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1/* ec.c - Elliptic Curve functions
2 * Copyright (C) 2007 Free Software Foundation, Inc.
3 * Copyright (C) 2013 g10 Code GmbH
4 *
5 * This file is part of Libgcrypt.
6 *
7 * Libgcrypt is free software; you can redistribute it and/or modify
8 * it under the terms of the GNU Lesser General Public License as
9 * published by the Free Software Foundation; either version 2.1 of
10 * the License, or (at your option) any later version.
11 *
12 * Libgcrypt is distributed in the hope that it will be useful,
13 * but WITHOUT ANY WARRANTY; without even the implied warranty of
14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
15 * GNU Lesser General Public License for more details.
16 *
17 * You should have received a copy of the GNU Lesser General Public
18 * License along with this program; if not, see <http://www.gnu.org/licenses/>.
19 */
20
21#include "mpi-internal.h"
22#include "longlong.h"
23
24#define point_init(a) mpi_point_init((a))
25#define point_free(a) mpi_point_free_parts((a))
26
27#define log_error(fmt, ...) pr_err(fmt, ##__VA_ARGS__)
28#define log_fatal(fmt, ...) pr_err(fmt, ##__VA_ARGS__)
29
30#define DIM(v) (sizeof(v)/sizeof((v)[0]))
31
32
33/* Create a new point option. NBITS gives the size in bits of one
34 * coordinate; it is only used to pre-allocate some resources and
35 * might also be passed as 0 to use a default value.
36 */
37MPI_POINT mpi_point_new(unsigned int nbits)
38{
39 MPI_POINT p;
40
41 (void)nbits; /* Currently not used. */
42
43 p = kmalloc(sizeof(*p), GFP_KERNEL);
44 if (p)
45 mpi_point_init(p);
46 return p;
47}
48EXPORT_SYMBOL_GPL(mpi_point_new);
49
50/* Release the point object P. P may be NULL. */
51void mpi_point_release(MPI_POINT p)
52{
53 if (p) {
54 mpi_point_free_parts(p);
55 kfree(p);
56 }
57}
58EXPORT_SYMBOL_GPL(mpi_point_release);
59
60/* Initialize the fields of a point object. gcry_mpi_point_free_parts
61 * may be used to release the fields.
62 */
63void mpi_point_init(MPI_POINT p)
64{
65 p->x = mpi_new(0);
66 p->y = mpi_new(0);
67 p->z = mpi_new(0);
68}
69EXPORT_SYMBOL_GPL(mpi_point_init);
70
71/* Release the parts of a point object. */
72void mpi_point_free_parts(MPI_POINT p)
73{
74 mpi_free(p->x); p->x = NULL;
75 mpi_free(p->y); p->y = NULL;
76 mpi_free(p->z); p->z = NULL;
77}
78EXPORT_SYMBOL_GPL(mpi_point_free_parts);
79
80/* Set the value from S into D. */
81static void point_set(MPI_POINT d, MPI_POINT s)
82{
83 mpi_set(d->x, s->x);
84 mpi_set(d->y, s->y);
85 mpi_set(d->z, s->z);
86}
87
88static void point_resize(MPI_POINT p, struct mpi_ec_ctx *ctx)
89{
90 size_t nlimbs = ctx->p->nlimbs;
91
92 mpi_resize(p->x, nlimbs);
93 p->x->nlimbs = nlimbs;
94 mpi_resize(p->z, nlimbs);
95 p->z->nlimbs = nlimbs;
96
97 if (ctx->model != MPI_EC_MONTGOMERY) {
98 mpi_resize(p->y, nlimbs);
99 p->y->nlimbs = nlimbs;
100 }
101}
102
103static void point_swap_cond(MPI_POINT d, MPI_POINT s, unsigned long swap,
104 struct mpi_ec_ctx *ctx)
105{
106 mpi_swap_cond(d->x, s->x, swap);
107 if (ctx->model != MPI_EC_MONTGOMERY)
108 mpi_swap_cond(d->y, s->y, swap);
109 mpi_swap_cond(d->z, s->z, swap);
110}
111
112
113/* W = W mod P. */
114static void ec_mod(MPI w, struct mpi_ec_ctx *ec)
115{
116 if (ec->t.p_barrett)
117 mpi_mod_barrett(w, w, ec->t.p_barrett);
118 else
119 mpi_mod(w, w, ec->p);
120}
121
122static void ec_addm(MPI w, MPI u, MPI v, struct mpi_ec_ctx *ctx)
123{
124 mpi_add(w, u, v);
125 ec_mod(w, ctx);
126}
127
128static void ec_subm(MPI w, MPI u, MPI v, struct mpi_ec_ctx *ec)
129{
130 mpi_sub(w, u, v);
131 while (w->sign)
132 mpi_add(w, w, ec->p);
133 /*ec_mod(w, ec);*/
134}
135
136static void ec_mulm(MPI w, MPI u, MPI v, struct mpi_ec_ctx *ctx)
137{
138 mpi_mul(w, u, v);
139 ec_mod(w, ctx);
140}
141
142/* W = 2 * U mod P. */
143static void ec_mul2(MPI w, MPI u, struct mpi_ec_ctx *ctx)
144{
145 mpi_lshift(w, u, 1);
146 ec_mod(w, ctx);
147}
148
149static void ec_powm(MPI w, const MPI b, const MPI e,
150 struct mpi_ec_ctx *ctx)
151{
152 mpi_powm(w, b, e, ctx->p);
153 /* mpi_abs(w); */
154}
155
156/* Shortcut for
157 * ec_powm(B, B, mpi_const(MPI_C_TWO), ctx);
158 * for easier optimization.
159 */
160static void ec_pow2(MPI w, const MPI b, struct mpi_ec_ctx *ctx)
161{
162 /* Using mpi_mul is slightly faster (at least on amd64). */
163 /* mpi_powm(w, b, mpi_const(MPI_C_TWO), ctx->p); */
164 ec_mulm(w, b, b, ctx);
165}
166
167/* Shortcut for
168 * ec_powm(B, B, mpi_const(MPI_C_THREE), ctx);
169 * for easier optimization.
