ec2_mult.c revision 296341 
1/* crypto/ec/ec2_mult.c */
2/* ====================================================================
3 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
4 *
5 * The Elliptic Curve Public-Key Crypto Library (ECC Code) included
6 * herein is developed by SUN MICROSYSTEMS, INC., and is contributed
7 * to the OpenSSL project.
8 *
9 * The ECC Code is licensed pursuant to the OpenSSL open source
10 * license provided below.
11 *
12 * The software is originally written by Sheueling Chang Shantz and
13 * Douglas Stebila of Sun Microsystems Laboratories.
14 *
15 */
16/* ====================================================================
17 * Copyright (c) 1998-2003 The OpenSSL Project.  All rights reserved.
18 *
19 * Redistribution and use in source and binary forms, with or without
20 * modification, are permitted provided that the following conditions
21 * are met:
22 *
23 * 1. Redistributions of source code must retain the above copyright
24 *    notice, this list of conditions and the following disclaimer.
25 *
26 * 2. Redistributions in binary form must reproduce the above copyright
27 *    notice, this list of conditions and the following disclaimer in
28 *    the documentation and/or other materials provided with the
29 *    distribution.
30 *
31 * 3. All advertising materials mentioning features or use of this
32 *    software must display the following acknowledgment:
33 *    "This product includes software developed by the OpenSSL Project
34 *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
35 *
36 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
37 *    endorse or promote products derived from this software without
38 *    prior written permission. For written permission, please contact
39 *    openssl-core@openssl.org.
40 *
41 * 5. Products derived from this software may not be called "OpenSSL"
42 *    nor may "OpenSSL" appear in their names without prior written
43 *    permission of the OpenSSL Project.
44 *
45 * 6. Redistributions of any form whatsoever must retain the following
46 *    acknowledgment:
47 *    "This product includes software developed by the OpenSSL Project
48 *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
49 *
50 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
51 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
52 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
53 * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR
54 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
55 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
56 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
57 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
58 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
59 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
60 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
61 * OF THE POSSIBILITY OF SUCH DAMAGE.
62 * ====================================================================
63 *
64 * This product includes cryptographic software written by Eric Young
65 * (eay@cryptsoft.com).  This product includes software written by Tim
66 * Hudson (tjh@cryptsoft.com).
67 *
68 */
69
70#include <openssl/err.h>
71
72#include "ec_lcl.h"
73
74#ifndef OPENSSL_NO_EC2M
75
76/*-
77 * Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery projective
78 * coordinates.
79 * Uses algorithm Mdouble in appendix of
80 *     Lopez, J. and Dahab, R.  "Fast multiplication on elliptic curves over
81 *     GF(2^m) without precomputation" (CHES '99, LNCS 1717).
82 * modified to not require precomputation of c=b^{2^{m-1}}.
83 */
84static int gf2m_Mdouble(const EC_GROUP *group, BIGNUM *x, BIGNUM *z,
85                        BN_CTX *ctx)
86{
87    BIGNUM *t1;
88    int ret = 0;
89
90    /* Since Mdouble is static we can guarantee that ctx != NULL. */
91    BN_CTX_start(ctx);
92    t1 = BN_CTX_get(ctx);
93    if (t1 == NULL)
94        goto err;
95
96    if (!group->meth->field_sqr(group, x, x, ctx))
97        goto err;
98    if (!group->meth->field_sqr(group, t1, z, ctx))
99        goto err;
100    if (!group->meth->field_mul(group, z, x, t1, ctx))
101        goto err;
102    if (!group->meth->field_sqr(group, x, x, ctx))
103        goto err;
104    if (!group->meth->field_sqr(group, t1, t1, ctx))
105        goto err;
106    if (!group->meth->field_mul(group, t1, &group->b, t1, ctx))
107        goto err;
108    if (!BN_GF2m_add(x, x, t1))
109        goto err;
110
111    ret = 1;
112
113 err:
114    BN_CTX_end(ctx);
115    return ret;
116}
117
118/*-
119 * Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in Montgomery
120 * projective coordinates.
