xref: /illumos-gate/usr/src/common/crypto/ecc/ecp_jac.c (revision f9fbec18)
1 /*
2  * ***** BEGIN LICENSE BLOCK *****
3  * Version: MPL 1.1/GPL 2.0/LGPL 2.1
4  *
5  * The contents of this file are subject to the Mozilla Public License Version
6  * 1.1 (the "License"); you may not use this file except in compliance with
7  * the License. You may obtain a copy of the License at
8  * http://www.mozilla.org/MPL/
9  *
10  * Software distributed under the License is distributed on an "AS IS" basis,
11  * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
12  * for the specific language governing rights and limitations under the
13  * License.
14  *
15  * The Original Code is the elliptic curve math library for prime field curves.
16  *
17  * The Initial Developer of the Original Code is
18  * Sun Microsystems, Inc.
19  * Portions created by the Initial Developer are Copyright (C) 2003
20  * the Initial Developer. All Rights Reserved.
21  *
22  * Contributor(s):
23  *   Sheueling Chang-Shantz <sheueling.chang@sun.com>,
24  *   Stephen Fung <fungstep@hotmail.com>, and
25  *   Douglas Stebila <douglas@stebila.ca>, Sun Microsystems Laboratories.
26  *   Bodo Moeller <moeller@cdc.informatik.tu-darmstadt.de>,
27  *   Nils Larsch <nla@trustcenter.de>, and
28  *   Lenka Fibikova <fibikova@exp-math.uni-essen.de>, the OpenSSL Project
29  *
30  * Alternatively, the contents of this file may be used under the terms of
31  * either the GNU General Public License Version 2 or later (the "GPL"), or
32  * the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
33  * in which case the provisions of the GPL or the LGPL are applicable instead
34  * of those above. If you wish to allow use of your version of this file only
35  * under the terms of either the GPL or the LGPL, and not to allow others to
36  * use your version of this file under the terms of the MPL, indicate your
37  * decision by deleting the provisions above and replace them with the notice
38  * and other provisions required by the GPL or the LGPL. If you do not delete
39  * the provisions above, a recipient may use your version of this file under
40  * the terms of any one of the MPL, the GPL or the LGPL.
41  *
42  * ***** END LICENSE BLOCK ***** */
43 /*
44  * Copyright 2007 Sun Microsystems, Inc.  All rights reserved.
45  * Use is subject to license terms.
46  *
47  * Sun elects to use this software under the MPL license.
48  */
49 
50 #pragma ident	"%Z%%M%	%I%	%E% SMI"
51 
52 #include "ecp.h"
53 #include "mplogic.h"
54 #ifndef _KERNEL
55 #include <stdlib.h>
56 #endif
57 #ifdef ECL_DEBUG
58 #include <assert.h>
59 #endif
60 
61 /* Converts a point P(px, py) from affine coordinates to Jacobian
62  * projective coordinates R(rx, ry, rz). Assumes input is already
63  * field-encoded using field_enc, and returns output that is still
64  * field-encoded. */
65 mp_err
ec_GFp_pt_aff2jac(const mp_int * px,const mp_int * py,mp_int * rx,mp_int * ry,mp_int * rz,const ECGroup * group)66 ec_GFp_pt_aff2jac(const mp_int *px, const mp_int *py, mp_int *rx,
67 				  mp_int *ry, mp_int *rz, const ECGroup *group)
68 {
69 	mp_err res = MP_OKAY;
70 
71 	if (ec_GFp_pt_is_inf_aff(px, py) == MP_YES) {
72 		MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, rz));
73 	} else {
74 		MP_CHECKOK(mp_copy(px, rx));
75 		MP_CHECKOK(mp_copy(py, ry));
76 		MP_CHECKOK(mp_set_int(rz, 1));
77 		if (group->meth->field_enc) {
78 			MP_CHECKOK(group->meth->field_enc(rz, rz, group->meth));
79 		}
80 	}
81   CLEANUP:
82 	return res;
83 }
84 
85 /* Converts a point P(px, py, pz) from Jacobian projective coordinates to
86  * affine coordinates R(rx, ry).  P and R can share x and y coordinates.