170 */
171static void ec_pow3(MPI w, const MPI b, struct mpi_ec_ctx *ctx)
172{
173 mpi_powm(w, b, mpi_const(MPI_C_THREE), ctx->p);
174}
175
176static void ec_invm(MPI x, MPI a, struct mpi_ec_ctx *ctx)
177{
178 if (!mpi_invm(x, a, ctx->p))
179 log_error("ec_invm: inverse does not exist:\n");
180}
181
182static void mpih_set_cond(mpi_ptr_t wp, mpi_ptr_t up,
183 mpi_size_t usize, unsigned long set)
184{
185 mpi_size_t i;
186 mpi_limb_t mask = ((mpi_limb_t)0) - set;
187 mpi_limb_t x;
188
189 for (i = 0; i < usize; i++) {
190 x = mask & (wp[i] ^ up[i]);
191 wp[i] = wp[i] ^ x;
192 }
193}
194
195/* Routines for 2^255 - 19. */
196
197#define LIMB_SIZE_25519 ((256+BITS_PER_MPI_LIMB-1)/BITS_PER_MPI_LIMB)
198
199static void ec_addm_25519(MPI w, MPI u, MPI v, struct mpi_ec_ctx *ctx)
200{
201 mpi_ptr_t wp, up, vp;
202 mpi_size_t wsize = LIMB_SIZE_25519;
203 mpi_limb_t n[LIMB_SIZE_25519];
204 mpi_limb_t borrow;
205
206 if (w->nlimbs != wsize || u->nlimbs != wsize || v->nlimbs != wsize)
207 log_bug("addm_25519: different sizes\n");
208
209 memset(n, 0, sizeof(n));
210 up = u->d;
211 vp = v->d;
212 wp = w->d;
213
214 mpihelp_add_n(wp, up, vp, wsize);
215 borrow = mpihelp_sub_n(wp, wp, ctx->p->d, wsize);
216 mpih_set_cond(n, ctx->p->d, wsize, (borrow != 0UL));
217 mpihelp_add_n(wp, wp, n, wsize);
218 wp[LIMB_SIZE_25519-1] &= ~((mpi_limb_t)1 << (255 % BITS_PER_MPI_LIMB));
219}
220
221static void ec_subm_25519(MPI w, MPI u, MPI v, struct mpi_ec_ctx *ctx)
222{
223 mpi_ptr_t wp, up, vp;
224 mpi_size_t wsize = LIMB_SIZE_25519;
225 mpi_limb_t n[LIMB_SIZE_25519];
226 mpi_limb_t borrow;
227
228 if (w->nlimbs != wsize || u->nlimbs != wsize || v->nlimbs != wsize)
229 log_bug("subm_25519: different sizes\n");
230
231 memset(n, 0, sizeof(n));
232 up = u->d;
233 vp = v->d;
234 wp = w->d;
235
236 borrow = mpihelp_sub_n(wp, up, vp, wsize);
237 mpih_set_cond(n, ctx->p->d, wsize, (borrow != 0UL));
238 mpihelp_add_n(wp, wp, n, wsize);
239 wp[LIMB_SIZE_25519-1] &= ~((mpi_limb_t)1 << (255 % BITS_PER_MPI_LIMB));
240}
241
242static void ec_mulm_25519(MPI w, MPI u, MPI v, struct mpi_ec_ctx *ctx)
243{
244 mpi_ptr_t wp, up, vp;
245 mpi_size_t wsize = LIMB_SIZE_25519;
246 mpi_limb_t n[LIMB_SIZE_25519*2];
247 mpi_limb_t m[LIMB_SIZE_25519+1];
248 mpi_limb_t cy;
249 int msb;
250
251 (void)ctx;
252 if (w->nlimbs != wsize || u->nlimbs != wsize || v->nlimbs != wsize)
253 log_bug("mulm_25519: different sizes\n");
254
255 up = u->d;
256 vp = v->d;
257 wp = w->d;
258
259 mpihelp_mul_n(n, up, vp, wsize);
260 memcpy(wp, n, wsize * BYTES_PER_MPI_LIMB);
261 wp[LIMB_SIZE_25519-1] &= ~((mpi_limb_t)1 << (255 % BITS_PER_MPI_LIMB));
262
263 memcpy(m, n+LIMB_SIZE_25519-1, (wsize+1) * BYTES_PER_MPI_LIMB);
264 mpihelp_rshift(m, m, LIMB_SIZE_25519+1, (255 % BITS_PER_MPI_LIMB));
265
266 memcpy(n, m, wsize * BYTES_PER_MPI_LIMB);
267 cy = mpihelp_lshift(m, m, LIMB_SIZE_25519, 4);
268 m[LIMB_SIZE_25519] = cy;
269 cy = mpihelp_add_n(m, m, n, wsize);
270 m[LIMB_SIZE_25519] += cy;
271 cy = mpihelp_add_n(m, m, n, wsize);
272 m[LIMB_SIZE_25519] += cy;
273 cy = mpihelp_add_n(m, m, n, wsize);
274 m[LIMB_SIZE_25519] += cy;
275
276 cy = mpihelp_add_n(wp, wp, m, wsize);
277 m[LIMB_SIZE_25519] += cy;
278
279 memset(m, 0, wsize * BYTES_PER_MPI_LIMB);
280 msb = (wp[LIMB_SIZE_25519-1] >> (255 % BITS_PER_MPI_LIMB));
281 m[0] = (m[LIMB_SIZE_25519] * 2 + msb) * 19;
282 wp[LIMB_SIZE_25519-1] &= ~((mpi_limb_t)1 << (255 % BITS_PER_MPI_LIMB));
283 mpihelp_add_n(wp, wp, m, wsize);
284
285 m[0] = 0;
286 cy = mpihelp_sub_n(wp, wp, ctx->p->d, wsize);
287 mpih_set_cond(m, ctx->p->d, wsize, (cy != 0UL));
288 mpihelp_add_n(wp, wp, m, wsize);
289}
290
291static void ec_mul2_25519(MPI w, MPI u, struct mpi_ec_ctx *ctx)
292{
293 ec_addm_25519(w, u, u, ctx);
294}
295
296static void ec_pow2_25519(MPI w, const MPI b, struct mpi_ec_ctx *ctx)
297{
298 ec_mulm_25519(w, b, b, ctx);
299}
300
301/* Routines for 2^448 - 2^224 - 1. */
302
303#define LIMB_SIZE_448 ((448+BITS_PER_MPI_LIMB-1)/BITS_PER_MPI_LIMB)
304#define LIMB_SIZE_HALF_448 ((LIMB_SIZE_448+1)/2)
305
306static void ec_addm_448(MPI w, MPI u, MPI v, struct mpi_ec_ctx *ctx)
307{
308 mpi_ptr_t wp, up, vp;
309 mpi_size_t wsize = LIMB_SIZE_448;
310 mpi_limb_t n[LIMB_SIZE_448];
311 mpi_limb_t cy;
312
313 if (w->nlimbs != wsize || u->nlimbs != wsize || v->nlimbs != wsize)
314 log_bug("addm_448: different sizes\n");
315
316 memset(n, 0, sizeof(n));
317 up = u->d;
318 vp = v->d;
319 wp = w->d;
320
321 cy = mpihelp_add_n(wp, up, vp, wsize);
322 mpih_set_cond(n, ctx->p->d, wsize, (cy != 0UL));
323 mpihelp_sub_n(wp, wp, n, wsize);
324}
325
326static void ec_subm_448(MPI w, MPI u, MPI v, struct mpi_ec_ctx *ctx)
327{
328 mpi_ptr_t wp, up, vp;
329 mpi_size_t wsize = LIMB_SIZE_448;
330 mpi_limb_t n[LIMB_SIZE_448];
331 mpi_limb_t borrow;
332
333 if (w->nlimbs != wsize || u->nlimbs != wsize || v->nlimbs != wsize)
334 log_bug("subm_448: different sizes\n");
335
336 memset(n, 0, sizeof(n));
337 up = u->d;
338 vp = v->d;
339 wp = w->d;
340
341 borrow = mpihelp_sub_n(wp, up, vp, wsize);
342 mpih_set_cond(n, ctx->p->d, wsize, (borrow != 0UL));
343 mpihelp_add_n(wp, wp, n, wsize);
344}
345
346static void ec_mulm_448(MPI w, MPI u, MPI v, struct mpi_ec_ctx *ctx)
347{
348 mpi_ptr_t wp, up, vp;
349 mpi_size_t wsize = LIMB_SIZE_448;
350 mpi_limb_t n[LIMB_SIZE_448*2];
351 mpi_limb_t a2[LIMB_SIZE_HALF_448];
352 mpi_limb_t a3[LIMB_SIZE_HALF_448];
353 mpi_limb_t b0[LIMB_SIZE_HALF_448];
354 mpi_limb_t b1[LIMB_SIZE_HALF_448];
355 mpi_limb_t cy;
356 int i;
357#if (LIMB_SIZE_HALF_448 > LIMB_SIZE_448/2)
358 mpi_limb_t b1_rest, a3_rest;
359#endif
360
361 if (w->nlimbs != wsize || u->nlimbs != wsize || v->nlimbs != wsize)
362 log_bug("mulm_448: different sizes\n");
363
364 up = u->d;
365 vp = v->d;
366 wp = w->d;
367
368 mpihelp_mul_n(n, up, vp, wsize);
369
370 for (i = 0; i < (wsize + 1) / 2; i++) {
371 b0[i] = n[i];
372 b1[i] = n[i+wsize/2];
373 a2[i] = n[i+wsize];
