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0586a3b5ab6d83b08712bc464139da49ce148557
[BearSSL] / src / ec / ec_prime_i31.c
1 /*
2 * Copyright (c) 2016 Thomas Pornin <pornin@bolet.org>
3 *
4 * Permission is hereby granted, free of charge, to any person obtaining
5 * a copy of this software and associated documentation files (the
6 * "Software"), to deal in the Software without restriction, including
7 * without limitation the rights to use, copy, modify, merge, publish,
8 * distribute, sublicense, and/or sell copies of the Software, and to
9 * permit persons to whom the Software is furnished to do so, subject to
10 * the following conditions:
11 *
12 * The above copyright notice and this permission notice shall be
13 * included in all copies or substantial portions of the Software.
14 *
15 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
16 * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
17 * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
18 * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
19 * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
20 * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
21 * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
22 * SOFTWARE.
23 */
24
25 #include "inner.h"
26
27 /*
28 * Parameters for supported curves (field modulus, and 'b' equation
29 * parameter; both values use the 'i31' format, and 'b' is in Montgomery
30 * representation).
31 */
32
33 static const uint32_t P256_P[] = {
34 0x00000108,
35 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x00000007,
36 0x00000000, 0x00000000, 0x00000040, 0x7FFFFF80,
37 0x000000FF
38 };
39
40 static const uint32_t P256_R2[] = {
41 0x00000108,
42 0x00014000, 0x00018000, 0x00000000, 0x7FF40000,
43 0x7FEFFFFF, 0x7FF7FFFF, 0x7FAFFFFF, 0x005FFFFF,
44 0x00000000
45 };
46
47 static const uint32_t P256_B[] = {
48 0x00000108,
49 0x6FEE1803, 0x6229C4BD, 0x21B139BE, 0x327150AA,
50 0x3567802E, 0x3F7212ED, 0x012E4355, 0x782DD38D,
51 0x0000000E
52 };
53
54 static const uint32_t P384_P[] = {
55 0x0000018C,
56 0x7FFFFFFF, 0x00000001, 0x00000000, 0x7FFFFFF8,
57 0x7FFFFFEF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF,
58 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF,
59 0x00000FFF
60 };
61
62 static const uint32_t P384_R2[] = {
63 0x0000018C,
64 0x00000000, 0x00000080, 0x7FFFFE00, 0x000001FF,
65 0x00000800, 0x00000000, 0x7FFFE000, 0x00001FFF,
66 0x00008000, 0x00008000, 0x00000000, 0x00000000,
67 0x00000000
68 };
69
70 static const uint32_t P384_B[] = {
71 0x0000018C,
72 0x6E666840, 0x070D0392, 0x5D810231, 0x7651D50C,
73 0x17E218D6, 0x1B192002, 0x44EFE441, 0x3A524E2B,
74 0x2719BA5F, 0x41F02209, 0x36C5643E, 0x5813EFFE,
75 0x000008A5
76 };
77
78 static const uint32_t P521_P[] = {
79 0x00000219,
80 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF,
81 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF,
82 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF,
83 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF,
84 0x01FFFFFF
85 };
86
87 static const uint32_t P521_R2[] = {
88 0x00000219,
89 0x00001000, 0x00000000, 0x00000000, 0x00000000,
90 0x00000000, 0x00000000, 0x00000000, 0x00000000,
91 0x00000000, 0x00000000, 0x00000000, 0x00000000,
92 0x00000000, 0x00000000, 0x00000000, 0x00000000,
93 0x00000000
94 };
95
96 static const uint32_t P521_B[] = {
97 0x00000219,
98 0x540FC00A, 0x228FEA35, 0x2C34F1EF, 0x67BF107A,
