security/nss/lib/freebl/ecl/ecp_jac.c@b8a032363ba2
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
1 /* This Source Code Form is subject to the terms of the Mozilla Public
2 * License, v. 2.0. If a copy of the MPL was not distributed with this
3 * file, You can obtain one at http://mozilla.org/MPL/2.0/. */
5 #include "ecp.h"
6 #include "mplogic.h"
7 #include <stdlib.h>
8 #ifdef ECL_DEBUG
9 #include <assert.h>
10 #endif
12 /* Converts a point P(px, py) from affine coordinates to Jacobian
13 * projective coordinates R(rx, ry, rz). Assumes input is already
14 * field-encoded using field_enc, and returns output that is still
15 * field-encoded. */
16 mp_err
17 ec_GFp_pt_aff2jac(const mp_int *px, const mp_int *py, mp_int *rx,
18 mp_int *ry, mp_int *rz, const ECGroup *group)
19 {
20 mp_err res = MP_OKAY;
22 if (ec_GFp_pt_is_inf_aff(px, py) == MP_YES) {
23 MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, rz));
24 } else {
25 MP_CHECKOK(mp_copy(px, rx));
26 MP_CHECKOK(mp_copy(py, ry));
27 MP_CHECKOK(mp_set_int(rz, 1));
28 if (group->meth->field_enc) {
29 MP_CHECKOK(group->meth->field_enc(rz, rz, group->meth));
30 }
31 }
32 CLEANUP:
33 return res;
34 }
36 /* Converts a point P(px, py, pz) from Jacobian projective coordinates to
37 * affine coordinates R(rx, ry). P and R can share x and y coordinates.
38 * Assumes input is already field-encoded using field_enc, and returns
39 * output that is still field-encoded. */
40 mp_err
41 ec_GFp_pt_jac2aff(const mp_int *px, const mp_int *py, const mp_int *pz,
42 mp_int *rx, mp_int *ry, const ECGroup *group)
43 {
44 mp_err res = MP_OKAY;
45 mp_int z1, z2, z3;
47 MP_DIGITS(&z1) = 0;
48 MP_DIGITS(&z2) = 0;
49 MP_DIGITS(&z3) = 0;
50 MP_CHECKOK(mp_init(&z1));
51 MP_CHECKOK(mp_init(&z2));
52 MP_CHECKOK(mp_init(&z3));
54 /* if point at infinity, then set point at infinity and exit */
55 if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {
56 MP_CHECKOK(ec_GFp_pt_set_inf_aff(rx, ry));
57 goto CLEANUP;
58 }
60 /* transform (px, py, pz) into (px / pz^2, py / pz^3) */
61 if (mp_cmp_d(pz, 1) == 0) {
62 MP_CHECKOK(mp_copy(px, rx));
63 MP_CHECKOK(mp_copy(py, ry));
64 } else {
65 MP_CHECKOK(group->meth->field_div(NULL, pz, &z1, group->meth));
66 MP_CHECKOK(group->meth->field_sqr(&z1, &z2, group->meth));
67 MP_CHECKOK(group->meth->field_mul(&z1, &z2, &z3, group->meth));
68 MP_CHECKOK(group->meth->field_mul(px, &z2, rx, group->meth));
69 MP_CHECKOK(group->meth->field_mul(py, &z3, ry, group->meth));
70 }
72 CLEANUP:
73 mp_clear(&z1);
74 mp_clear(&z2);
75 mp_clear(&z3);
76 return res;
77 }
79 /* Checks if point P(px, py, pz) is at infinity. Uses Jacobian
80 * coordinates. */
81 mp_err
82 ec_GFp_pt_is_inf_jac(const mp_int *px, const mp_int *py, const mp_int *pz)
83 {
84 return mp_cmp_z(pz);
85 }
87 /* Sets P(px, py, pz) to be the point at infinity. Uses Jacobian
88 * coordinates. */
89 mp_err
90 ec_GFp_pt_set_inf_jac(mp_int *px, mp_int *py, mp_int *pz)
91 {
92 mp_zero(pz);
93 return MP_OKAY;
94 }
96 /* Computes R = P + Q where R is (rx, ry, rz), P is (px, py, pz) and Q is
97 * (qx, qy, 1). Elliptic curve points P, Q, and R can all be identical.