374 a3[i] = n[i+wsize+wsize/2];
375 }
376
377#if (LIMB_SIZE_HALF_448 > LIMB_SIZE_448/2)
378 b0[LIMB_SIZE_HALF_448-1] &= ((mpi_limb_t)1UL << 32)-1;
379 a2[LIMB_SIZE_HALF_448-1] &= ((mpi_limb_t)1UL << 32)-1;
380
381 b1_rest = 0;
382 a3_rest = 0;
383
384 for (i = (wsize + 1) / 2 - 1; i >= 0; i--) {
385 mpi_limb_t b1v, a3v;
386 b1v = b1[i];
387 a3v = a3[i];
388 b1[i] = (b1_rest << 32) | (b1v >> 32);
389 a3[i] = (a3_rest << 32) | (a3v >> 32);
390 b1_rest = b1v & (((mpi_limb_t)1UL << 32)-1);
391 a3_rest = a3v & (((mpi_limb_t)1UL << 32)-1);
392 }
393#endif
394
395 cy = mpihelp_add_n(b0, b0, a2, LIMB_SIZE_HALF_448);
396 cy += mpihelp_add_n(b0, b0, a3, LIMB_SIZE_HALF_448);
397 for (i = 0; i < (wsize + 1) / 2; i++)
398 wp[i] = b0[i];
399#if (LIMB_SIZE_HALF_448 > LIMB_SIZE_448/2)
400 wp[LIMB_SIZE_HALF_448-1] &= (((mpi_limb_t)1UL << 32)-1);
401#endif
402
403#if (LIMB_SIZE_HALF_448 > LIMB_SIZE_448/2)
404 cy = b0[LIMB_SIZE_HALF_448-1] >> 32;
405#endif
406
407 cy = mpihelp_add_1(b1, b1, LIMB_SIZE_HALF_448, cy);
408 cy += mpihelp_add_n(b1, b1, a2, LIMB_SIZE_HALF_448);
409 cy += mpihelp_add_n(b1, b1, a3, LIMB_SIZE_HALF_448);
410 cy += mpihelp_add_n(b1, b1, a3, LIMB_SIZE_HALF_448);
411#if (LIMB_SIZE_HALF_448 > LIMB_SIZE_448/2)
412 b1_rest = 0;
413 for (i = (wsize + 1) / 2 - 1; i >= 0; i--) {
414 mpi_limb_t b1v = b1[i];
415 b1[i] = (b1_rest << 32) | (b1v >> 32);
416 b1_rest = b1v & (((mpi_limb_t)1UL << 32)-1);
417 }
418 wp[LIMB_SIZE_HALF_448-1] |= (b1_rest << 32);
419#endif
420 for (i = 0; i < wsize / 2; i++)
421 wp[i+(wsize + 1) / 2] = b1[i];
422
423#if (LIMB_SIZE_HALF_448 > LIMB_SIZE_448/2)
424 cy = b1[LIMB_SIZE_HALF_448-1];
425#endif
426
427 memset(n, 0, wsize * BYTES_PER_MPI_LIMB);
428
429#if (LIMB_SIZE_HALF_448 > LIMB_SIZE_448/2)
430 n[LIMB_SIZE_HALF_448-1] = cy << 32;
431#else
432 n[LIMB_SIZE_HALF_448] = cy;
433#endif
434 n[0] = cy;
435 mpihelp_add_n(wp, wp, n, wsize);
436
437 memset(n, 0, wsize * BYTES_PER_MPI_LIMB);
438 cy = mpihelp_sub_n(wp, wp, ctx->p->d, wsize);
439 mpih_set_cond(n, ctx->p->d, wsize, (cy != 0UL));
440 mpihelp_add_n(wp, wp, n, wsize);
441}
442
443static void ec_mul2_448(MPI w, MPI u, struct mpi_ec_ctx *ctx)
444{
445 ec_addm_448(w, u, u, ctx);
446}
447
448static void ec_pow2_448(MPI w, const MPI b, struct mpi_ec_ctx *ctx)
449{
450 ec_mulm_448(w, b, b, ctx);
451}
452
453struct field_table {
454 const char *p;
455
456 /* computation routines for the field. */
457 void (*addm)(MPI w, MPI u, MPI v, struct mpi_ec_ctx *ctx);
458 void (*subm)(MPI w, MPI u, MPI v, struct mpi_ec_ctx *ctx);
459 void (*mulm)(MPI w, MPI u, MPI v, struct mpi_ec_ctx *ctx);
460 void (*mul2)(MPI w, MPI u, struct mpi_ec_ctx *ctx);
461 void (*pow2)(MPI w, const MPI b, struct mpi_ec_ctx *ctx);
462};
463
464static const struct field_table field_table[] = {
465 {
466 "0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFED",
467 ec_addm_25519,
468 ec_subm_25519,
469 ec_mulm_25519,
470 ec_mul2_25519,
471 ec_pow2_25519
472 },
473 {
474 "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE"
475 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
476 ec_addm_448,
477 ec_subm_448,
478 ec_mulm_448,
479 ec_mul2_448,
480 ec_pow2_448
481 },
482 { NULL, NULL, NULL, NULL, NULL, NULL },
483};
484
485/* Force recomputation of all helper variables. */
486static void mpi_ec_get_reset(struct mpi_ec_ctx *ec)
487{
488 ec->t.valid.a_is_pminus3 = 0;
489 ec->t.valid.two_inv_p = 0;
490}
491
492/* Accessor for helper variable. */
493static int ec_get_a_is_pminus3(struct mpi_ec_ctx *ec)
494{
495 MPI tmp;
496
497 if (!ec->t.valid.a_is_pminus3) {
498 ec->t.valid.a_is_pminus3 = 1;
499 tmp = mpi_alloc_like(ec->p);
500 mpi_sub_ui(tmp, ec->p, 3);
501 ec->t.a_is_pminus3 = !mpi_cmp(ec->a, tmp);
502 mpi_free(tmp);
503 }
504
505 return ec->t.a_is_pminus3;
506}
507
508/* Accessor for helper variable. */
509static MPI ec_get_two_inv_p(struct mpi_ec_ctx *ec)
510{
511 if (!ec->t.valid.two_inv_p) {
512 ec->t.valid.two_inv_p = 1;
513 if (!ec->t.two_inv_p)
514 ec->t.two_inv_p = mpi_alloc(0);
515 ec_invm(ec->t.two_inv_p, mpi_const(MPI_C_TWO), ec);
516 }
517 return ec->t.two_inv_p;
518}
519
520static const char *const curve25519_bad_points[] = {
521 "0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed",
522 "0x0000000000000000000000000000000000000000000000000000000000000000",
523 "0x0000000000000000000000000000000000000000000000000000000000000001",
524 "0x00b8495f16056286fdb1329ceb8d09da6ac49ff1fae35616aeb8413b7c7aebe0",
525 "0x57119fd0dd4e22d8868e1c58c45c44045bef839c55b1d0b1248c50a3bc959c5f",
526 "0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffec",
527 "0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffee",
528 NULL
529};
530
531static const char *const curve448_bad_points[] = {
532 "0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffe"
533 "ffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
534 "0x00000000000000000000000000000000000000000000000000000000"
535 "00000000000000000000000000000000000000000000000000000000",
536 "0x00000000000000000000000000000000000000000000000000000000"
537 "00000000000000000000000000000000000000000000000000000001",
538 "0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffe"
539 "fffffffffffffffffffffffffffffffffffffffffffffffffffffffe",
540 "0xffffffffffffffffffffffffffffffffffffffffffffffffffffffff"
541 "00000000000000000000000000000000000000000000000000000000",
542 NULL
543};
544
545static const char *const *bad_points_table[] = {
546 curve25519_bad_points,
547 curve448_bad_points,
548};
549
550static void mpi_ec_coefficient_normalize(MPI a, MPI p)
551{
552 if (a->sign) {
553 mpi_resize(a, p->nlimbs);
554 mpihelp_sub_n(a->d, p->d, a->d, p->nlimbs);
555 a->nlimbs = p->nlimbs;
556 a->sign = 0;
557 }
558}
559
560/* This function initialized a context for elliptic curve based on the
561 * field GF(p). P is the prime specifying this field, A is the first
562 * coefficient. CTX is expected to be zeroized.