121 * Uses algorithm Madd in appendix of
122 *     Lopez, J. and Dahab, R.  "Fast multiplication on elliptic curves over
123 *     GF(2^m) without precomputation" (CHES '99, LNCS 1717).
124 */
125static int gf2m_Madd(const EC_GROUP *group, const BIGNUM *x, BIGNUM *x1,
126                     BIGNUM *z1, const BIGNUM *x2, const BIGNUM *z2,
127                     BN_CTX *ctx)
128{
129    BIGNUM *t1, *t2;
130    int ret = 0;
131
132    /* Since Madd is static we can guarantee that ctx != NULL. */
133    BN_CTX_start(ctx);
134    t1 = BN_CTX_get(ctx);
135    t2 = BN_CTX_get(ctx);
136    if (t2 == NULL)
137        goto err;
138
139    if (!BN_copy(t1, x))
140        goto err;
141    if (!group->meth->field_mul(group, x1, x1, z2, ctx))
142        goto err;
143    if (!group->meth->field_mul(group, z1, z1, x2, ctx))
144        goto err;
145    if (!group->meth->field_mul(group, t2, x1, z1, ctx))
146        goto err;
147    if (!BN_GF2m_add(z1, z1, x1))
148        goto err;
149    if (!group->meth->field_sqr(group, z1, z1, ctx))
150        goto err;
151    if (!group->meth->field_mul(group, x1, z1, t1, ctx))
152        goto err;
153    if (!BN_GF2m_add(x1, x1, t2))
154        goto err;
155
156    ret = 1;
157
158 err:
159    BN_CTX_end(ctx);
160    return ret;
161}
162
163/*-
164 * Compute the x, y affine coordinates from the point (x1, z1) (x2, z2)
165 * using Montgomery point multiplication algorithm Mxy() in appendix of
166 *     Lopez, J. and Dahab, R.  "Fast multiplication on elliptic curves over
167 *     GF(2^m) without precomputation" (CHES '99, LNCS 1717).
168 * Returns:
169 *     0 on error
170 *     1 if return value should be the point at infinity
171 *     2 otherwise
172 */
173static int gf2m_Mxy(const EC_GROUP *group, const BIGNUM *x, const BIGNUM *y,
174                    BIGNUM *x1, BIGNUM *z1, BIGNUM *x2, BIGNUM *z2,
175                    BN_CTX *ctx)
176{
177    BIGNUM *t3, *t4, *t5;
178    int ret = 0;
179
180    if (BN_is_zero(z1)) {
181        BN_zero(x2);
182        BN_zero(z2);
183        return 1;
184    }
185
186    if (BN_is_zero(z2)) {
187        if (!BN_copy(x2, x))
188            return 0;
189        if (!BN_GF2m_add(z2, x, y))
190            return 0;
191        return 2;
192    }
193
194    /* Since Mxy is static we can guarantee that ctx != NULL. */
195    BN_CTX_start(ctx);
196    t3 = BN_CTX_get(ctx);
197    t4 = BN_CTX_get(ctx);
198    t5 = BN_CTX_get(ctx);
199    if (t5 == NULL)
200        goto err;
201
202    if (!BN_one(t5))
203        goto err;
204
205    if (!group->meth->field_mul(group, t3, z1, z2, ctx))
206        goto err;
207
208    if (!group->meth->field_mul(group, z1, z1, x, ctx))
209        goto err;
210    if (!BN_GF2m_add(z1, z1, x1))
211        goto err;
212    if (!group->meth->field_mul(group, z2, z2, x, ctx))
213        goto err;
214    if (!group->meth->field_mul(group, x1, z2, x1, ctx))
215        goto err;
216    if (!BN_GF2m_add(z2, z2, x2))
217        goto err;
218
219    if (!group->meth->field_mul(group, z2, z2, z1, ctx))
220        goto err;
221    if (!group->meth->field_sqr(group, t4, x, ctx))
222        goto err;
223    if (!BN_GF2m_add(t4, t4, y))
224        goto err;
225    if (!group->meth->field_mul(group, t4, t4, t3, ctx))
226        goto err;
227    if (!BN_GF2m_add(t4, t4, z2))
228        goto err;
229
230    if (!group->meth->field_mul(group, t3, t3, x, ctx))
231        goto err;
232    if (!group->meth->field_div(group, t3, t5, t3, ctx))
233        goto err;
234    if (!group->meth->field_mul(group, t4, t3, t4, ctx))
235        goto err;
236    if (!group->meth->field_mul(group, x2, x1, t3, ctx))
237        goto err;
238    if (!BN_GF2m_add(z2, x2, x))
239        goto err;
240
241    if (!group->meth->field_mul(group, z2, z2, t4, ctx))
242        goto err;
243    if (!BN_GF2m_add(z2, z2, y))
244        goto err;
245
246    ret = 2;
247
248 err:
249    BN_CTX_end(ctx);
250    return ret;
251}
252
253/*-
254 * Computes scalar*point and stores the result in r.