98 * Uses mixed Jacobian-affine coordinates. Assumes input is already
99 * field-encoded using field_enc, and returns output that is still
100 * field-encoded. Uses equation (2) from Brown, Hankerson, Lopez, and
101 * Menezes. Software Implementation of the NIST Elliptic Curves Over Prime
102 * Fields. */
103 mp_err
104 ec_GFp_pt_add_jac_aff(const mp_int *px, const mp_int *py, const mp_int *pz,
105 const mp_int *qx, const mp_int *qy, mp_int *rx,
106 mp_int *ry, mp_int *rz, const ECGroup *group)
107 {
108 mp_err res = MP_OKAY;
109 mp_int A, B, C, D, C2, C3;
111 MP_DIGITS(&A) = 0;
112 MP_DIGITS(&B) = 0;
113 MP_DIGITS(&C) = 0;
114 MP_DIGITS(&D) = 0;
115 MP_DIGITS(&C2) = 0;
116 MP_DIGITS(&C3) = 0;
117 MP_CHECKOK(mp_init(&A));
118 MP_CHECKOK(mp_init(&B));
119 MP_CHECKOK(mp_init(&C));
120 MP_CHECKOK(mp_init(&D));
121 MP_CHECKOK(mp_init(&C2));
122 MP_CHECKOK(mp_init(&C3));
124 /* If either P or Q is the point at infinity, then return the other
125 * point */
126 if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {
127 MP_CHECKOK(ec_GFp_pt_aff2jac(qx, qy, rx, ry, rz, group));
128 goto CLEANUP;
129 }
130 if (ec_GFp_pt_is_inf_aff(qx, qy) == MP_YES) {
131 MP_CHECKOK(mp_copy(px, rx));
132 MP_CHECKOK(mp_copy(py, ry));
133 MP_CHECKOK(mp_copy(pz, rz));
134 goto CLEANUP;
135 }
137 /* A = qx * pz^2, B = qy * pz^3 */
138 MP_CHECKOK(group->meth->field_sqr(pz, &A, group->meth));
139 MP_CHECKOK(group->meth->field_mul(&A, pz, &B, group->meth));
140 MP_CHECKOK(group->meth->field_mul(&A, qx, &A, group->meth));
141 MP_CHECKOK(group->meth->field_mul(&B, qy, &B, group->meth));
143 /* C = A - px, D = B - py */
144 MP_CHECKOK(group->meth->field_sub(&A, px, &C, group->meth));
145 MP_CHECKOK(group->meth->field_sub(&B, py, &D, group->meth));
147 /* C2 = C^2, C3 = C^3 */
148 MP_CHECKOK(group->meth->field_sqr(&C, &C2, group->meth));
149 MP_CHECKOK(group->meth->field_mul(&C, &C2, &C3, group->meth));
151 /* rz = pz * C */
152 MP_CHECKOK(group->meth->field_mul(pz, &C, rz, group->meth));
154 /* C = px * C^2 */
155 MP_CHECKOK(group->meth->field_mul(px, &C2, &C, group->meth));
156 /* A = D^2 */
157 MP_CHECKOK(group->meth->field_sqr(&D, &A, group->meth));
159 /* rx = D^2 - (C^3 + 2 * (px * C^2)) */
160 MP_CHECKOK(group->meth->field_add(&C, &C, rx, group->meth));
161 MP_CHECKOK(group->meth->field_add(&C3, rx, rx, group->meth));
162 MP_CHECKOK(group->meth->field_sub(&A, rx, rx, group->meth));
164 /* C3 = py * C^3 */
165 MP_CHECKOK(group->meth->field_mul(py, &C3, &C3, group->meth));
167 /* ry = D * (px * C^2 - rx) - py * C^3 */
168 MP_CHECKOK(group->meth->field_sub(&C, rx, ry, group->meth));
169 MP_CHECKOK(group->meth->field_mul(&D, ry, ry, group->meth));
170 MP_CHECKOK(group->meth->field_sub(ry, &C3, ry, group->meth));
172 CLEANUP:
173 mp_clear(&A);
174 mp_clear(&B);
175 mp_clear(&C);
176 mp_clear(&D);
177 mp_clear(&C2);
178 mp_clear(&C3);
179 return res;
180 }
182 /* Computes R = 2P. Elliptic curve points P and R can be identical. Uses
183 * Jacobian coordinates.