563 */
564void mpi_ec_init(struct mpi_ec_ctx *ctx, enum gcry_mpi_ec_models model,
565 enum ecc_dialects dialect,
566 int flags, MPI p, MPI a, MPI b)
567{
568 int i;
569 static int use_barrett = -1 /* TODO: 1 or -1 */;
570
571 mpi_ec_coefficient_normalize(a, p);
572 mpi_ec_coefficient_normalize(b, p);
573
574 /* Fixme: Do we want to check some constraints? e.g. a < p */
575
576 ctx->model = model;
577 ctx->dialect = dialect;
578 ctx->flags = flags;
579 if (dialect == ECC_DIALECT_ED25519)
580 ctx->nbits = 256;
581 else
582 ctx->nbits = mpi_get_nbits(p);
583 ctx->p = mpi_copy(p);
584 ctx->a = mpi_copy(a);
585 ctx->b = mpi_copy(b);
586
587 ctx->t.p_barrett = use_barrett > 0 ? mpi_barrett_init(ctx->p, 0) : NULL;
588
589 mpi_ec_get_reset(ctx);
590
591 if (model == MPI_EC_MONTGOMERY) {
592 for (i = 0; i < DIM(bad_points_table); i++) {
593 MPI p_candidate = mpi_scanval(bad_points_table[i][0]);
594 int match_p = !mpi_cmp(ctx->p, p_candidate);
595 int j;
596
597 mpi_free(p_candidate);
598 if (!match_p)
599 continue;
600
601 for (j = 0; i < DIM(ctx->t.scratch) && bad_points_table[i][j]; j++)
602 ctx->t.scratch[j] = mpi_scanval(bad_points_table[i][j]);
603 }
604 } else {
605 /* Allocate scratch variables. */
606 for (i = 0; i < DIM(ctx->t.scratch); i++)
607 ctx->t.scratch[i] = mpi_alloc_like(ctx->p);
608 }
609
610 ctx->addm = ec_addm;
611 ctx->subm = ec_subm;
612 ctx->mulm = ec_mulm;
613 ctx->mul2 = ec_mul2;
614 ctx->pow2 = ec_pow2;
615
616 for (i = 0; field_table[i].p; i++) {
617 MPI f_p;
618
619 f_p = mpi_scanval(field_table[i].p);
620 if (!f_p)
621 break;
622
623 if (!mpi_cmp(p, f_p)) {
624 ctx->addm = field_table[i].addm;
625 ctx->subm = field_table[i].subm;
626 ctx->mulm = field_table[i].mulm;
627 ctx->mul2 = field_table[i].mul2;
628 ctx->pow2 = field_table[i].pow2;
629 mpi_free(f_p);
630
631 mpi_resize(ctx->a, ctx->p->nlimbs);
632 ctx->a->nlimbs = ctx->p->nlimbs;
633
634 mpi_resize(ctx->b, ctx->p->nlimbs);
635 ctx->b->nlimbs = ctx->p->nlimbs;
636
637 for (i = 0; i < DIM(ctx->t.scratch) && ctx->t.scratch[i]; i++)
638 ctx->t.scratch[i]->nlimbs = ctx->p->nlimbs;
639
640 break;
641 }
642
643 mpi_free(f_p);
644 }
645}
646EXPORT_SYMBOL_GPL(mpi_ec_init);
647
648void mpi_ec_deinit(struct mpi_ec_ctx *ctx)
649{
650 int i;
651
652 mpi_barrett_free(ctx->t.p_barrett);
653
654 /* Domain parameter. */
655 mpi_free(ctx->p);
656 mpi_free(ctx->a);
657 mpi_free(ctx->b);
658 mpi_point_release(ctx->G);
659 mpi_free(ctx->n);
660
661 /* The key. */
662 mpi_point_release(ctx->Q);
663 mpi_free(ctx->d);
664
665 /* Private data of ec.c. */
666 mpi_free(ctx->t.two_inv_p);
667
668 for (i = 0; i < DIM(ctx->t.scratch); i++)
669 mpi_free(ctx->t.scratch[i]);
670}
671EXPORT_SYMBOL_GPL(mpi_ec_deinit);
672
673/* Compute the affine coordinates from the projective coordinates in
674 * POINT. Set them into X and Y. If one coordinate is not required,
675 * X or Y may be passed as NULL. CTX is the usual context. Returns: 0
676 * on success or !0 if POINT is at infinity.
677 */
678int mpi_ec_get_affine(MPI x, MPI y, MPI_POINT point, struct mpi_ec_ctx *ctx)
679{
680 if (!mpi_cmp_ui(point->z, 0))
681 return -1;
682
683 switch (ctx->model) {
684 case MPI_EC_WEIERSTRASS: /* Using Jacobian coordinates. */
685 {
686 MPI z1, z2, z3;
687
688 z1 = mpi_new(0);
689 z2 = mpi_new(0);
690 ec_invm(z1, point->z, ctx); /* z1 = z^(-1) mod p */
691 ec_mulm(z2, z1, z1, ctx); /* z2 = z^(-2) mod p */
692
693 if (x)
694 ec_mulm(x, point->x, z2, ctx);
695
696 if (y) {
697 z3 = mpi_new(0);
698 ec_mulm(z3, z2, z1, ctx); /* z3 = z^(-3) mod p */
699 ec_mulm(y, point->y, z3, ctx);
700 mpi_free(z3);
701 }
702
703 mpi_free(z2);
704 mpi_free(z1);
705 }
706 return 0;
707
708 case MPI_EC_MONTGOMERY:
709 {
710 if (x)
711 mpi_set(x, point->x);
712
713 if (y) {
714 log_fatal("%s: Getting Y-coordinate on %s is not supported\n",
715 "mpi_ec_get_affine", "Montgomery");
716 return -1;
717 }
718 }
719 return 0;
720
721 case MPI_EC_EDWARDS:
722 {
723 MPI z;
724
725 z = mpi_new(0);
726 ec_invm(z, point->z, ctx);
727
728 mpi_resize(z, ctx->p->nlimbs);
729 z->nlimbs = ctx->p->nlimbs;
730
731 if (x) {
732 mpi_resize(x, ctx->p->nlimbs);
733 x->nlimbs = ctx->p->nlimbs;
734 ctx->mulm(x, point->x, z, ctx);
735 }
736 if (y) {
737 mpi_resize(y, ctx->p->nlimbs);
738 y->nlimbs = ctx->p->nlimbs;
739 ctx->mulm(y, point->y, z, ctx);
740 }
741
742 mpi_free(z);
743 }
744 return 0;
745
746 default:
747 return -1;
748 }
749}
750EXPORT_SYMBOL_GPL(mpi_ec_get_affine);
751
752/* RESULT = 2 * POINT (Weierstrass version). */
753static void dup_point_weierstrass(MPI_POINT result,
754 MPI_POINT point, struct mpi_ec_ctx *ctx)
755{
756#define x3 (result->x)
757#define y3 (result->y)
758#define z3 (result->z)
759#define t1 (ctx->t.scratch[0])
760#define t2 (ctx->t.scratch[1])
761#define t3 (ctx->t.scratch[2])
762#define l1 (ctx->t.scratch[3])
763#define l2 (ctx->t.scratch[4])