87  * Assumes input is already field-encoded using field_enc, and returns
88  * output that is still field-encoded. */
89 mp_err
ec_GFp_pt_jac2aff(const mp_int * px,const mp_int * py,const mp_int * pz,mp_int * rx,mp_int * ry,const ECGroup * group)90 ec_GFp_pt_jac2aff(const mp_int *px, const mp_int *py, const mp_int *pz,
91 				  mp_int *rx, mp_int *ry, const ECGroup *group)
92 {
93 	mp_err res = MP_OKAY;
94 	mp_int z1, z2, z3;
95 
96 	MP_DIGITS(&z1) = 0;
97 	MP_DIGITS(&z2) = 0;
98 	MP_DIGITS(&z3) = 0;
99 	MP_CHECKOK(mp_init(&z1, FLAG(px)));
100 	MP_CHECKOK(mp_init(&z2, FLAG(px)));
101 	MP_CHECKOK(mp_init(&z3, FLAG(px)));
102 
103 	/* if point at infinity, then set point at infinity and exit */
104 	if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {
105 		MP_CHECKOK(ec_GFp_pt_set_inf_aff(rx, ry));
106 		goto CLEANUP;
107 	}
108 
109 	/* transform (px, py, pz) into (px / pz^2, py / pz^3) */
110 	if (mp_cmp_d(pz, 1) == 0) {
111 		MP_CHECKOK(mp_copy(px, rx));
112 		MP_CHECKOK(mp_copy(py, ry));
113 	} else {
114 		MP_CHECKOK(group->meth->field_div(NULL, pz, &z1, group->meth));
115 		MP_CHECKOK(group->meth->field_sqr(&z1, &z2, group->meth));
116 		MP_CHECKOK(group->meth->field_mul(&z1, &z2, &z3, group->meth));
117 		MP_CHECKOK(group->meth->field_mul(px, &z2, rx, group->meth));
118 		MP_CHECKOK(group->meth->field_mul(py, &z3, ry, group->meth));
119 	}
120 
121   CLEANUP:
122 	mp_clear(&z1);
123 	mp_clear(&z2);
124 	mp_clear(&z3);
125 	return res;
126 }
127 
128 /* Checks if point P(px, py, pz) is at infinity. Uses Jacobian
129  * coordinates. */
130 mp_err
ec_GFp_pt_is_inf_jac(const mp_int * px,const mp_int * py,const mp_int * pz)131 ec_GFp_pt_is_inf_jac(const mp_int *px, const mp_int *py, const mp_int *pz)
132 {
133 	return mp_cmp_z(pz);
134 }
135 
136 /* Sets P(px, py, pz) to be the point at infinity.  Uses Jacobian
137  * coordinates. */
138 mp_err
ec_GFp_pt_set_inf_jac(mp_int * px,mp_int * py,mp_int * pz)139 ec_GFp_pt_set_inf_jac(mp_int *px, mp_int *py, mp_int *pz)
140 {
141 	mp_zero(pz);
142 	return MP_OKAY;
143 }
144 
145 /* Computes R = P + Q where R is (rx, ry, rz), P is (px, py, pz) and Q is
146  * (qx, qy, 1).  Elliptic curve points P, Q, and R can all be identical.
