0 305 MP_CHECKOK(mp_init(&precomp[i][1]));
michael@0 306 }
michael@0 307
michael@0 308 /* fill precomputation table */
michael@0 309 mp_zero(&precomp[0][0]);
michael@0 310 mp_zero(&precomp[0][1]);
michael@0 311 MP_CHECKOK(mp_copy(px, &precomp[1][0]));
michael@0 312 MP_CHECKOK(mp_copy(py, &precomp[1][1]));
michael@0 313 for (i = 2; i < 16; i++) {
michael@0 314 MP_CHECKOK(group->
michael@0 315 point_add(&precomp[1][0], &precomp[1][1],
michael@0 316 &precomp[i - 1][0], &precomp[i - 1][1],
michael@0 317 &precomp[i][0], &precomp[i][1], group));
michael@0 318 }
michael@0 319
michael@0 320 d = (mpl_significant_bits(n) + 3) / 4;
michael@0 321
michael@0 322 /* R = inf */
michael@0 323 MP_CHECKOK(mp_init(&rz));
michael@0 324 MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, &rz));
michael@0 325
michael@0 326 for (i = d - 1; i >= 0; i--) {
michael@0 327 /* compute window ni */
michael@0 328 ni = MP_GET_BIT(n, 4 * i + 3);
michael@0 329 ni <<= 1;
michael@0 330 ni |= MP_GET_BIT(n, 4 * i + 2);
michael@0 331 ni <<= 1;
michael@0 332 ni |= MP_GET_BIT(n, 4 * i + 1);
michael@0 333 ni <<= 1;
michael@0 334 ni |= MP_GET_BIT(n, 4 * i);
michael@0 335 /* R = 2^4 * R */
michael@0 336 MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group));
michael@0 337 MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group));
michael@0 338 MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group));
michael@0 339 MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group));
michael@0 340 /* R = R + (ni * P) */
michael@0 341 MP_CHECKOK(ec_GFp_pt_add_jac_aff
michael@0 342 (rx, ry, &rz, &precomp[ni][0], &precomp[ni][1], rx, ry,
michael@0 343 &rz, group));
michael@0 344 }
michael@0 345
michael@0 346 /* convert result S to affine coordinates */
michael@0 347 MP_CHECKOK(ec_GFp_pt_jac2aff(rx, ry, &rz, rx, ry, group));
michael@0 348
michael@0 349 CLEANUP:
michael@0 350 mp_clear(&rz);
michael@0 351 for (i = 0; i < 16; i++) {
michael@0 352 mp_clear(&precomp[i][0]);
michael@0 353 mp_clear(&precomp[i][1]);
michael@0 354 }
michael@0 355 return res;
michael@0 356 }
michael@0 357 #endif
michael@0 358
michael@0 359 /* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G +
michael@0 360 * k2 * P(x, y), where G is the generator (base point) of the group of
michael@0 361 * points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL.
michael@0 362 * Uses mixed Jacobian-affine coordinates. Input and output values are
michael@0 363 * assumed to be NOT field-encoded. Uses algorithm 15 (simultaneous
michael@0 364 * multiple point multiplication) from Brown, Hankerson, Lopez, Menezes.