764#define l3 (ctx->t.scratch[5])
765
766 if (!mpi_cmp_ui(point->y, 0) || !mpi_cmp_ui(point->z, 0)) {
767 /* P_y == 0 || P_z == 0 => [1:1:0] */
768 mpi_set_ui(x3, 1);
769 mpi_set_ui(y3, 1);
770 mpi_set_ui(z3, 0);
771 } else {
772 if (ec_get_a_is_pminus3(ctx)) {
773 /* Use the faster case. */
774 /* L1 = 3(X - Z^2)(X + Z^2) */
775 /* T1: used for Z^2. */
776 /* T2: used for the right term. */
777 ec_pow2(t1, point->z, ctx);
778 ec_subm(l1, point->x, t1, ctx);
779 ec_mulm(l1, l1, mpi_const(MPI_C_THREE), ctx);
780 ec_addm(t2, point->x, t1, ctx);
781 ec_mulm(l1, l1, t2, ctx);
782 } else {
783 /* Standard case. */
784 /* L1 = 3X^2 + aZ^4 */
785 /* T1: used for aZ^4. */
786 ec_pow2(l1, point->x, ctx);
787 ec_mulm(l1, l1, mpi_const(MPI_C_THREE), ctx);
788 ec_powm(t1, point->z, mpi_const(MPI_C_FOUR), ctx);
789 ec_mulm(t1, t1, ctx->a, ctx);
790 ec_addm(l1, l1, t1, ctx);
791 }
792 /* Z3 = 2YZ */
793 ec_mulm(z3, point->y, point->z, ctx);
794 ec_mul2(z3, z3, ctx);
795
796 /* L2 = 4XY^2 */
797 /* T2: used for Y2; required later. */
798 ec_pow2(t2, point->y, ctx);
799 ec_mulm(l2, t2, point->x, ctx);
800 ec_mulm(l2, l2, mpi_const(MPI_C_FOUR), ctx);
801
802 /* X3 = L1^2 - 2L2 */
803 /* T1: used for L2^2. */
804 ec_pow2(x3, l1, ctx);
805 ec_mul2(t1, l2, ctx);
806 ec_subm(x3, x3, t1, ctx);
807
808 /* L3 = 8Y^4 */
809 /* T2: taken from above. */
810 ec_pow2(t2, t2, ctx);
811 ec_mulm(l3, t2, mpi_const(MPI_C_EIGHT), ctx);
812
813 /* Y3 = L1(L2 - X3) - L3 */
814 ec_subm(y3, l2, x3, ctx);
815 ec_mulm(y3, y3, l1, ctx);
816 ec_subm(y3, y3, l3, ctx);
817 }
818
819#undef x3
820#undef y3
821#undef z3
822#undef t1
823#undef t2
824#undef t3
825#undef l1
826#undef l2
827#undef l3
828}
829
830/* RESULT = 2 * POINT (Montgomery version). */
831static void dup_point_montgomery(MPI_POINT result,
832 MPI_POINT point, struct mpi_ec_ctx *ctx)
833{
834 (void)result;
835 (void)point;
836 (void)ctx;
837 log_fatal("%s: %s not yet supported\n",
838 "mpi_ec_dup_point", "Montgomery");
839}
840
841/* RESULT = 2 * POINT (Twisted Edwards version). */
842static void dup_point_edwards(MPI_POINT result,
843 MPI_POINT point, struct mpi_ec_ctx *ctx)
844{
845#define X1 (point->x)
846#define Y1 (point->y)
847#define Z1 (point->z)
848#define X3 (result->x)
849#define Y3 (result->y)
850#define Z3 (result->z)
851#define B (ctx->t.scratch[0])
852#define C (ctx->t.scratch[1])
853#define D (ctx->t.scratch[2])
854#define E (ctx->t.scratch[3])
855#define F (ctx->t.scratch[4])
856#define H (ctx->t.scratch[5])
857#define J (ctx->t.scratch[6])
858
859 /* Compute: (X_3 : Y_3 : Z_3) = 2( X_1 : Y_1 : Z_1 ) */
860
861 /* B = (X_1 + Y_1)^2 */
862 ctx->addm(B, X1, Y1, ctx);
863 ctx->pow2(B, B, ctx);
864
865 /* C = X_1^2 */
866 /* D = Y_1^2 */
867 ctx->pow2(C, X1, ctx);
868 ctx->pow2(D, Y1, ctx);
869
870 /* E = aC */
871 if (ctx->dialect == ECC_DIALECT_ED25519)
872 ctx->subm(E, ctx->p, C, ctx);
873 else
874 ctx->mulm(E, ctx->a, C, ctx);
875
876 /* F = E + D */
877 ctx->addm(F, E, D, ctx);
878
879 /* H = Z_1^2 */
880 ctx->pow2(H, Z1, ctx);
881
882 /* J = F - 2H */
883 ctx->mul2(J, H, ctx);
884 ctx->subm(J, F, J, ctx);
885
886 /* X_3 = (B - C - D) · J */
887 ctx->subm(X3, B, C, ctx);
888 ctx->subm(X3, X3, D, ctx);
889 ctx->mulm(X3, X3, J, ctx);
890
891 /* Y_3 = F · (E - D) */
892 ctx->subm(Y3, E, D, ctx);
893 ctx->mulm(Y3, Y3, F, ctx);
894
895 /* Z_3 = F · J */
896 ctx->mulm(Z3, F, J, ctx);
897
898#undef X1
899#undef Y1
900#undef Z1
901#undef X3
902#undef Y3
903#undef Z3
904#undef B
905#undef C
906#undef D
907#undef E
908#undef F
909#undef H
910#undef J
911}
912
913/* RESULT = 2 * POINT */
914static void
915mpi_ec_dup_point(MPI_POINT result, MPI_POINT point, struct mpi_ec_ctx *ctx)
916{
917 switch (ctx->model) {
918 case MPI_EC_WEIERSTRASS:
919 dup_point_weierstrass(result, point, ctx);
920 break;
921 case MPI_EC_MONTGOMERY:
922 dup_point_montgomery(result, point, ctx);
923 break;
924 case MPI_EC_EDWARDS:
925 dup_point_edwards(result, point, ctx);
926 break;
927 }
928}
929
930/* RESULT = P1 + P2 (Weierstrass version).*/
931static void add_points_weierstrass(MPI_POINT result,
932 MPI_POINT p1, MPI_POINT p2,
933 struct mpi_ec_ctx *ctx)
934{
935#define x1 (p1->x)
936#define y1 (p1->y)
937#define z1 (p1->z)
938#define x2 (p2->x)
939#define y2 (p2->y)
940#define z2 (p2->z)
941#define x3 (result->x)
942#define y3 (result->y)
943#define z3 (result->z)
944#define l1 (ctx->t.scratch[0])
945#define l2 (ctx->t.scratch[1])
946#define l3 (ctx->t.scratch[2])
947#define l4 (ctx->t.scratch[3])
948#define l5 (ctx->t.scratch[4])
949#define l6 (ctx->t.scratch[5])
950#define l7 (ctx->t.scratch[6])
951#define l8 (ctx->t.scratch[7])
952#define l9 (ctx->t.scratch[8])
953#define t1 (ctx->t.scratch[9])
954#define t2 (ctx->t.scratch[10])
955
956 if ((!mpi_cmp(x1, x2)) && (!mpi_cmp(y1, y2)) && (!mpi_cmp(z1, z2))) {
957 /* Same point; need to call the duplicate function. */