147  * Uses mixed Jacobian-affine coordinates. Assumes input is already
148  * field-encoded using field_enc, and returns output that is still
149  * field-encoded. Uses equation (2) from Brown, Hankerson, Lopez, and
150  * Menezes. Software Implementation of the NIST Elliptic Curves Over Prime
151  * Fields. */
152 mp_err
ec_GFp_pt_add_jac_aff(const mp_int * px,const mp_int * py,const mp_int * pz,const mp_int * qx,const mp_int * qy,mp_int * rx,mp_int * ry,mp_int * rz,const ECGroup * group)153 ec_GFp_pt_add_jac_aff(const mp_int *px, const mp_int *py, const mp_int *pz,
154 					  const mp_int *qx, const mp_int *qy, mp_int *rx,
155 					  mp_int *ry, mp_int *rz, const ECGroup *group)
156 {
157 	mp_err res = MP_OKAY;
158 	mp_int A, B, C, D, C2, C3;
159 
160 	MP_DIGITS(&A) = 0;
161 	MP_DIGITS(&B) = 0;
162 	MP_DIGITS(&C) = 0;
163 	MP_DIGITS(&D) = 0;
164 	MP_DIGITS(&C2) = 0;
165 	MP_DIGITS(&C3) = 0;
166 	MP_CHECKOK(mp_init(&A, FLAG(px)));
167 	MP_CHECKOK(mp_init(&B, FLAG(px)));
168 	MP_CHECKOK(mp_init(&C, FLAG(px)));
169 	MP_CHECKOK(mp_init(&D, FLAG(px)));
170 	MP_CHECKOK(mp_init(&C2, FLAG(px)));
171 	MP_CHECKOK(mp_init(&C3, FLAG(px)));
172 
173 	/* If either P or Q is the point at infinity, then return the other
174 	 * point */
175 	if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {
176 		MP_CHECKOK(ec_GFp_pt_aff2jac(qx, qy, rx, ry, rz, group));
177 		goto CLEANUP;
178 	}
179 	if (ec_GFp_pt_is_inf_aff(qx, qy) == MP_YES) {
180 		MP_CHECKOK(mp_copy(px, rx));
181 		MP_CHECKOK(mp_copy(py, ry));
182 		MP_CHECKOK(mp_copy(pz, rz));
183 		goto CLEANUP;
184 	}
185 
186 	/* A = qx * pz^2, B = qy * pz^3 */
187 	MP_CHECKOK(group->meth->field_sqr(pz, &A, group->meth));
188 	MP_CHECKOK(group->meth->field_mul(&A, pz, &B, group->meth));
189 	MP_CHECKOK(group->meth->field_mul(&A, qx, &A, group->meth));
190 	MP_CHECKOK(group->meth->field_mul(&B, qy, &B, group->meth));
191 
192 	/* C = A - px, D = B - py */
193 	MP_CHECKOK(group->meth->field_sub(&A, px, &C, group->meth));
194 	MP_CHECKOK(group->meth->field_sub(&B, py, &D, group->meth));
195 
196 	/* C2 = C^2, C3 = C^3 */
197 	MP_CHECKOK(group->meth->field_sqr(&C, &C2, group->meth));
198 	MP_CHECKOK(group->meth->field_mul(&C, &C2, &C3, group->meth));
199 
200 	/* rz = pz * C */
201 	MP_CHECKOK(group->meth->field_mul(pz, &C, rz, group->meth));
202 
203 	/* C = px * C^2 */
204 	MP_CHECKOK(group->meth->field_mul(px, &C2, &C, group->meth));
205 	/* A = D^2 */
206 	MP_CHECKOK(group->meth->field_sqr(&D, &A, group->meth));
207 
208 	/* rx = D^2 - (C^3 + 2 * (px * C^2)) */
209 	MP_CHECKOK(group->meth->field_add(&C, &C, rx, group->meth));
210 	MP_CHECKOK(group->meth->field_add(&C3, rx, rx, group->meth));
211 	MP_CHECKOK(group->meth->field_sub(&A, rx, rx, group->meth));
212 
213 	/* C3 = py * C^3 */
214 	MP_CHECKOK(group->meth->field_mul(py, &C3, &C3, group->meth));
215 
216 	/* ry = D * (px * C^2 - rx) - py * C^3 */
217 	MP_CHECKOK(group->meth->field_sub(&C, rx, ry, group->meth));
218 	MP_CHECKOK(group->meth->field_mul(&D, ry, ry, group->meth));
219 	MP_CHECKOK(group->meth->field_sub(ry, &C3, ry, group->meth));
220 
221   CLEANUP:
222 	mp_clear(&A);
223 	mp_clear(&B);
224 	mp_clear(&C);
225 	mp_clear(&D);
226 	mp_clear(&C2);
227 	mp_clear(&C3);
228 	return res;
229 }
230 
231 /* Computes R = 2P.  Elliptic curve points P and R can be identical.  Uses
232  * Jacobian coordinates.
233  *
234  * Assumes input is already field-encoded using field_enc, and returns
235  * output that is still field-encoded.
236  *
237  * This routine implements Point Doubling in the Jacobian Projective
238  * space as described in the paper "Efficient elliptic curve exponentiation
239  * using mixed coordinates", by H. Cohen, A Miyaji, T. Ono.