michael@0 365 * Software Implementation of the NIST Elliptic Curves over Prime Fields. */
michael@0 366 mp_err
michael@0 367 ec_GFp_pts_mul_jac(const mp_int *k1, const mp_int *k2, const mp_int *px,
michael@0 368 const mp_int *py, mp_int *rx, mp_int *ry,
michael@0 369 const ECGroup *group)
michael@0 370 {
michael@0 371 mp_err res = MP_OKAY;
michael@0 372 mp_int precomp[4][4][2];
michael@0 373 mp_int rz;
michael@0 374 const mp_int *a, *b;
michael@0 375 int i, j;
michael@0 376 int ai, bi, d;
michael@0 377
michael@0 378 for (i = 0; i < 4; i++) {
michael@0 379 for (j = 0; j < 4; j++) {
michael@0 380 MP_DIGITS(&precomp[i][j][0]) = 0;
michael@0 381 MP_DIGITS(&precomp[i][j][1]) = 0;
michael@0 382 }
michael@0 383 }
michael@0 384 MP_DIGITS(&rz) = 0;
michael@0 385
michael@0 386 ARGCHK(group != NULL, MP_BADARG);
michael@0 387 ARGCHK(!((k1 == NULL)
michael@0 388 && ((k2 == NULL) || (px == NULL)
michael@0 389 || (py == NULL))), MP_BADARG);
michael@0 390
michael@0 391 /* if some arguments are not defined used ECPoint_mul */
michael@0 392 if (k1 == NULL) {
michael@0 393 return ECPoint_mul(group, k2, px, py, rx, ry);
michael@0 394 } else if ((k2 == NULL) || (px == NULL) || (py == NULL)) {
michael@0 395 return ECPoint_mul(group, k1, NULL, NULL, rx, ry);
michael@0 396 }
michael@0 397
michael@0 398 /* initialize precomputation table */
michael@0 399 for (i = 0; i < 4; i++) {
michael@0 400 for (j = 0; j < 4; j++) {
michael@0 401 MP_CHECKOK(mp_init(&precomp[i][j][0]));
michael@0 402 MP_CHECKOK(mp_init(&precomp[i][j][1]));
michael@0 403 }
michael@0 404 }
michael@0 405
michael@0 406 /* fill precomputation table */
michael@0 407 /* assign {k1, k2} = {a, b} such that len(a) >= len(b) */
michael@0 408 if (mpl_significant_bits(k1) < mpl_significant_bits(k2)) {
michael@0 409 a = k2;
michael@0 410 b = k1;
michael@0 411 if (group->meth->field_enc) {
michael@0 412 MP_CHECKOK(group->meth->
michael@0 413 field_enc(px, &precomp[1][0][0], group->meth));
michael@0 414 MP_CHECKOK(group->meth->
michael@0 415 field_enc(py, &precomp[1][0][1], group->meth));
michael@0 416 } else {
michael@0 417 MP_CHECKOK(mp_copy(px, &precomp[1][0][0]));
michael@0 418 MP_CHECKOK(mp_copy(py, &precomp[1][0][1]));
michael@0 419 }
michael@0 420 MP_CHECKOK(mp_copy(&group->genx, &precomp[0][1][0]));
michael@0 421 MP_CHECKOK(mp_copy(&group->geny, &precomp[0][1][1]));
michael@0 422 } else {
michael@0 423 a = k1;
michael@0 424 b = k2;
michael@0 425 MP_CHECKOK(mp_copy(&group->genx, &precomp[1][0][0]));
michael@0 426 MP_CHECKOK(mp_copy(&group->geny, &precomp[1][0][1]));
michael@0 427 if (group->meth->field_enc) {
michael@0 428 MP_CHECKOK(group->meth->
michael@0 429 field_enc(px, &precomp[0][1][0], group->meth));
michael@0 430 MP_CHECKOK(group->meth->
michael@0 431 field_enc(py, &precomp[0][1][1], group->meth));
michael@0 432 } else {
michael@0 433 MP_CHECKOK(mp_copy(px, &precomp[0][1][0]));
michael@0 434 MP_CHECKOK(mp_copy(py, &precomp[0][1][1]));
michael@0 435 }
michael@0 436 }
michael@0 437 /* precompute [*][0][*] */
michael@0 438 mp_zero(&precomp[0][0][0]);
michael@0 439 mp_zero(&precomp[0][0][1]);
michael@0 440 MP_CHECKOK(group->
michael@0 441 point_dbl(&precomp[1][0][0], &precomp[1][0][1],