99 0x46FC1CD5, 0x1605E9DD, 0x6937B165, 0x272A3D8F,
100 0x42785586, 0x44C8C778, 0x15F3B8B4, 0x64B73366,
101 0x03BA8B69, 0x0D05B42A, 0x21F929A2, 0x2C31C393,
102 0x00654FAE
103 };
104
105 typedef struct {
106 const uint32_t *p;
107 const uint32_t *b;
108 const uint32_t *R2;
109 uint32_t p0i;
110 } curve_params;
111
112 static inline const curve_params *
113 id_to_curve(int curve)
114 {
115 static const curve_params pp[] = {
116 { P256_P, P256_B, P256_R2, 0x00000001 },
117 { P384_P, P384_B, P384_R2, 0x00000001 },
118 { P521_P, P521_B, P521_R2, 0x00000001 }
119 };
120
121 return &pp[curve - BR_EC_secp256r1];
122 }
123
124 #define I31_LEN ((BR_MAX_EC_SIZE + 61) / 31)
125
126 /*
127 * Type for a point in Jacobian coordinates:
128 * -- three values, x, y and z, in Montgomery representation
129 * -- affine coordinates are X = x / z^2 and Y = y / z^3
130 * -- for the point at infinity, z = 0
131 */
132 typedef struct {
133 uint32_t c[3][I31_LEN];
134 } jacobian;
135
136 /*
137 * We use a custom interpreter that uses a dozen registers, and
138 * only six operations:
139 * MSET(d, a) copy a into d
140 * MADD(d, a) d = d+a (modular)
141 * MSUB(d, a) d = d-a (modular)
142 * MMUL(d, a, b) d = a*b (Montgomery multiplication)
143 * MINV(d, a, b) invert d modulo p; a and b are used as scratch registers
144 * MTZ(d) clear return value if d = 0
145 * Destination of MMUL (d) must be distinct from operands (a and b).
146 * There is no such constraint for MSUB and MADD.
147 *
148 * Registers include the operand coordinates, and temporaries.
149 */
150 #define MSET(d, a) (0x0000 + ((d) << 8) + ((a) << 4))
151 #define MADD(d, a) (0x1000 + ((d) << 8) + ((a) << 4))
152 #define MSUB(d, a) (0x2000 + ((d) << 8) + ((a) << 4))
153 #define MMUL(d, a, b) (0x3000 + ((d) << 8) + ((a) << 4) + (b))
154 #define MINV(d, a, b) (0x4000 + ((d) << 8) + ((a) << 4) + (b))
155 #define MTZ(d) (0x5000 + ((d) << 8))
156 #define ENDCODE 0
157
158 /*
159 * Registers for the input operands.
160 */
161 #define P1x 0
162 #define P1y 1
163 #define P1z 2
164 #define P2x 3
165 #define P2y 4
166 #define P2z 5
167
168 /*
169 * Alternate names for the first input operand.
170 */
171 #define Px 0
172 #define Py 1
173 #define Pz 2
174
175 /*
176 * Temporaries.
177 */
178 #define t1 6
179 #define t2 7
180 #define t3 8
181 #define t4 9
182 #define t5 10
183 #define t6 11
184 #define t7 12
185
186 /*
187 * Extra scratch registers available when there is no second operand (e.g.
188 * for "double" and "affine").
189 */
190 #define t8 3
191 #define t9 4
192 #define t10 5
193
194 /*
195 * Doubling formulas are:
196 *
197 * s = 4*x*y^2
198 * m = 3*(x + z^2)*(x - z^2)
199 * x' = m^2 - 2*s
200 * y' = m*(s - x') - 8*y^4
201 * z' = 2*y*z
202 *
203 * If y = 0 (P has order 2) then this yields infinity (z' = 0), as it
204 * should. This case should not happen anyway, because our curves have
205 * prime order, and thus do not contain any point of order 2.
206 *
207 * If P is infinity (z = 0), then again the formulas yield infinity,
208 * which is correct. Thus, this code works for all points.
209 *
210 * Cost: 8 multiplications
211 */
212 static const uint16_t code_double[] = {
213 /*
214 * Compute z^2 (in t1).
215 */
216 MMUL(t1, Pz, Pz),
217
218 /*
219 * Compute x-z^2 (in t2) and then x+z^2 (in t1).
220 */
221 MSET(t2, Px),
222 MSUB(t2, t1),
223 MADD(t1, Px),
224
225 /*
226 * Compute m = 3*(x+z^2)*(x-z^2) (in t1).