184 *
185 * Assumes input is already field-encoded using field_enc, and returns
186 * output that is still field-encoded.
187 *
188 * This routine implements Point Doubling in the Jacobian Projective
189 * space as described in the paper "Efficient elliptic curve exponentiation
190 * using mixed coordinates", by H. Cohen, A Miyaji, T. Ono.
191 */
192 mp_err
193 ec_GFp_pt_dbl_jac(const mp_int *px, const mp_int *py, const mp_int *pz,
194 mp_int *rx, mp_int *ry, mp_int *rz, const ECGroup *group)
195 {
196 mp_err res = MP_OKAY;
197 mp_int t0, t1, M, S;
199 MP_DIGITS(&t0) = 0;
200 MP_DIGITS(&t1) = 0;
201 MP_DIGITS(&M) = 0;
202 MP_DIGITS(&S) = 0;
203 MP_CHECKOK(mp_init(&t0));
204 MP_CHECKOK(mp_init(&t1));
205 MP_CHECKOK(mp_init(&M));
206 MP_CHECKOK(mp_init(&S));
208 if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {
209 MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, rz));
210 goto CLEANUP;
211 }
213 if (mp_cmp_d(pz, 1) == 0) {
214 /* M = 3 * px^2 + a */
215 MP_CHECKOK(group->meth->field_sqr(px, &t0, group->meth));
216 MP_CHECKOK(group->meth->field_add(&t0, &t0, &M, group->meth));
217 MP_CHECKOK(group->meth->field_add(&t0, &M, &t0, group->meth));
218 MP_CHECKOK(group->meth->
219 field_add(&t0, &group->curvea, &M, group->meth));
220 } else if (mp_cmp_int(&group->curvea, -3) == 0) {
221 /* M = 3 * (px + pz^2) * (px - pz^2) */
222 MP_CHECKOK(group->meth->field_sqr(pz, &M, group->meth));
223 MP_CHECKOK(group->meth->field_add(px, &M, &t0, group->meth));
224 MP_CHECKOK(group->meth->field_sub(px, &M, &t1, group->meth));
225 MP_CHECKOK(group->meth->field_mul(&t0, &t1, &M, group->meth));
226 MP_CHECKOK(group->meth->field_add(&M, &M, &t0, group->meth));
227 MP_CHECKOK(group->meth->field_add(&t0, &M, &M, group->meth));
228 } else {
229 /* M = 3 * (px^2) + a * (pz^4) */
230 MP_CHECKOK(group->meth->field_sqr(px, &t0, group->meth));
231 MP_CHECKOK(group->meth->field_add(&t0, &t0, &M, group->meth));
232 MP_CHECKOK(group->meth->field_add(&t0, &M, &t0, group->meth));
233 MP_CHECKOK(group->meth->field_sqr(pz, &M, group->meth));
234 MP_CHECKOK(group->meth->field_sqr(&M, &M, group->meth));
235 MP_CHECKOK(group->meth->
236 field_mul(&M, &group->curvea, &M, group->meth));
237 MP_CHECKOK(group->meth->field_add(&M, &t0, &M, group->meth));
238 }
240 /* rz = 2 * py * pz */
241 /* t0 = 4 * py^2 */
242 if (mp_cmp_d(pz, 1) == 0) {
243 MP_CHECKOK(group->meth->field_add(py, py, rz, group->meth));
244 MP_CHECKOK(group->meth->field_sqr(rz, &t0, group->meth));
245 } else {
246 MP_CHECKOK(group->meth->field_add(py, py, &t0, group->meth));
247 MP_CHECKOK(group->meth->field_mul(&t0, pz, rz, group->meth));
248 MP_CHECKOK(group->meth->field_sqr(&t0, &t0, group->meth));
249 }
251 /* S = 4 * px * py^2 = px * (2 * py)^2 */
252 MP_CHECKOK(group->meth->field_mul(px, &t0, &S, group->meth));
254 /* rx = M^2 - 2 * S */
255 MP_CHECKOK(group->meth->field_add(&S, &S, &t1, group->meth));
256 MP_CHECKOK(group->meth->field_sqr(&M, rx, group->meth));
257 MP_CHECKOK(group->meth->field_sub(rx, &t1, rx, group->meth));
259 /* ry = M * (S - rx) - 8 * py^4 */
260 MP_CHECKOK(group->meth->field_sqr(&t0, &t1, group->meth));
261 if (mp_isodd(&t1)) {
262 MP_CHECKOK(mp_add(&t1, &group->meth->irr, &t1));