michael@0 442 &precomp[2][0][0], &precomp[2][0][1], group));
michael@0 443 MP_CHECKOK(group->
michael@0 444 point_add(&precomp[1][0][0], &precomp[1][0][1],
michael@0 445 &precomp[2][0][0], &precomp[2][0][1],
michael@0 446 &precomp[3][0][0], &precomp[3][0][1], group));
michael@0 447 /* precompute [*][1][*] */
michael@0 448 for (i = 1; i < 4; i++) {
michael@0 449 MP_CHECKOK(group->
michael@0 450 point_add(&precomp[0][1][0], &precomp[0][1][1],
michael@0 451 &precomp[i][0][0], &precomp[i][0][1],
michael@0 452 &precomp[i][1][0], &precomp[i][1][1], group));
michael@0 453 }
michael@0 454 /* precompute [*][2][*] */
michael@0 455 MP_CHECKOK(group->
michael@0 456 point_dbl(&precomp[0][1][0], &precomp[0][1][1],
michael@0 457 &precomp[0][2][0], &precomp[0][2][1], group));
michael@0 458 for (i = 1; i < 4; i++) {
michael@0 459 MP_CHECKOK(group->
michael@0 460 point_add(&precomp[0][2][0], &precomp[0][2][1],
michael@0 461 &precomp[i][0][0], &precomp[i][0][1],
michael@0 462 &precomp[i][2][0], &precomp[i][2][1], group));
michael@0 463 }
michael@0 464 /* precompute [*][3][*] */
michael@0 465 MP_CHECKOK(group->
michael@0 466 point_add(&precomp[0][1][0], &precomp[0][1][1],
michael@0 467 &precomp[0][2][0], &precomp[0][2][1],
michael@0 468 &precomp[0][3][0], &precomp[0][3][1], group));
michael@0 469 for (i = 1; i < 4; i++) {
michael@0 470 MP_CHECKOK(group->
michael@0 471 point_add(&precomp[0][3][0], &precomp[0][3][1],
michael@0 472 &precomp[i][0][0], &precomp[i][0][1],
michael@0 473 &precomp[i][3][0], &precomp[i][3][1], group));
michael@0 474 }
michael@0 475
michael@0 476 d = (mpl_significant_bits(a) + 1) / 2;
michael@0 477
michael@0 478 /* R = inf */
michael@0 479 MP_CHECKOK(mp_init(&rz));
michael@0 480 MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, &rz));
michael@0 481
michael@0 482 for (i = d - 1; i >= 0; i--) {
michael@0 483 ai = MP_GET_BIT(a, 2 * i + 1);
michael@0 484 ai <<= 1;
michael@0 485 ai |= MP_GET_BIT(a, 2 * i);
michael@0 486 bi = MP_GET_BIT(b, 2 * i + 1);
michael@0 487 bi <<= 1;
michael@0 488 bi |= MP_GET_BIT(b, 2 * i);
michael@0 489 /* R = 2^2 * R */
michael@0 490 MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group));
michael@0 491 MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group));
michael@0 492 /* R = R + (ai * A + bi * B) */
michael@0 493 MP_CHECKOK(ec_GFp_pt_add_jac_aff
michael@0 494 (rx, ry, &rz, &precomp[ai][bi][0], &precomp[ai][bi][1],
michael@0 495 rx, ry, &rz, group));
michael@0 496 }
michael@0 497
michael@0 498 MP_CHECKOK(ec_GFp_pt_jac2aff(rx, ry, &rz, rx, ry, group));
michael@0 499
michael@0 500 if (group->meth->field_dec) {
michael@0 501 MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth));
michael@0 502 MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth));
michael@0 503 }
michael@0 504
michael@0 505 CLEANUP:
michael@0 506 mp_clear(&rz);
michael@0 507 for (i = 0; i < 4; i++) {
michael@0 508 for (j = 0; j < 4; j++) {
michael@0 509 mp_clear(&precomp[i][j][0]);
michael@0 510 mp_clear(&precomp[i][j][1]);
michael@0 511 }
michael@0 512 }
michael@0 513 return res;
michael@0 514 }

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