240  */
241 mp_err
ec_GFp_pt_dbl_jac(const mp_int * px,const mp_int * py,const mp_int * pz,mp_int * rx,mp_int * ry,mp_int * rz,const ECGroup * group)242 ec_GFp_pt_dbl_jac(const mp_int *px, const mp_int *py, const mp_int *pz,
243 				  mp_int *rx, mp_int *ry, mp_int *rz, const ECGroup *group)
244 {
245 	mp_err res = MP_OKAY;
246 	mp_int t0, t1, M, S;
247 
248 	MP_DIGITS(&t0) = 0;
249 	MP_DIGITS(&t1) = 0;
250 	MP_DIGITS(&M) = 0;
251 	MP_DIGITS(&S) = 0;
252 	MP_CHECKOK(mp_init(&t0, FLAG(px)));
253 	MP_CHECKOK(mp_init(&t1, FLAG(px)));
254 	MP_CHECKOK(mp_init(&M, FLAG(px)));
255 	MP_CHECKOK(mp_init(&S, FLAG(px)));
256 
257 	if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {
258 		MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, rz));
259 		goto CLEANUP;
260 	}
261 
262 	if (mp_cmp_d(pz, 1) == 0) {
263 		/* M = 3 * px^2 + a */
264 		MP_CHECKOK(group->meth->field_sqr(px, &t0, group->meth));
265 		MP_CHECKOK(group->meth->field_add(&t0, &t0, &M, group->meth));
266 		MP_CHECKOK(group->meth->field_add(&t0, &M, &t0, group->meth));
267 		MP_CHECKOK(group->meth->
268 				   field_add(&t0, &group->curvea, &M, group->meth));
269 	} else if (mp_cmp_int(&group->curvea, -3, FLAG(px)) == 0) {
270 		/* M = 3 * (px + pz^2) * (px - pz^2) */
271 		MP_CHECKOK(group->meth->field_sqr(pz, &M, group->meth));
272 		MP_CHECKOK(group->meth->field_add(px, &M, &t0, group->meth));
273 		MP_CHECKOK(group->meth->field_sub(px, &M, &t1, group->meth));
274 		MP_CHECKOK(group->meth->field_mul(&t0, &t1, &M, group->meth));
275 		MP_CHECKOK(group->meth->field_add(&M, &M, &t0, group->meth));
276 		MP_CHECKOK(group->meth->field_add(&t0, &M, &M, group->meth));
277 	} else {
278 		/* M = 3 * (px^2) + a * (pz^4) */
279 		MP_CHECKOK(group->meth->field_sqr(px, &t0, group->meth));
280 		MP_CHECKOK(group->meth->field_add(&t0, &t0, &M, group->meth));
281 		MP_CHECKOK(group->meth->field_add(&t0, &M, &t0, group->meth));
282 		MP_CHECKOK(group->meth->field_sqr(pz, &M, group->meth));
283 		MP_CHECKOK(group->meth->field_sqr(&M, &M, group->meth));
284 		MP_CHECKOK(group->meth->
285 				   field_mul(&M, &group->curvea, &M, group->meth));
286 		MP_CHECKOK(group->meth->field_add(&M, &t0, &M, group->meth));
287 	}
288 
289 	/* rz = 2 * py * pz */
290 	/* t0 = 4 * py^2 */
291 	if (mp_cmp_d(pz, 1) == 0) {
292 		MP_CHECKOK(group->meth->field_add(py, py, rz, group->meth));
293 		MP_CHECKOK(group->meth->field_sqr(rz, &t0, group->meth));
294 	} else {
295 		MP_CHECKOK(group->meth->field_add(py, py, &t0, group->meth));
296 		MP_CHECKOK(group->meth->field_mul(&t0, pz, rz, group->meth));
297 		MP_CHECKOK(group->meth->field_sqr(&t0, &t0, group->meth));
298 	}
299 
300 	/* S = 4 * px * py^2 = px * (2 * py)^2 */
301 	MP_CHECKOK(group->meth->field_mul(px, &t0, &S, group->meth));
302 
303 	/* rx = M^2 - 2 * S */
304 	MP_CHECKOK(group->meth->field_add(&S, &S, &t1, group->meth));
305 	MP_CHECKOK(group->meth->field_sqr(&M, rx, group->meth));
306 	MP_CHECKOK(group->meth->field_sub(rx, &t1, rx, group->meth));
307 
308 	/* ry = M * (S - rx) - 8 * py^4 */
309 	MP_CHECKOK(group->meth->field_sqr(&t0, &t1, group->meth));
310 	if (mp_isodd(&t1)) {
311 		MP_CHECKOK(mp_add(&t1, &group->meth->irr, &t1));
312 	}
313 	MP_CHECKOK(mp_div_2(&t1, &t1));
314 	MP_CHECKOK(group->meth->field_sub(&S, rx, &S, group->meth));
315 	MP_CHECKOK(group->meth->field_mul(&M, &S, &M, group->meth));