255 * point can not equal r.
256 * Uses a modified algorithm 2P of
257 *     Lopez, J. and Dahab, R.  "Fast multiplication on elliptic curves over
258 *     GF(2^m) without precomputation" (CHES '99, LNCS 1717).
259 *
260 * To protect against side-channel attack the function uses constant time swap,
261 * avoiding conditional branches.
262 */
263static int ec_GF2m_montgomery_point_multiply(const EC_GROUP *group,
264                                             EC_POINT *r,
265                                             const BIGNUM *scalar,
266                                             const EC_POINT *point,
267                                             BN_CTX *ctx)
268{
269    BIGNUM *x1, *x2, *z1, *z2;
270    int ret = 0, i;
271    BN_ULONG mask, word;
272
273    if (r == point) {
274        ECerr(EC_F_EC_GF2M_MONTGOMERY_POINT_MULTIPLY, EC_R_INVALID_ARGUMENT);
275        return 0;
276    }
277
278    /* if result should be point at infinity */
279    if ((scalar == NULL) || BN_is_zero(scalar) || (point == NULL) ||
280        EC_POINT_is_at_infinity(group, point)) {
281        return EC_POINT_set_to_infinity(group, r);
282    }
283
284    /* only support affine coordinates */
285    if (!point->Z_is_one)
286        return 0;
287
288    /*
289     * Since point_multiply is static we can guarantee that ctx != NULL.
290     */
291    BN_CTX_start(ctx);
292    x1 = BN_CTX_get(ctx);
293    z1 = BN_CTX_get(ctx);
294    if (z1 == NULL)
295        goto err;
296
297    x2 = &r->X;
298    z2 = &r->Y;
299
300    bn_wexpand(x1, group->field.top);
301    bn_wexpand(z1, group->field.top);
302    bn_wexpand(x2, group->field.top);
303    bn_wexpand(z2, group->field.top);
304
305    if (!BN_GF2m_mod_arr(x1, &point->X, group->poly))
306        goto err;               /* x1 = x */
307    if (!BN_one(z1))
308        goto err;               /* z1 = 1 */
309    if (!group->meth->field_sqr(group, z2, x1, ctx))
310        goto err;               /* z2 = x1^2 = x^2 */
311    if (!group->meth->field_sqr(group, x2, z2, ctx))
312        goto err;
313    if (!BN_GF2m_add(x2, x2, &group->b))
314        goto err;               /* x2 = x^4 + b */
315
316    /* find top most bit and go one past it */
317    i = scalar->top - 1;
318    mask = BN_TBIT;
319    word = scalar->d[i];
320    while (!(word & mask))
321        mask >>= 1;
322    mask >>= 1;
323    /* if top most bit was at word break, go to next word */
324    if (!mask) {
325        i--;
326        mask = BN_TBIT;
327    }
328
329    for (; i >= 0; i--) {
330        word = scalar->d[i];
331        while (mask) {
332            BN_consttime_swap(word & mask, x1, x2, group->field.top);
333            BN_consttime_swap(word & mask, z1, z2, group->field.top);
334            if (!gf2m_Madd(group, &point->X, x2, z2, x1, z1, ctx))
335                goto err;
336            if (!gf2m_Mdouble(group, x1, z1, ctx))
337                goto err;
338            BN_consttime_swap(word & mask, x1, x2, group->field.top);
339            BN_consttime_swap(word & mask, z1, z2, group->field.top);
340            mask >>= 1;
341        }
342        mask = BN_TBIT;
343    }
344
345    /* convert out of "projective" coordinates */
346    i = gf2m_Mxy(group, &point->X, &point->Y, x1, z1, x2, z2, ctx);
347    if (i == 0)
348        goto err;
