1 /*
2 * Copyright (c) 2013, 2014 Kenneth MacKay. All rights reserved.
3 * Copyright (c) 2019 Vitaly Chikunov <vt@altlinux.org>
4 *
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions are
7 * met:
8 * * Redistributions of source code must retain the above copyright
9 * notice, this list of conditions and the following disclaimer.
10 * * Redistributions in binary form must reproduce the above copyright
11 * notice, this list of conditions and the following disclaimer in the
12 * documentation and/or other materials provided with the distribution.
13 *
14 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
15 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
16 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
17 * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
18 * HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
19 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
20 * LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
21 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
22 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
23 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
24 * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
25 */
26
27 #include <crypto/ecc_curve.h>
28 #include <linux/module.h>
29 #include <linux/random.h>
30 #include <linux/slab.h>
31 #include <linux/swab.h>
32 #include <linux/fips.h>
33 #include <crypto/ecdh.h>
34 #include <crypto/rng.h>
35 #include <crypto/internal/ecc.h>
36 #include <asm/unaligned.h>
37 #include <linux/ratelimit.h>
38
39 #include "ecc_curve_defs.h"
40
41 typedef struct {
42 u64 m_low;
43 u64 m_high;
44 } uint128_t;
45
46 /* Returns curv25519 curve param */
47 const struct ecc_curve *ecc_get_curve25519(void)
48 {
49 return &ecc_25519;
50 }
51 EXPORT_SYMBOL(ecc_get_curve25519);
52
53 const struct ecc_curve *ecc_get_curve(unsigned int curve_id)
54 {
55 switch (curve_id) {
56 /* In FIPS mode only allow P256 and higher */
57 case ECC_CURVE_NIST_P192:
58 return fips_enabled ? NULL : &nist_p192;
59 case ECC_CURVE_NIST_P256:
60 return &nist_p256;
61 case ECC_CURVE_NIST_P384:
62 return &nist_p384;
63 case ECC_CURVE_NIST_P521:
64 return &nist_p521;
65 default:
66 return NULL;
67 }
68 }
69 EXPORT_SYMBOL(ecc_get_curve);
70
71 void ecc_digits_from_bytes(const u8 *in, unsigned int nbytes,
72 u64 *out, unsigned int ndigits)
73 {
74 int diff = ndigits - DIV_ROUND_UP(nbytes, sizeof(u64));
75 unsigned int o = nbytes & 7;
76 __be64 msd = 0;
77
78 /* diff > 0: not enough input bytes: set most significant digits to 0 */
79 if (diff > 0) {
80 ndigits -= diff;
81 memset(&out[ndigits], 0, diff * sizeof(u64));
82 }
83
84 if (o) {
85 memcpy((u8 *)&msd + sizeof(msd) - o, in, o);
86 out[--ndigits] = be64_to_cpu(msd);
87 in += o;
88 }
89 ecc_swap_digits(in, out, ndigits);
90 }
91 EXPORT_SYMBOL(ecc_digits_from_bytes);
92
93 static u64 *ecc_alloc_digits_space(unsigned int ndigits)
94 {
95 size_t len = ndigits * sizeof(u64);
96
97 if (!len)
98 return NULL;
99
100 return kmalloc(len, GFP_KERNEL);
101 }
102
103 static void ecc_free_digits_space(u64 *space)
104 {
105 kfree_sensitive(space);
106 }
107
108 struct ecc_point *ecc_alloc_point(unsigned int ndigits)
109 {
110 struct ecc_point *p = kmalloc(sizeof(*p), GFP_KERNEL);