316 	MP_CHECKOK(group->meth->field_sub(&M, &t1, ry, group->meth));
317 
318   CLEANUP:
319 	mp_clear(&t0);
320 	mp_clear(&t1);
321 	mp_clear(&M);
322 	mp_clear(&S);
323 	return res;
324 }
325 
326 /* by default, this routine is unused and thus doesn't need to be compiled */
327 #ifdef ECL_ENABLE_GFP_PT_MUL_JAC
328 /* Computes R = nP where R is (rx, ry) and P is (px, py). The parameters
329  * a, b and p are the elliptic curve coefficients and the prime that
330  * determines the field GFp.  Elliptic curve points P and R can be
331  * identical.  Uses mixed Jacobian-affine coordinates. Assumes input is
332  * already field-encoded using field_enc, and returns output that is still
333  * field-encoded. Uses 4-bit window method. */
334 mp_err
ec_GFp_pt_mul_jac(const mp_int * n,const mp_int * px,const mp_int * py,mp_int * rx,mp_int * ry,const ECGroup * group)335 ec_GFp_pt_mul_jac(const mp_int *n, const mp_int *px, const mp_int *py,
336 				  mp_int *rx, mp_int *ry, const ECGroup *group)
337 {
338 	mp_err res = MP_OKAY;
339 	mp_int precomp[16][2], rz;
340 	int i, ni, d;
341 
342 	MP_DIGITS(&rz) = 0;
343 	for (i = 0; i < 16; i++) {
344 		MP_DIGITS(&precomp[i][0]) = 0;
345 		MP_DIGITS(&precomp[i][1]) = 0;
346 	}
347 
348 	ARGCHK(group != NULL, MP_BADARG);
349 	ARGCHK((n != NULL) && (px != NULL) && (py != NULL), MP_BADARG);
350 
351 	/* initialize precomputation table */
352 	for (i = 0; i < 16; i++) {
353 		MP_CHECKOK(mp_init(&precomp[i][0]));
354 		MP_CHECKOK(mp_init(&precomp[i][1]));
355 	}
356 
357 	/* fill precomputation table */
358 	mp_zero(&precomp[0][0]);
359 	mp_zero(&precomp[0][1]);
360 	MP_CHECKOK(mp_copy(px, &precomp[1][0]));
361 	MP_CHECKOK(mp_copy(py, &precomp[1][1]));
362 	for (i = 2; i < 16; i++) {
363 		MP_CHECKOK(group->
364 				   point_add(&precomp[1][0], &precomp[1][1],
365 							 &precomp[i - 1][0], &precomp[i - 1][1],
366 							 &precomp[i][0], &precomp[i][1], group));
367 	}
368 
369 	d = (mpl_significant_bits(n) + 3) / 4;
370 
371 	/* R = inf */
372 	MP_CHECKOK(mp_init(&rz));
373 	MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, &rz));
374 
375 	for (i = d - 1; i >= 0; i--) {
376 		/* compute window ni */
377 		ni = MP_GET_BIT(n, 4 * i + 3);
378 		ni <<= 1;
379 		ni |= MP_GET_BIT(n, 4 * i + 2);
380 		ni <<= 1;
381 		ni |= MP_GET_BIT(n, 4 * i + 1);
382 		ni <<= 1;
383 		ni |= MP_GET_BIT(n, 4 * i);
384 		/* R = 2^4 * R */
385 		MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group));
386 		MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group));
387 		MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group));
388 		MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group));
389 		/* R = R + (ni * P) */
390 		MP_CHECKOK(ec_GFp_pt_add_jac_aff
391 				   (rx, ry, &rz, &precomp[ni][0], &precomp[ni][1], rx, ry,
392 					&rz, group));
393 	}
394 
395 	/* convert result S to affine coordinates */
396 	MP_CHECKOK(ec_GFp_pt_jac2aff(rx, ry, &rz, rx, ry, group));
397 
398   CLEANUP:
399 	mp_clear(&rz);
400 	for (i = 0; i < 16; i++) {
401 		mp_clear(&precomp[i][0]);
402 		mp_clear(&precomp[i][1]);
403 	}
404 	return res;
405 }
406 #endif
407 
408 /* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G +
409  * k2 * P(x, y), where G is the generator (base point) of the group of
410  * points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL.