349    else if (i == 1) {
350        if (!EC_POINT_set_to_infinity(group, r))
351            goto err;
352    } else {
353        if (!BN_one(&r->Z))
354            goto err;
355        r->Z_is_one = 1;
356    }
357
358    /* GF(2^m) field elements should always have BIGNUM::neg = 0 */
359    BN_set_negative(&r->X, 0);
360    BN_set_negative(&r->Y, 0);
361
362    ret = 1;
363
364 err:
365    BN_CTX_end(ctx);
366    return ret;
367}
368
369/*-
370 * Computes the sum
371 *     scalar*group->generator + scalars[0]*points[0] + ... + scalars[num-1]*points[num-1]
372 * gracefully ignoring NULL scalar values.
373 */
374int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r,
375                       const BIGNUM *scalar, size_t num,
376                       const EC_POINT *points[], const BIGNUM *scalars[],
377                       BN_CTX *ctx)
378{
379    BN_CTX *new_ctx = NULL;
380    int ret = 0;
381    size_t i;
382    EC_POINT *p = NULL;
383    EC_POINT *acc = NULL;
384
385    if (ctx == NULL) {
386        ctx = new_ctx = BN_CTX_new();
387        if (ctx == NULL)
388            return 0;
389    }
390
391    /*
392     * This implementation is more efficient than the wNAF implementation for
393     * 2 or fewer points.  Use the ec_wNAF_mul implementation for 3 or more
394     * points, or if we can perform a fast multiplication based on
395     * precomputation.
396     */
397    if ((scalar && (num > 1)) || (num > 2)
398        || (num == 0 && EC_GROUP_have_precompute_mult(group))) {
399        ret = ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx);
400        goto err;
401    }
402
403    if ((p = EC_POINT_new(group)) == NULL)
404        goto err;
405    if ((acc = EC_POINT_new(group)) == NULL)
406        goto err;
407
408    if (!EC_POINT_set_to_infinity(group, acc))
409        goto err;
410
411    if (scalar) {
412        if (!ec_GF2m_montgomery_point_multiply
413            (group, p, scalar, group->generator, ctx))
414            goto err;
415        if (BN_is_negative(scalar))
416            if (!group->meth->invert(group, p, ctx))
417                goto err;
418        if (!group->meth->add(group, acc, acc, p, ctx))
419            goto err;
420    }
421
422    for (i = 0; i < num; i++) {
423        if (!ec_GF2m_montgomery_point_multiply
424            (group, p, scalars[i], points[i], ctx))
425            goto err;
426        if (BN_is_negative(scalars[i]))
427            if (!group->meth->invert(group, p, ctx))
428                goto err;
429        if (!group->meth->add(group, acc, acc, p, ctx))
430            goto err;
431    }
432
433    if (!EC_POINT_copy(r, acc))
434        goto err;
435
436    ret = 1;
437
438 err:
439    if (p)
440        EC_POINT_free(p);
441    if (acc)
442        EC_POINT_free(acc);
443    if (new_ctx != NULL)
444        BN_CTX_free(new_ctx);
445    return ret;
446}
447
448/*
449 * Precomputation for point multiplication: fall back to wNAF methods because
450 * ec_GF2m_simple_mul() uses ec_wNAF_mul() if appropriate
451 */
452
453int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
454{
455    return ec_wNAF_precompute_mult(group, ctx);
456}
457
458int ec_GF2m_have_precompute_mult(const EC_GROUP *group)
459{
460    return ec_wNAF_have_precompute_mult(group);
461}
462
463#endif
464