227 */
228 MMUL(t3, t1, t2),
229 MSET(t1, t3),
230 MADD(t1, t3),
231 MADD(t1, t3),
232
233 /*
234 * Compute s = 4*x*y^2 (in t2) and 2*y^2 (in t3).
235 */
236 MMUL(t3, Py, Py),
237 MADD(t3, t3),
238 MMUL(t2, Px, t3),
239 MADD(t2, t2),
240
241 /*
242 * Compute x' = m^2 - 2*s.
243 */
244 MMUL(Px, t1, t1),
245 MSUB(Px, t2),
246 MSUB(Px, t2),
247
248 /*
249 * Compute z' = 2*y*z.
250 */
251 MMUL(t4, Py, Pz),
252 MSET(Pz, t4),
253 MADD(Pz, t4),
254
255 /*
256 * Compute y' = m*(s - x') - 8*y^4. Note that we already have
257 * 2*y^2 in t3.
258 */
259 MSUB(t2, Px),
260 MMUL(Py, t1, t2),
261 MMUL(t4, t3, t3),
262 MSUB(Py, t4),
263 MSUB(Py, t4),
264
265 ENDCODE
266 };
267
268 /*
269 * Addtions formulas are:
270 *
271 * u1 = x1 * z2^2
272 * u2 = x2 * z1^2
273 * s1 = y1 * z2^3
274 * s2 = y2 * z1^3
275 * h = u2 - u1
276 * r = s2 - s1
277 * x3 = r^2 - h^3 - 2 * u1 * h^2
278 * y3 = r * (u1 * h^2 - x3) - s1 * h^3
279 * z3 = h * z1 * z2
280 *
281 * If both P1 and P2 are infinity, then z1 == 0 and z2 == 0, implying that
282 * z3 == 0, so the result is correct.
283 * If either of P1 or P2 is infinity, but not both, then z3 == 0, which is
284 * not correct.
285 * h == 0 only if u1 == u2; this happens in two cases:
286 * -- if s1 == s2 then P1 and/or P2 is infinity, or P1 == P2
287 * -- if s1 != s2 then P1 + P2 == infinity (but neither P1 or P2 is infinity)
288 *
289 * Thus, the following situations are not handled correctly:
290 * -- P1 = 0 and P2 != 0
291 * -- P1 != 0 and P2 = 0
292 * -- P1 = P2
293 * All other cases are properly computed. However, even in "incorrect"
294 * situations, the three coordinates still are properly formed field
295 * elements.
296 *
297 * The returned flag is cleared if r == 0. This happens in the following
298 * cases:
299 * -- Both points are on the same horizontal line (same Y coordinate).
300 * -- Both points are infinity.
301 * -- One point is infinity and the other is on line Y = 0.
302 * The third case cannot happen with our curves (there is no valid point
303 * on line Y = 0 since that would be a point of order 2). If the two
304 * source points are non-infinity, then remains only the case where the
305 * two points are on the same horizontal line.
306 *
307 * This allows us to detect the "P1 == P2" case, assuming that P1 != 0 and
308 * P2 != 0:
309 * -- If the returned value is not the point at infinity, then it was properly
310 * computed.
311 * -- Otherwise, if the returned flag is 1, then P1+P2 = 0, and the result
312 * is indeed the point at infinity.
313 * -- Otherwise (result is infinity, flag is 0), then P1 = P2 and we should
314 * use the 'double' code.
315 *
316 * Cost: 16 multiplications
317 */
318 static const uint16_t code_add[] = {
319 /*
320 * Compute u1 = x1*z2^2 (in t1) and s1 = y1*z2^3 (in t3).
321 */
322 MMUL(t3, P2z, P2z),
323 MMUL(t1, P1x, t3),
324 MMUL(t4, P2z, t3),
325 MMUL(t3, P1y, t4),
326
327 /*
328 * Compute u2 = x2*z1^2 (in t2) and s2 = y2*z1^3 (in t4).