958 mpi_ec_dup_point(result, p1, ctx);
959 } else if (!mpi_cmp_ui(z1, 0)) {
960 /* P1 is at infinity. */
961 mpi_set(x3, p2->x);
962 mpi_set(y3, p2->y);
963 mpi_set(z3, p2->z);
964 } else if (!mpi_cmp_ui(z2, 0)) {
965 /* P2 is at infinity. */
966 mpi_set(x3, p1->x);
967 mpi_set(y3, p1->y);
968 mpi_set(z3, p1->z);
969 } else {
970 int z1_is_one = !mpi_cmp_ui(z1, 1);
971 int z2_is_one = !mpi_cmp_ui(z2, 1);
972
973 /* l1 = x1 z2^2 */
974 /* l2 = x2 z1^2 */
975 if (z2_is_one)
976 mpi_set(l1, x1);
977 else {
978 ec_pow2(l1, z2, ctx);
979 ec_mulm(l1, l1, x1, ctx);
980 }
981 if (z1_is_one)
982 mpi_set(l2, x2);
983 else {
984 ec_pow2(l2, z1, ctx);
985 ec_mulm(l2, l2, x2, ctx);
986 }
987 /* l3 = l1 - l2 */
988 ec_subm(l3, l1, l2, ctx);
989 /* l4 = y1 z2^3 */
990 ec_powm(l4, z2, mpi_const(MPI_C_THREE), ctx);
991 ec_mulm(l4, l4, y1, ctx);
992 /* l5 = y2 z1^3 */
993 ec_powm(l5, z1, mpi_const(MPI_C_THREE), ctx);
994 ec_mulm(l5, l5, y2, ctx);
995 /* l6 = l4 - l5 */
996 ec_subm(l6, l4, l5, ctx);
997
998 if (!mpi_cmp_ui(l3, 0)) {
999 if (!mpi_cmp_ui(l6, 0)) {
1000 /* P1 and P2 are the same - use duplicate function. */
1001 mpi_ec_dup_point(result, p1, ctx);
1002 } else {
1003 /* P1 is the inverse of P2. */
1004 mpi_set_ui(x3, 1);
1005 mpi_set_ui(y3, 1);
1006 mpi_set_ui(z3, 0);
1007 }
1008 } else {
1009 /* l7 = l1 + l2 */
1010 ec_addm(l7, l1, l2, ctx);
1011 /* l8 = l4 + l5 */
1012 ec_addm(l8, l4, l5, ctx);
1013 /* z3 = z1 z2 l3 */
1014 ec_mulm(z3, z1, z2, ctx);
1015 ec_mulm(z3, z3, l3, ctx);
1016 /* x3 = l6^2 - l7 l3^2 */
1017 ec_pow2(t1, l6, ctx);
1018 ec_pow2(t2, l3, ctx);
1019 ec_mulm(t2, t2, l7, ctx);
1020 ec_subm(x3, t1, t2, ctx);
1021 /* l9 = l7 l3^2 - 2 x3 */
1022 ec_mul2(t1, x3, ctx);
1023 ec_subm(l9, t2, t1, ctx);
1024 /* y3 = (l9 l6 - l8 l3^3)/2 */
1025 ec_mulm(l9, l9, l6, ctx);
1026 ec_powm(t1, l3, mpi_const(MPI_C_THREE), ctx); /* fixme: Use saved value*/
1027 ec_mulm(t1, t1, l8, ctx);
1028 ec_subm(y3, l9, t1, ctx);
1029 ec_mulm(y3, y3, ec_get_two_inv_p(ctx), ctx);
1030 }
1031 }
1032
1033#undef x1
1034#undef y1
1035#undef z1
1036#undef x2
1037#undef y2
1038#undef z2
1039#undef x3
1040#undef y3
1041#undef z3
1042#undef l1
1043#undef l2
1044#undef l3
1045#undef l4
1046#undef l5
1047#undef l6
1048#undef l7
1049#undef l8
1050#undef l9
1051#undef t1
1052#undef t2
1053}
1054
1055/* RESULT = P1 + P2 (Montgomery version).*/
1056static void add_points_montgomery(MPI_POINT result,
1057 MPI_POINT p1, MPI_POINT p2,
1058 struct mpi_ec_ctx *ctx)
1059{
1060 (void)result;
1061 (void)p1;
1062 (void)p2;
1063 (void)ctx;
1064 log_fatal("%s: %s not yet supported\n",
1065 "mpi_ec_add_points", "Montgomery");
1066}
1067
1068/* RESULT = P1 + P2 (Twisted Edwards version).*/
1069static void add_points_edwards(MPI_POINT result,
1070 MPI_POINT p1, MPI_POINT p2,
1071 struct mpi_ec_ctx *ctx)
1072{
1073#define X1 (p1->x)
1074#define Y1 (p1->y)
1075#define Z1 (p1->z)
1076#define X2 (p2->x)
1077#define Y2 (p2->y)
1078#define Z2 (p2->z)
1079#define X3 (result->x)
1080#define Y3 (result->y)
1081#define Z3 (result->z)
1082#define A (ctx->t.scratch[0])
1083#define B (ctx->t.scratch[1])
1084#define C (ctx->t.scratch[2])
1085#define D (ctx->t.scratch[3])
1086#define E (ctx->t.scratch[4])
1087#define F (ctx->t.scratch[5])
1088#define G (ctx->t.scratch[6])
1089#define tmp (ctx->t.scratch[7])
1090
1091 point_resize(result, ctx);
1092
1093 /* Compute: (X_3 : Y_3 : Z_3) = (X_1 : Y_1 : Z_1) + (X_2 : Y_2 : Z_3) */
1094
1095 /* A = Z1 · Z2 */
1096 ctx->mulm(A, Z1, Z2, ctx);
1097
1098 /* B = A^2 */
1099 ctx->pow2(B, A, ctx);
1100
1101 /* C = X1 · X2 */
1102 ctx->mulm(C, X1, X2, ctx);
1103
1104 /* D = Y1 · Y2 */
1105 ctx->mulm(D, Y1, Y2, ctx);
1106
1107 /* E = d · C · D */
1108 ctx->mulm(E, ctx->b, C, ctx);
1109 ctx->mulm(E, E, D, ctx);
1110
1111 /* F = B - E */
1112 ctx->subm(F, B, E, ctx);
1113
1114 /* G = B + E */
1115 ctx->addm(G, B, E, ctx);
1116
1117 /* X_3 = A · F · ((X_1 + Y_1) · (X_2 + Y_2) - C - D) */
1118 ctx->addm(tmp, X1, Y1, ctx);
1119 ctx->addm(X3, X2, Y2, ctx);
1120 ctx->mulm(X3, X3, tmp, ctx);
1121 ctx->subm(X3, X3, C, ctx);
1122 ctx->subm(X3, X3, D, ctx);
1123 ctx->mulm(X3, X3, F, ctx);
1124 ctx->mulm(X3, X3, A, ctx);
1125
1126 /* Y_3 = A · G · (D - aC) */
1127 if (ctx->dialect == ECC_DIALECT_ED25519) {
1128 ctx->addm(Y3, D, C, ctx);
1129 } else {
1130 ctx->mulm(Y3, ctx->a, C, ctx);
1131 ctx->subm(Y3, D, Y3, ctx);
1132 }
1133 ctx->mulm(Y3, Y3, G, ctx);
1134 ctx->mulm(Y3, Y3, A, ctx);
1135
1136 /* Z_3 = F · G */
1137 ctx->mulm(Z3, F, G, ctx);
1138
1139
1140#undef X1
1141#undef Y1
1142#undef Z1
1143#undef X2
1144#undef Y2
1145#undef Z2
1146#undef X3
1147#undef Y3
1148#undef Z3
1149#undef A
1150#undef B
1151#undef C
1152#undef D
1153#undef E
1154#undef F
1155#undef G
1156#undef tmp
1157}
1158
1159/* Compute a step of Montgomery Ladder (only use X and Z in the point).