263 }
264 MP_CHECKOK(mp_div_2(&t1, &t1));
265 MP_CHECKOK(group->meth->field_sub(&S, rx, &S, group->meth));
266 MP_CHECKOK(group->meth->field_mul(&M, &S, &M, group->meth));
267 MP_CHECKOK(group->meth->field_sub(&M, &t1, ry, group->meth));
269 CLEANUP:
270 mp_clear(&t0);
271 mp_clear(&t1);
272 mp_clear(&M);
273 mp_clear(&S);
274 return res;
275 }
277 /* by default, this routine is unused and thus doesn't need to be compiled */
278 #ifdef ECL_ENABLE_GFP_PT_MUL_JAC
279 /* Computes R = nP where R is (rx, ry) and P is (px, py). The parameters
280 * a, b and p are the elliptic curve coefficients and the prime that
281 * determines the field GFp. Elliptic curve points P and R can be
282 * identical. Uses mixed Jacobian-affine coordinates. Assumes input is
283 * already field-encoded using field_enc, and returns output that is still
284 * field-encoded. Uses 4-bit window method. */
285 mp_err
286 ec_GFp_pt_mul_jac(const mp_int *n, const mp_int *px, const mp_int *py,
287 mp_int *rx, mp_int *ry, const ECGroup *group)
288 {
289 mp_err res = MP_OKAY;
290 mp_int precomp[16][2], rz;
291 int i, ni, d;
293 MP_DIGITS(&rz) = 0;
294 for (i = 0; i < 16; i++) {
295 MP_DIGITS(&precomp[i][0]) = 0;
296 MP_DIGITS(&precomp[i][1]) = 0;
297 }
299 ARGCHK(group != NULL, MP_BADARG);
300 ARGCHK((n != NULL) && (px != NULL) && (py != NULL), MP_BADARG);
302 /* initialize precomputation table */
303 for (i = 0; i < 16; i++) {
304 MP_CHECKOK(mp_init(&precomp[i][0]));
305 MP_CHECKOK(mp_init(&precomp[i][1]));
306 }
308 /* fill precomputation table */
309 mp_zero(&precomp[0][0]);
310 mp_zero(&precomp[0][1]);
311 MP_CHECKOK(mp_copy(px, &precomp[1][0]));
312 MP_CHECKOK(mp_copy(py, &precomp[1][1]));
313 for (i = 2; i < 16; i++) {
314 MP_CHECKOK(group->
315 point_add(&precomp[1][0], &precomp[1][1],
316 &precomp[i - 1][0], &precomp[i - 1][1],
317 &precomp[i][0], &precomp[i][1], group));
318 }
320 d = (mpl_significant_bits(n) + 3) / 4;
322 /* R = inf */
323 MP_CHECKOK(mp_init(&rz));
324 MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, &rz));
326 for (i = d - 1; i >= 0; i--) {
327 /* compute window ni */
328 ni = MP_GET_BIT(n, 4 * i + 3);
329 ni <<= 1;
330 ni |= MP_GET_BIT(n, 4 * i + 2);
331 ni <<= 1;
332 ni |= MP_GET_BIT(n, 4 * i + 1);
333 ni <<= 1;
334 ni |= MP_GET_BIT(n, 4 * i);
335 /* R = 2^4 * R */
336 MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group));
337 MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group));
338 MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group));
339 MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group));
340 /* R = R + (ni * P) */
341 MP_CHECKOK(ec_GFp_pt_add_jac_aff
342 (rx, ry, &rz, &precomp[ni][0], &precomp[ni][1], rx, ry,
343 &rz, group));
344 }
346 /* convert result S to affine coordinates */
347 MP_CHECKOK(ec_GFp_pt_jac2aff(rx, ry, &rz, rx, ry, group));
349 CLEANUP:
350 mp_clear(&rz);
351 for (i = 0; i < 16; i++) {
352 mp_clear(&precomp[i][0]);
353 mp_clear(&precomp[i][1]);
354 }
355 return res;
356 }
357 #endif
359 /* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G +
360 * k2 * P(x, y), where G is the generator (base point) of the group of
361 * points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL.