329 */
330 MMUL(t4, P1z, P1z),
331 MMUL(t2, P2x, t4),
332 MMUL(t5, P1z, t4),
333 MMUL(t4, P2y, t5),
334
335 /*
336 * Compute h = u2 - u1 (in t2) and r = s2 - s1 (in t4).
337 */
338 MSUB(t2, t1),
339 MSUB(t4, t3),
340
341 /*
342 * Report cases where r = 0 through the returned flag.
343 */
344 MTZ(t4),
345
346 /*
347 * Compute u1*h^2 (in t6) and h^3 (in t5).
348 */
349 MMUL(t7, t2, t2),
350 MMUL(t6, t1, t7),
351 MMUL(t5, t7, t2),
352
353 /*
354 * Compute x3 = r^2 - h^3 - 2*u1*h^2.
355 * t1 and t7 can be used as scratch registers.
356 */
357 MMUL(P1x, t4, t4),
358 MSUB(P1x, t5),
359 MSUB(P1x, t6),
360 MSUB(P1x, t6),
361
362 /*
363 * Compute y3 = r*(u1*h^2 - x3) - s1*h^3.
364 */
365 MSUB(t6, P1x),
366 MMUL(P1y, t4, t6),
367 MMUL(t1, t5, t3),
368 MSUB(P1y, t1),
369
370 /*
371 * Compute z3 = h*z1*z2.
372 */
373 MMUL(t1, P1z, P2z),
374 MMUL(P1z, t1, t2),
375
376 ENDCODE
377 };
378
379 /*
380 * Check that the point is on the curve. This code snippet assumes the
381 * following conventions:
382 * -- Coordinates x and y have been freshly decoded in P1 (but not
383 * converted to Montgomery coordinates yet).
384 * -- P2x, P2y and P2z are set to, respectively, R^2, b*R and 1.
385 */
386 static const uint16_t code_check[] = {
387
388 /* Convert x and y to Montgomery representation. */
389 MMUL(t1, P1x, P2x),
390 MMUL(t2, P1y, P2x),
391 MSET(P1x, t1),
392 MSET(P1y, t2),
393
394 /* Compute x^3 in t1. */
395 MMUL(t2, P1x, P1x),
396 MMUL(t1, P1x, t2),
397
398 /* Subtract 3*x from t1. */
399 MSUB(t1, P1x),
400 MSUB(t1, P1x),
401 MSUB(t1, P1x),
402
403 /* Add b. */
404 MADD(t1, P2y),
405
406 /* Compute y^2 in t2. */
407 MMUL(t2, P1y, P1y),
408
409 /* Compare y^2 with x^3 - 3*x + b; they must match. */
410 MSUB(t1, t2),
411 MTZ(t1),
412
413 /* Set z to 1 (in Montgomery representation). */
414 MMUL(P1z, P2x, P2z),
415
416 ENDCODE
417 };
418
419 /*
420 * Conversion back to affine coordinates. This code snippet assumes that
421 * the z coordinate of P2 is set to 1 (not in Montgomery representation).
422 */
423 static const uint16_t code_affine[] = {
424
425 /* Save z*R in t1. */
426 MSET(t1, P1z),
427
428 /* Compute z^3 in t2. */
429 MMUL(t2, P1z, P1z),
430 MMUL(t3, P1z, t2),
431 MMUL(t2, t3, P2z),
432
433 /* Invert to (1/z^3) in t2. */
434 MINV(t2, t3, t4),
435
436 /* Compute y. */
437 MSET(t3, P1y),
438 MMUL(P1y, t2, t3),
439
440 /* Compute (1/z^2) in t3. */
441 MMUL(t3, t2, t1),
442
443 /* Compute x. */
444 MSET(t2, P1x),
445 MMUL(P1x, t2, t3),
446
447 ENDCODE
448 };
449
450 static uint32_t
451 run_code(jacobian *P1, const jacobian *P2,
452 const curve_params *cc, const uint16_t *code)
453 {
454 uint32_t r;
455 uint32_t t[13][I31_LEN];
456 size_t u;
457
458 r = 1;
459
460 /*
461 * Copy the two operands in the dedicated registers.