1160 * Inputs: P1, P2, and x-coordinate of DIF = P1 - P1.
1161 * Outputs: PRD = 2 * P1 and SUM = P1 + P2.
1162 */
1163static void montgomery_ladder(MPI_POINT prd, MPI_POINT sum,
1164 MPI_POINT p1, MPI_POINT p2, MPI dif_x,
1165 struct mpi_ec_ctx *ctx)
1166{
1167 ctx->addm(sum->x, p2->x, p2->z, ctx);
1168 ctx->subm(p2->z, p2->x, p2->z, ctx);
1169 ctx->addm(prd->x, p1->x, p1->z, ctx);
1170 ctx->subm(p1->z, p1->x, p1->z, ctx);
1171 ctx->mulm(p2->x, p1->z, sum->x, ctx);
1172 ctx->mulm(p2->z, prd->x, p2->z, ctx);
1173 ctx->pow2(p1->x, prd->x, ctx);
1174 ctx->pow2(p1->z, p1->z, ctx);
1175 ctx->addm(sum->x, p2->x, p2->z, ctx);
1176 ctx->subm(p2->z, p2->x, p2->z, ctx);
1177 ctx->mulm(prd->x, p1->x, p1->z, ctx);
1178 ctx->subm(p1->z, p1->x, p1->z, ctx);
1179 ctx->pow2(sum->x, sum->x, ctx);
1180 ctx->pow2(sum->z, p2->z, ctx);
1181 ctx->mulm(prd->z, p1->z, ctx->a, ctx); /* CTX->A: (a-2)/4 */
1182 ctx->mulm(sum->z, sum->z, dif_x, ctx);
1183 ctx->addm(prd->z, p1->x, prd->z, ctx);
1184 ctx->mulm(prd->z, prd->z, p1->z, ctx);
1185}
1186
1187/* RESULT = P1 + P2 */
1188void mpi_ec_add_points(MPI_POINT result,
1189 MPI_POINT p1, MPI_POINT p2,
1190 struct mpi_ec_ctx *ctx)
1191{
1192 switch (ctx->model) {
1193 case MPI_EC_WEIERSTRASS:
1194 add_points_weierstrass(result, p1, p2, ctx);
1195 break;
1196 case MPI_EC_MONTGOMERY:
1197 add_points_montgomery(result, p1, p2, ctx);
1198 break;
1199 case MPI_EC_EDWARDS:
1200 add_points_edwards(result, p1, p2, ctx);
1201 break;
1202 }
1203}
1204EXPORT_SYMBOL_GPL(mpi_ec_add_points);
1205
1206/* Scalar point multiplication - the main function for ECC. If takes
1207 * an integer SCALAR and a POINT as well as the usual context CTX.
1208 * RESULT will be set to the resulting point.
1209 */
1210void mpi_ec_mul_point(MPI_POINT result,
1211 MPI scalar, MPI_POINT point,
1212 struct mpi_ec_ctx *ctx)
1213{
1214 MPI x1, y1, z1, k, h, yy;
1215 unsigned int i, loops;
1216 struct gcry_mpi_point p1, p2, p1inv;
1217
1218 if (ctx->model == MPI_EC_EDWARDS) {
1219 /* Simple left to right binary method. Algorithm 3.27 from
1220 * {author={Hankerson, Darrel and Menezes, Alfred J. and Vanstone, Scott},
1221 * title = {Guide to Elliptic Curve Cryptography},
1222 * year = {2003}, isbn = {038795273X},
1223 * url = {http://www.cacr.math.uwaterloo.ca/ecc/},
1224 * publisher = {Springer-Verlag New York, Inc.}}
1225 */
1226 unsigned int nbits;
1227 int j;
1228
1229 if (mpi_cmp(scalar, ctx->p) >= 0)
1230 nbits = mpi_get_nbits(scalar);
1231 else
1232 nbits = mpi_get_nbits(ctx->p);
1233
1234 mpi_set_ui(result->x, 0);
1235 mpi_set_ui(result->y, 1);
1236 mpi_set_ui(result->z, 1);
1237 point_resize(point, ctx);
1238
1239 point_resize(result, ctx);
1240 point_resize(point, ctx);
1241
1242 for (j = nbits-1; j >= 0; j--) {
1243 mpi_ec_dup_point(result, result, ctx);
1244 if (mpi_test_bit(scalar, j))
1245 mpi_ec_add_points(result, result, point, ctx);
1246 }
1247 return;
1248 } else if (ctx->model == MPI_EC_MONTGOMERY) {
1249 unsigned int nbits;
1250 int j;
1251 struct gcry_mpi_point p1_, p2_;
1252 MPI_POINT q1, q2, prd, sum;
1253 unsigned long sw;
1254 mpi_size_t rsize;
1255
1256 /* Compute scalar point multiplication with Montgomery Ladder.
1257 * Note that we don't use Y-coordinate in the points at all.
1258 * RESULT->Y will be filled by zero.
1259 */
1260
1261 nbits = mpi_get_nbits(scalar);
1262 point_init(&p1);
1263 point_init(&p2);
1264 point_init(&p1_);
1265 point_init(&p2_);
1266 mpi_set_ui(p1.x, 1);
1267 mpi_free(p2.x);
1268 p2.x = mpi_copy(point->x);
1269 mpi_set_ui(p2.z, 1);
1270
1271 point_resize(&p1, ctx);
1272 point_resize(&p2, ctx);
1273 point_resize(&p1_, ctx);
1274 point_resize(&p2_, ctx);
1275
1276 mpi_resize(point->x, ctx->p->nlimbs);
1277 point->x->nlimbs = ctx->p->nlimbs;
1278
1279 q1 = &p1;
1280 q2 = &p2;
1281 prd = &p1_;
1282 sum = &p2_;
1283
1284 for (j = nbits-1; j >= 0; j--) {
1285 MPI_POINT t;
1286
1287 sw = mpi_test_bit(scalar, j);
1288 point_swap_cond(q1, q2, sw, ctx);
1289 montgomery_ladder(prd, sum, q1, q2, point->x, ctx);
1290 point_swap_cond(prd, sum, sw, ctx);
1291 t = q1; q1 = prd; prd = t;
1292 t = q2; q2 = sum; sum = t;
1293 }
1294
1295 mpi_clear(result->y);
1296 sw = (nbits & 1);
1297 point_swap_cond(&p1, &p1_, sw, ctx);
1298
1299 rsize = p1.z->nlimbs;
1300 MPN_NORMALIZE(p1.z->d, rsize);
1301 if (rsize == 0) {
1302 mpi_set_ui(result->x, 1);
1303 mpi_set_ui(result->z, 0);
1304 } else {
1305 z1 = mpi_new(0);
1306 ec_invm(z1, p1.z, ctx);
1307 ec_mulm(result->x, p1.x, z1, ctx);
1308 mpi_set_ui(result->z, 1);
1309 mpi_free(z1);
1310 }
1311
1312 point_free(&p1);
1313 point_free(&p2);
1314 point_free(&p1_);
1315 point_free(&p2_);
1316 return;
1317 }
1318
1319 x1 = mpi_alloc_like(ctx->p);
1320 y1 = mpi_alloc_like(ctx->p);
1321 h = mpi_alloc_like(ctx->p);
1322 k = mpi_copy(scalar);
1323 yy = mpi_copy(point->y);
1324
1325 if (mpi_has_sign(k)) {
1326 k->sign = 0;
1327 ec_invm(yy, yy, ctx);
1328 }
1329
1330 if (!mpi_cmp_ui(point->z, 1)) {
1331 mpi_set(x1, point->x);
1332 mpi_set(y1, yy);
1333 } else {
1334 MPI z2, z3;
1335
1336 z2 = mpi_alloc_like(ctx->p);
1337 z3 = mpi_alloc_like(ctx->p);
1338 ec_mulm(z2, point->z, point->z, ctx);
1339 ec_mulm(z3, point->z, z2, ctx);
1340 ec_invm(z2, z2, ctx);
1341 ec_mulm(x1, point->x, z2, ctx);
1342 ec_invm(z3, z3, ctx);
1343 ec_mulm(y1, yy, z3, ctx);
1344 mpi_free(z2);
1345 mpi_free(z3);
1346 }
1347 z1 = mpi_copy(mpi_const(MPI_C_ONE));
1348
1349 mpi_mul(h, k, mpi_const(MPI_C_THREE)); /* h = 3k */
1350 loops = mpi_get_nbits(h);
1351 if (loops < 2) {
1352 /* If SCALAR is zero, the above mpi_mul sets H to zero and thus
1353 * LOOPs will be zero. To avoid an underflow of I in the main
1354 * loop we set LOOP to 2 and the result to (0,0,0).
