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. */
65mp_err
66ec_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. */
89mp_err
90ec_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. */
130mp_err
131ec_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. */
138mp_err
139ec_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. */
152mp_err
153ec_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 */
241mp_err
242ec_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. */
334mp_err
335ec_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. */
415mp_err
416ec_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