462 */
463 memcpy(t[P1x], P1->c, 3 * I31_LEN * sizeof(uint32_t));
464 memcpy(t[P2x], P2->c, 3 * I31_LEN * sizeof(uint32_t));
465
466 /*
467 * Run formulas.
468 */
469 for (u = 0;; u ++) {
470 unsigned op, d, a, b;
471
472 op = code[u];
473 if (op == 0) {
474 break;
475 }
476 d = (op >> 8) & 0x0F;
477 a = (op >> 4) & 0x0F;
478 b = op & 0x0F;
479 op >>= 12;
480 switch (op) {
481 uint32_t ctl;
482 size_t plen;
483 unsigned char tp[(BR_MAX_EC_SIZE + 7) >> 3];
484
485 case 0:
486 memcpy(t[d], t[a], I31_LEN * sizeof(uint32_t));
487 break;
488 case 1:
489 ctl = br_i31_add(t[d], t[a], 1);
490 ctl |= NOT(br_i31_sub(t[d], cc->p, 0));
491 br_i31_sub(t[d], cc->p, ctl);
492 break;
493 case 2:
494 br_i31_add(t[d], cc->p, br_i31_sub(t[d], t[a], 1));
495 break;
496 case 3:
497 br_i31_montymul(t[d], t[a], t[b], cc->p, cc->p0i);
498 break;
499 case 4:
500 plen = (cc->p[0] - (cc->p[0] >> 5) + 7) >> 3;
501 br_i31_encode(tp, plen, cc->p);
502 tp[plen - 1] -= 2;
503 br_i31_modpow(t[d], tp, plen,
504 cc->p, cc->p0i, t[a], t[b]);
505 break;
506 default:
507 r &= ~br_i31_iszero(t[d]);
508 break;
509 }
510 }
511
512 /*
513 * Copy back result.
514 */
515 memcpy(P1->c, t[P1x], 3 * I31_LEN * sizeof(uint32_t));
516 return r;
517 }
518
519 static void
520 set_one(uint32_t *x, const uint32_t *p)
521 {
522 size_t plen;
523
524 plen = (p[0] + 63) >> 5;
525 memset(x, 0, plen * sizeof *x);
526 x[0] = p[0];
527 x[1] = 0x00000001;
528 }
529
530 static void
531 point_zero(jacobian *P, const curve_params *cc)
532 {
533 memset(P, 0, sizeof *P);
534 P->c[0][0] = P->c[1][0] = P->c[2][0] = cc->p[0];
535 }
536
537 static inline void
538 point_double(jacobian *P, const curve_params *cc)
539 {
540 run_code(P, P, cc, code_double);
541 }
542
543 static inline uint32_t
544 point_add(jacobian *P1, const jacobian *P2, const curve_params *cc)
545 {
546 return run_code(P1, P2, cc, code_add);
547 }
548
549 static void
550 point_mul(jacobian *P, const unsigned char *x, size_t xlen,
551 const curve_params *cc)
552 {
553 /*
554 * We do a simple double-and-add ladder with a 2-bit window
555 * to make only one add every two doublings. We thus first
556 * precompute 2P and 3P in some local buffers.
557 *
558 * We always perform two doublings and one addition; the
559 * addition is with P, 2P and 3P and is done in a temporary
560 * array.
561 *
562 * The addition code cannot handle cases where one of the
563 * operands is infinity, which is the case at the start of the
564 * ladder. We therefore need to maintain a flag that controls
565 * this situation.