362 * Uses mixed Jacobian-affine coordinates. Input and output values are
363 * assumed to be NOT field-encoded. Uses algorithm 15 (simultaneous
364 * multiple point multiplication) from Brown, Hankerson, Lopez, Menezes.
365 * Software Implementation of the NIST Elliptic Curves over Prime Fields. */
366 mp_err
367 ec_GFp_pts_mul_jac(const mp_int *k1, const mp_int *k2, const mp_int *px,
368 const mp_int *py, mp_int *rx, mp_int *ry,
369 const ECGroup *group)
370 {
371 mp_err res = MP_OKAY;
372 mp_int precomp[4][4][2];
373 mp_int rz;
374 const mp_int *a, *b;
375 int i, j;
376 int ai, bi, d;
378 for (i = 0; i < 4; i++) {
379 for (j = 0; j < 4; j++) {
380 MP_DIGITS(&precomp[i][j][0]) = 0;
381 MP_DIGITS(&precomp[i][j][1]) = 0;
382 }
383 }
384 MP_DIGITS(&rz) = 0;
386 ARGCHK(group != NULL, MP_BADARG);
387 ARGCHK(!((k1 == NULL)
388 && ((k2 == NULL) || (px == NULL)
389 || (py == NULL))), MP_BADARG);
391 /* if some arguments are not defined used ECPoint_mul */
392 if (k1 == NULL) {
393 return ECPoint_mul(group, k2, px, py, rx, ry);
394 } else if ((k2 == NULL) || (px == NULL) || (py == NULL)) {
395 return ECPoint_mul(group, k1, NULL, NULL, rx, ry);
396 }
398 /* initialize precomputation table */
399 for (i = 0; i < 4; i++) {
400 for (j = 0; j < 4; j++) {
401 MP_CHECKOK(mp_init(&precomp[i][j][0]));
402 MP_CHECKOK(mp_init(&precomp[i][j][1]));
403 }
404 }
406 /* fill precomputation table */
407 /* assign {k1, k2} = {a, b} such that len(a) >= len(b) */
408 if (mpl_significant_bits(k1) < mpl_significant_bits(k2)) {
409 a = k2;
410 b = k1;
411 if (group->meth->field_enc) {
412 MP_CHECKOK(group->meth->
413 field_enc(px, &precomp[1][0][0], group->meth));
414 MP_CHECKOK(group->meth->
415 field_enc(py, &precomp[1][0][1], group->meth));
416 } else {
417 MP_CHECKOK(mp_copy(px, &precomp[1][0][0]));
418 MP_CHECKOK(mp_copy(py, &precomp[1][0][1]));
419 }
420 MP_CHECKOK(mp_copy(&group->genx, &precomp[0][1][0]));
421 MP_CHECKOK(mp_copy(&group->geny, &precomp[0][1][1]));
422 } else {
423 a = k1;
424 b = k2;
425 MP_CHECKOK(mp_copy(&group->genx, &precomp[1][0][0]));
426 MP_CHECKOK(mp_copy(&group->geny, &precomp[1][0][1]));
427 if (group->meth->field_enc) {
428 MP_CHECKOK(group->meth->
429 field_enc(px, &precomp[0][1][0], group->meth));
430 MP_CHECKOK(group->meth->
431 field_enc(py, &precomp[0][1][1], group->meth));
432 } else {
433 MP_CHECKOK(mp_copy(px, &precomp[0][1][0]));
434 MP_CHECKOK(mp_copy(py, &precomp[0][1][1]));
435 }
436 }
437 /* precompute [*][0][*] */