411  * Uses mixed Jacobian-affine coordinates. Input and output values are
412  * assumed to be NOT field-encoded. Uses algorithm 15 (simultaneous
413  * multiple point multiplication) from Brown, Hankerson, Lopez, Menezes.
414  * Software Implementation of the NIST Elliptic Curves over Prime Fields. */
415 mp_err
ec_GFp_pts_mul_jac(const mp_int * k1,const mp_int * k2,const mp_int * px,const mp_int * py,mp_int * rx,mp_int * ry,const ECGroup * group)416 ec_GFp_pts_mul_jac(const mp_int *k1, const mp_int *k2, const mp_int *px,
417 				   const mp_int *py, mp_int *rx, mp_int *ry,
418 				   const ECGroup *group)
419 {
420 	mp_err res = MP_OKAY;
421 	mp_int precomp[4][4][2];
422 	mp_int rz;
423 	const mp_int *a, *b;
424 	int i, j;
425 	int ai, bi, d;
426 
427 	for (i = 0; i < 4; i++) {
428 		for (j = 0; j < 4; j++) {
429 			MP_DIGITS(&precomp[i][j][0]) = 0;
430 			MP_DIGITS(&precomp[i][j][1]) = 0;
431 		}
432 	}
433 	MP_DIGITS(&rz) = 0;
434 
435 	ARGCHK(group != NULL, MP_BADARG);
436 	ARGCHK(!((k1 == NULL)
437 			 && ((k2 == NULL) || (px == NULL)
438 				 || (py == NULL))), MP_BADARG);
439 
440 	/* if some arguments are not defined used ECPoint_mul */
441 	if (k1 == NULL) {
442 		return ECPoint_mul(group, k2, px, py, rx, ry);
443 	} else if ((k2 == NULL) || (px == NULL) || (py == NULL)) {
444 		return ECPoint_mul(group, k1, NULL, NULL, rx, ry);
445 	}
446 
447 	/* initialize precomputation table */
448 	for (i = 0; i < 4; i++) {
449 		for (j = 0; j < 4; j++) {
450 			MP_CHECKOK(mp_init(&precomp[i][j][0], FLAG(k1)));
451 			MP_CHECKOK(mp_init(&precomp[i][j][1], FLAG(k1)));
452 		}
453 	}
454 
455 	/* fill precomputation table */
456 	/* assign {k1, k2} = {a, b} such that len(a) >= len(b) */
457 	if (mpl_significant_bits(k1) < mpl_significant_bits(k2)) {
458 		a = k2;
459 		b = k1;
460 		if (group->meth->field_enc) {
461 			MP_CHECKOK(group->meth->
462 					   field_enc(px, &precomp[1][0][0], group->meth));
463 			MP_CHECKOK(group->meth->
464 					   field_enc(py, &precomp[1][0][1], group->meth));
465 		} else {
466 			MP_CHECKOK(mp_copy(px, &precomp[1][0][0]));
467 			MP_CHECKOK(mp_copy(py, &precomp[1][0][1]));
468 		}
469 		MP_CHECKOK(mp_copy(&group->genx, &precomp[0][1][0]));
470 		MP_CHECKOK(mp_copy(&group->geny, &precomp[0][1][1]));
471 	} else {
472 		a = k1;
473 		b = k2;
474 		MP_CHECKOK(mp_copy(&group->genx, &precomp[1][0][0]));
475 		MP_CHECKOK(mp_copy(&group->geny, &precomp[1][0][1]));
476 		if (group->meth->field_enc) {
477 			MP_CHECKOK(group->meth->
478 					   field_enc(px, &precomp[0][1][0], group->meth));
479 			MP_CHECKOK(group->meth->
480 					   field_enc(py, &precomp[0][1][1], group->meth));
481 		} else {
482 			MP_CHECKOK(mp_copy(px, &precomp[0][1][0]));
483 			MP_CHECKOK(mp_copy(py, &precomp[0][1][1]));