566 */
567 uint32_t qz;
568 jacobian P2, P3, Q, T, U;
569
570 memcpy(&P2, P, sizeof P2);
571 point_double(&P2, cc);
572 memcpy(&P3, P, sizeof P3);
573 point_add(&P3, &P2, cc);
574
575 point_zero(&Q, cc);
576 qz = 1;
577 while (xlen -- > 0) {
578 int k;
579
580 for (k = 6; k >= 0; k -= 2) {
581 uint32_t bits;
582 uint32_t bnz;
583
584 point_double(&Q, cc);
585 point_double(&Q, cc);
586 memcpy(&T, P, sizeof T);
587 memcpy(&U, &Q, sizeof U);
588 bits = (*x >> k) & (uint32_t)3;
589 bnz = NEQ(bits, 0);
590 CCOPY(EQ(bits, 2), &T, &P2, sizeof T);
591 CCOPY(EQ(bits, 3), &T, &P3, sizeof T);
592 point_add(&U, &T, cc);
593 CCOPY(bnz & qz, &Q, &T, sizeof Q);
594 CCOPY(bnz & ~qz, &Q, &U, sizeof Q);
595 qz &= ~bnz;
596 }
597 x ++;
598 }
599 memcpy(P, &Q, sizeof Q);
600 }
601
602 /*
603 * Decode point into Jacobian coordinates. This function does not support
604 * the point at infinity. If the point is invalid then this returns 0, but
605 * the coordinates are still set to properly formed field elements.
606 */
607 static uint32_t
608 point_decode(jacobian *P, const void *src, size_t len, const curve_params *cc)
609 {
610 /*
611 * Points must use uncompressed format:
612 * -- first byte is 0x04;
613 * -- coordinates X and Y use unsigned big-endian, with the same
614 * length as the field modulus.
615 *
616 * We don't support hybrid format (uncompressed, but first byte
617 * has value 0x06 or 0x07, depending on the least significant bit
618 * of Y) because it is rather useless, and explicitly forbidden
619 * by PKIX (RFC 5480, section 2.2).
620 *
621 * We don't support compressed format either, because it is not
622 * much used in practice (there are or were patent-related
623 * concerns about point compression, which explains the lack of
624 * generalised support). Also, point compression support would
625 * need a bit more code.
626 */
627 const unsigned char *buf;
628 size_t plen, zlen;
629 uint32_t r;
630 jacobian Q;
631
632 buf = src;
633 point_zero(P, cc);
634 plen = (cc->p[0] - (cc->p[0] >> 5) + 7) >> 3;
635 if (len != 1 + (plen << 1)) {
636 return 0;
637 }
638 r = br_i31_decode_mod(P->c[0], buf + 1, plen, cc->p);
639 r &= br_i31_decode_mod(P->c[1], buf + 1 + plen, plen, cc->p);
640
641 /*
642 * Check first byte.
643 */
644 r &= EQ(buf[0], 0x04);
645 /* obsolete
646 r &= EQ(buf[0], 0x04) | (EQ(buf[0] & 0xFE, 0x06)
647 & ~(uint32_t)(buf[0] ^ buf[plen << 1]));
648 */
649
650 /*
651 * Convert coordinates and check that the point is valid.
652 */
653 zlen = ((cc->p[0] + 63) >> 5) * sizeof(uint32_t);
654 memcpy(Q.c[0], cc->R2, zlen);
655 memcpy(Q.c[1], cc->b, zlen);
656 set_one(Q.c[2], cc->p);
657 r &= ~run_code(P, &Q, cc, code_check);
658 return r;
659 }
660
661 /*
662 * Encode a point. This method assumes that the point is correct and is
663 * not the point at infinity. Encoded size is always 1+2*plen, where
664 * plen is the field modulus length, in bytes.