438 mp_zero(&precomp[0][0][0]);
439 mp_zero(&precomp[0][0][1]);
440 MP_CHECKOK(group->
441 point_dbl(&precomp[1][0][0], &precomp[1][0][1],
442 &precomp[2][0][0], &precomp[2][0][1], group));
443 MP_CHECKOK(group->
444 point_add(&precomp[1][0][0], &precomp[1][0][1],
445 &precomp[2][0][0], &precomp[2][0][1],
446 &precomp[3][0][0], &precomp[3][0][1], group));
447 /* precompute [*][1][*] */
448 for (i = 1; i < 4; i++) {
449 MP_CHECKOK(group->
450 point_add(&precomp[0][1][0], &precomp[0][1][1],
451 &precomp[i][0][0], &precomp[i][0][1],
452 &precomp[i][1][0], &precomp[i][1][1], group));
453 }
454 /* precompute [*][2][*] */
455 MP_CHECKOK(group->
456 point_dbl(&precomp[0][1][0], &precomp[0][1][1],
457 &precomp[0][2][0], &precomp[0][2][1], group));
458 for (i = 1; i < 4; i++) {
459 MP_CHECKOK(group->
460 point_add(&precomp[0][2][0], &precomp[0][2][1],
461 &precomp[i][0][0], &precomp[i][0][1],
462 &precomp[i][2][0], &precomp[i][2][1], group));
463 }
464 /* precompute [*][3][*] */
465 MP_CHECKOK(group->
466 point_add(&precomp[0][1][0], &precomp[0][1][1],
467 &precomp[0][2][0], &precomp[0][2][1],
468 &precomp[0][3][0], &precomp[0][3][1], group));
469 for (i = 1; i < 4; i++) {
470 MP_CHECKOK(group->
471 point_add(&precomp[0][3][0], &precomp[0][3][1],
472 &precomp[i][0][0], &precomp[i][0][1],
473 &precomp[i][3][0], &precomp[i][3][1], group));
474 }
476 d = (mpl_significant_bits(a) + 1) / 2;
478 /* R = inf */
479 MP_CHECKOK(mp_init(&rz));
480 MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, &rz));
482 for (i = d - 1; i >= 0; i--) {
483 ai = MP_GET_BIT(a, 2 * i + 1);
484 ai <<= 1;
485 ai |= MP_GET_BIT(a, 2 * i);
486 bi = MP_GET_BIT(b, 2 * i + 1);
487 bi <<= 1;
488 bi |= MP_GET_BIT(b, 2 * i);
489 /* R = 2^2 * R */
490 MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group));
491 MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group));
492 /* R = R + (ai * A + bi * B) */
493 MP_CHECKOK(ec_GFp_pt_add_jac_aff
494 (rx, ry, &rz, &precomp[ai][bi][0], &precomp[ai][bi][1],
495 rx, ry, &rz, group));
496 }
498 MP_CHECKOK(ec_GFp_pt_jac2aff(rx, ry, &rz, rx, ry, group));
500 if (group->meth->field_dec) {
501 MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth));
502 MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth));
503 }
505 CLEANUP:
506 mp_clear(&rz);
507 for (i = 0; i < 4; i++) {
508 for (j = 0; j < 4; j++) {
509 mp_clear(&precomp[i][j][0]);
510 mp_clear(&precomp[i][j][1]);
511 }
512 }
513 return res;
514 }