1355 */
1356 loops = 2;
1357 mpi_clear(result->x);
1358 mpi_clear(result->y);
1359 mpi_clear(result->z);
1360 } else {
1361 mpi_set(result->x, point->x);
1362 mpi_set(result->y, yy);
1363 mpi_set(result->z, point->z);
1364 }
1365 mpi_free(yy); yy = NULL;
1366
1367 p1.x = x1; x1 = NULL;
1368 p1.y = y1; y1 = NULL;
1369 p1.z = z1; z1 = NULL;
1370 point_init(&p2);
1371 point_init(&p1inv);
1372
1373 /* Invert point: y = p - y mod p */
1374 point_set(&p1inv, &p1);
1375 ec_subm(p1inv.y, ctx->p, p1inv.y, ctx);
1376
1377 for (i = loops-2; i > 0; i--) {
1378 mpi_ec_dup_point(result, result, ctx);
1379 if (mpi_test_bit(h, i) == 1 && mpi_test_bit(k, i) == 0) {
1380 point_set(&p2, result);
1381 mpi_ec_add_points(result, &p2, &p1, ctx);
1382 }
1383 if (mpi_test_bit(h, i) == 0 && mpi_test_bit(k, i) == 1) {
1384 point_set(&p2, result);
1385 mpi_ec_add_points(result, &p2, &p1inv, ctx);
1386 }
1387 }
1388
1389 point_free(&p1);
1390 point_free(&p2);
1391 point_free(&p1inv);
1392 mpi_free(h);
1393 mpi_free(k);
1394}
1395EXPORT_SYMBOL_GPL(mpi_ec_mul_point);
1396
1397/* Return true if POINT is on the curve described by CTX. */
1398int mpi_ec_curve_point(MPI_POINT point, struct mpi_ec_ctx *ctx)
1399{
1400 int res = 0;
1401 MPI x, y, w;
1402
1403 x = mpi_new(0);
1404 y = mpi_new(0);
1405 w = mpi_new(0);
1406
1407 /* Check that the point is in range. This needs to be done here and
1408 * not after conversion to affine coordinates.
1409 */
1410 if (mpi_cmpabs(point->x, ctx->p) >= 0)
1411 goto leave;
1412 if (mpi_cmpabs(point->y, ctx->p) >= 0)
1413 goto leave;
1414 if (mpi_cmpabs(point->z, ctx->p) >= 0)
1415 goto leave;
1416
1417 switch (ctx->model) {
1418 case MPI_EC_WEIERSTRASS:
1419 {
1420 MPI xxx;
1421
1422 if (mpi_ec_get_affine(x, y, point, ctx))
1423 goto leave;
1424
1425 xxx = mpi_new(0);
1426
1427 /* y^2 == x^3 + a·x + b */
1428 ec_pow2(y, y, ctx);
1429
1430 ec_pow3(xxx, x, ctx);
1431 ec_mulm(w, ctx->a, x, ctx);
1432 ec_addm(w, w, ctx->b, ctx);
1433 ec_addm(w, w, xxx, ctx);
1434
1435 if (!mpi_cmp(y, w))
1436 res = 1;
1437
1438 mpi_free(xxx);
1439 }
1440 break;
1441
1442 case MPI_EC_MONTGOMERY:
1443 {
1444#define xx y
1445 /* With Montgomery curve, only X-coordinate is valid. */
1446 if (mpi_ec_get_affine(x, NULL, point, ctx))
1447 goto leave;
1448
1449 /* The equation is: b * y^2 == x^3 + a · x^2 + x */
1450 /* We check if right hand is quadratic residue or not by
1451 * Euler's criterion.
1452 */
1453 /* CTX->A has (a-2)/4 and CTX->B has b^-1 */
1454 ec_mulm(w, ctx->a, mpi_const(MPI_C_FOUR), ctx);
1455 ec_addm(w, w, mpi_const(MPI_C_TWO), ctx);
1456 ec_mulm(w, w, x, ctx);
1457 ec_pow2(xx, x, ctx);
1458 ec_addm(w, w, xx, ctx);
1459 ec_addm(w, w, mpi_const(MPI_C_ONE), ctx);
1460 ec_mulm(w, w, x, ctx);
1461 ec_mulm(w, w, ctx->b, ctx);
1462#undef xx
1463 /* Compute Euler's criterion: w^(p-1)/2 */
1464#define p_minus1 y
1465 ec_subm(p_minus1, ctx->p, mpi_const(MPI_C_ONE), ctx);
1466 mpi_rshift(p_minus1, p_minus1, 1);
1467 ec_powm(w, w, p_minus1, ctx);
1468
1469 res = !mpi_cmp_ui(w, 1);
1470#undef p_minus1
1471 }
1472 break;
1473
1474 case MPI_EC_EDWARDS:
1475 {
1476 if (mpi_ec_get_affine(x, y, point, ctx))
1477 goto leave;
1478
1479 mpi_resize(w, ctx->p->nlimbs);
1480 w->nlimbs = ctx->p->nlimbs;
1481
1482 /* a · x^2 + y^2 - 1 - b · x^2 · y^2 == 0 */
1483 ctx->pow2(x, x, ctx);
1484 ctx->pow2(y, y, ctx);
1485 if (ctx->dialect == ECC_DIALECT_ED25519)
1486 ctx->subm(w, ctx->p, x, ctx);
1487 else
1488 ctx->mulm(w, ctx->a, x, ctx);
1489 ctx->addm(w, w, y, ctx);
1490 ctx->mulm(x, x, y, ctx);
1491 ctx->mulm(x, x, ctx->b, ctx);
1492 ctx->subm(w, w, x, ctx);
1493 if (!mpi_cmp_ui(w, 1))
1494 res = 1;
1495 }
1496 break;
1497 }
1498
1499leave:
1500 mpi_free(w);
1501 mpi_free(x);
1502 mpi_free(y);
1503
1504 return res;
1505}
1506EXPORT_SYMBOL_GPL(mpi_ec_curve_point);