484 		}
485 	}
486 	/* precompute [*][0][*] */
487 	mp_zero(&precomp[0][0][0]);
488 	mp_zero(&precomp[0][0][1]);
489 	MP_CHECKOK(group->
490 			   point_dbl(&precomp[1][0][0], &precomp[1][0][1],
491 						 &precomp[2][0][0], &precomp[2][0][1], group));
492 	MP_CHECKOK(group->
493 			   point_add(&precomp[1][0][0], &precomp[1][0][1],
494 						 &precomp[2][0][0], &precomp[2][0][1],
495 						 &precomp[3][0][0], &precomp[3][0][1], group));
496 	/* precompute [*][1][*] */
497 	for (i = 1; i < 4; i++) {
498 		MP_CHECKOK(group->
499 				   point_add(&precomp[0][1][0], &precomp[0][1][1],
500 							 &precomp[i][0][0], &precomp[i][0][1],
501 							 &precomp[i][1][0], &precomp[i][1][1], group));
502 	}
503 	/* precompute [*][2][*] */
504 	MP_CHECKOK(group->
505 			   point_dbl(&precomp[0][1][0], &precomp[0][1][1],
506 						 &precomp[0][2][0], &precomp[0][2][1], group));
507 	for (i = 1; i < 4; i++) {
508 		MP_CHECKOK(group->
509 				   point_add(&precomp[0][2][0], &precomp[0][2][1],
510 							 &precomp[i][0][0], &precomp[i][0][1],
511 							 &precomp[i][2][0], &precomp[i][2][1], group));
512 	}
513 	/* precompute [*][3][*] */
514 	MP_CHECKOK(group->
515 			   point_add(&precomp[0][1][0], &precomp[0][1][1],
516 						 &precomp[0][2][0], &precomp[0][2][1],
517 						 &precomp[0][3][0], &precomp[0][3][1], group));
518 	for (i = 1; i < 4; i++) {
519 		MP_CHECKOK(group->
520 				   point_add(&precomp[0][3][0], &precomp[0][3][1],
521 							 &precomp[i][0][0], &precomp[i][0][1],
522 							 &precomp[i][3][0], &precomp[i][3][1], group));
523 	}
524 
525 	d = (mpl_significant_bits(a) + 1) / 2;
526 
527 	/* R = inf */
528 	MP_CHECKOK(mp_init(&rz, FLAG(k1)));
529 	MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, &rz));
530 
531 	for (i = d - 1; i >= 0; i--) {
532 		ai = MP_GET_BIT(a, 2 * i + 1);
533 		ai <<= 1;
534 		ai |= MP_GET_BIT(a, 2 * i);
535 		bi = MP_GET_BIT(b, 2 * i + 1);
536 		bi <<= 1;
537 		bi |= MP_GET_BIT(b, 2 * i);
538 		/* R = 2^2 * R */
539 		MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group));
540 		MP_CHECKOK(ec_GFp_pt_dbl_jac(rx, ry, &rz, rx, ry, &rz, group));
541 		/* R = R + (ai * A + bi * B) */
542 		MP_CHECKOK(ec_GFp_pt_add_jac_aff
543 				   (rx, ry, &rz, &precomp[ai][bi][0], &precomp[ai][bi][1],
544 					rx, ry, &rz, group));
545 	}
546 
547 	MP_CHECKOK(ec_GFp_pt_jac2aff(rx, ry, &rz, rx, ry, group));
548 
549 	if (group->meth->field_dec) {
550 		MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth));
551 		MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth));
552 	}
553 
554   CLEANUP:
555 	mp_clear(&rz);
556 	for (i = 0; i < 4; i++) {
557 		for (j = 0; j < 4; j++) {
558 			mp_clear(&precomp[i][j][0]);
559 			mp_clear(&precomp[i][j][1]);
560 		}
561 	}
562 	return res;
563 }
564