665 */
666 static void
667 point_encode(void *dst, const jacobian *P, const curve_params *cc)
668 {
669 unsigned char *buf;
670 uint32_t xbl;
671 size_t plen;
672 jacobian Q, T;
673
674 buf = dst;
675 xbl = cc->p[0];
676 xbl -= (xbl >> 5);
677 plen = (xbl + 7) >> 3;
678 buf[0] = 0x04;
679 memcpy(&Q, P, sizeof *P);
680 set_one(T.c[2], cc->p);
681 run_code(&Q, &T, cc, code_affine);
682 br_i31_encode(buf + 1, plen, Q.c[0]);
683 br_i31_encode(buf + 1 + plen, plen, Q.c[1]);
684 }
685
686 static const br_ec_curve_def *
687 id_to_curve_def(int curve)
688 {
689 switch (curve) {
690 case BR_EC_secp256r1:
691 return &br_secp256r1;
692 case BR_EC_secp384r1:
693 return &br_secp384r1;
694 case BR_EC_secp521r1:
695 return &br_secp521r1;
696 }
697 return NULL;
698 }
699
700 static const unsigned char *
701 api_generator(int curve, size_t *len)
702 {
703 const br_ec_curve_def *cd;
704
705 cd = id_to_curve_def(curve);
706 *len = cd->generator_len;
707 return cd->generator;
708 }
709
710 static const unsigned char *
711 api_order(int curve, size_t *len)
712 {
713 const br_ec_curve_def *cd;
714
715 cd = id_to_curve_def(curve);
716 *len = cd->order_len;
717 return cd->order;
718 }
719
720 static size_t
721 api_xoff(int curve, size_t *len)
722 {
723 api_generator(curve, len);
724 *len >>= 1;
725 return 1;
726 }
727
728 static uint32_t
729 api_mul(unsigned char *G, size_t Glen,
730 const unsigned char *x, size_t xlen, int curve)
731 {
732 uint32_t r;
733 const curve_params *cc;
734 jacobian P;
735
736 cc = id_to_curve(curve);
737 r = point_decode(&P, G, Glen, cc);
738 point_mul(&P, x, xlen, cc);
739 point_encode(G, &P, cc);
740 return r;
741 }
742
743 static size_t
744 api_mulgen(unsigned char *R,
745 const unsigned char *x, size_t xlen, int curve)
746 {
747 const unsigned char *G;
748 size_t Glen;
749
750 G = api_generator(curve, &Glen);
751 memcpy(R, G, Glen);
752 api_mul(R, Glen, x, xlen, curve);
753 return Glen;
754 }
755
756 static uint32_t
757 api_muladd(unsigned char *A, const unsigned char *B, size_t len,
758 const unsigned char *x, size_t xlen,
759 const unsigned char *y, size_t ylen, int curve)
760 {
761 uint32_t r, t, z;
762 const curve_params *cc;
763 jacobian P, Q;
764
765 /*
766 * TODO: see about merging the two ladders. Right now, we do
767 * two independent point multiplications, which is a bit
768 * wasteful of CPU resources (but yields short code).
769 */
770
771 cc = id_to_curve(curve);
772 r = point_decode(&P, A, len, cc);
773 if (B == NULL) {
774 size_t Glen;
775
776 B = api_generator(curve, &Glen);
777 }
778 r &= point_decode(&Q, B, len, cc);
779 point_mul(&P, x, xlen, cc);
780 point_mul(&Q, y, ylen, cc);
781
782 /*
783 * We want to compute P+Q. Since the base points A and B are distinct
784 * from infinity, and the multipliers are non-zero and lower than the
785 * curve order, then we know that P and Q are non-infinity. This
786 * leaves two special situations to test for:
787 * -- If P = Q then we must use point_double().
788 * -- If P+Q = 0 then we must report an error.
789 */
790 t = point_add(&P, &Q, cc);
791 point_double(&Q, cc);
792 z = br_i31_iszero(P.c[2]);
793
794 /*
795 * If z is 1 then either P+Q = 0 (t = 1) or P = Q (t = 0). So we
796 * have the following:
797 *
798 * z = 0, t = 0 return P (normal addition)
799 * z = 0, t = 1 return P (normal addition)
800 * z = 1, t = 0 return Q (a 'double' case)
801 * z = 1, t = 1 report an error (P+Q = 0)
802 */
803 CCOPY(z & ~t, &P, &Q, sizeof Q);
804 point_encode(A, &P, cc);
805 r &= ~(z & t);
806
807 return r;
808 }
809
810 /* see bearssl_ec.h */
811 const br_ec_impl br_ec_prime_i31 = {
812 (uint32_t)0x03800000,
813 &api_generator,
814 &api_order,
815 &api_xoff,
816 &api_mul,
817 &api_mulgen,
818 &api_muladd
819 };
The BearSSL library and tools.