111
112 if (!p)
113 return NULL;
114
115 p->x = ecc_alloc_digits_space(ndigits);
116 if (!p->x)
117 goto err_alloc_x;
118
119 p->y = ecc_alloc_digits_space(ndigits);
120 if (!p->y)
121 goto err_alloc_y;
122
123 p->ndigits = ndigits;
124
125 return p;
126
127 err_alloc_y:
128 ecc_free_digits_space(p->x);
129 err_alloc_x:
130 kfree(p);
131 return NULL;
132 }
133 EXPORT_SYMBOL(ecc_alloc_point);
134
135 void ecc_free_point(struct ecc_point *p)
136 {
137 if (!p)
138 return;
139
140 kfree_sensitive(p->x);
141 kfree_sensitive(p->y);
142 kfree_sensitive(p);
143 }
144 EXPORT_SYMBOL(ecc_free_point);
145
146 static void vli_clear(u64 *vli, unsigned int ndigits)
147 {
148 int i;
149
150 for (i = 0; i < ndigits; i++)
151 vli[i] = 0;
152 }
153
154 /* Returns true if vli == 0, false otherwise. */
155 bool vli_is_zero(const u64 *vli, unsigned int ndigits)
156 {
157 int i;
158
159 for (i = 0; i < ndigits; i++) {
160 if (vli[i])
161 return false;
162 }
163
164 return true;
165 }
166 EXPORT_SYMBOL(vli_is_zero);
167
168 /* Returns nonzero if bit of vli is set. */
169 static u64 vli_test_bit(const u64 *vli, unsigned int bit)
170 {
171 return (vli[bit / 64] & ((u64)1 << (bit % 64)));
172 }
173
174 static bool vli_is_negative(const u64 *vli, unsigned int ndigits)
175 {
176 return vli_test_bit(vli, ndigits * 64 - 1);
177 }
178
179 /* Counts the number of 64-bit "digits" in vli. */
180 static unsigned int vli_num_digits(const u64 *vli, unsigned int ndigits)
181 {
182 int i;
183
184 /* Search from the end until we find a non-zero digit.
185 * We do it in reverse because we expect that most digits will
186 * be nonzero.
187 */
188 for (i = ndigits - 1; i >= 0 && vli[i] == 0; i--);
189
190 return (i + 1);
191 }
192
193 /* Counts the number of bits required for vli. */
194 unsigned int vli_num_bits(const u64 *vli, unsigned int ndigits)
195 {
196 unsigned int i, num_digits;
197 u64 digit;
198
199 num_digits = vli_num_digits(vli, ndigits);
200 if (num_digits == 0)
201 return 0;
202
203 digit = vli[num_digits - 1];
204 for (i = 0; digit; i++)
205 digit >>= 1;
206
207 return ((num_digits - 1) * 64 + i);
208 }
209 EXPORT_SYMBOL(vli_num_bits);
210
211 /* Set dest from unaligned bit string src. */
212 void vli_from_be64(u64 *dest, const void *src, unsigned int ndigits)
213 {
214 int i;
215 const u64 *from = src;
216
217 for (i = 0; i < ndigits; i++)
218 dest[i] = get_unaligned_be64(&from[ndigits - 1 - i]);
219 }
220 EXPORT_SYMBOL(vli_from_be64);
221
222 void vli_from_le64(u64 *dest, const void *src, unsigned int ndigits)
223 {
224 int i;
225 const u64 *from = src;
226
227 for (i = 0; i < ndigits; i++)
228 dest[i] = get_unaligned_le64(&from[i]);
229 }
230 EXPORT_SYMBOL(vli_from_le64);
231
232 /* Sets dest = src. */
233 static void vli_set(u64 *dest, const u64 *src, unsigned int ndigits)
234 {
235 int i;
236
237 for (i = 0; i < ndigits; i++)
238 dest[i] = src[i];
239 }
240
241 /* Returns sign of left - right. */
242 int vli_cmp(const u64 *left, const u64 *right, unsigned int ndigits)
243 {
244 int i;
245
246 for (i = ndigits - 1; i >= 0; i--) {
247 if (left[i] > right[i])
248 return 1;
249 else if (left[i] < right[i])
250 return -1;
251 }
252
253 return 0;
254 }
255 EXPORT_SYMBOL(vli_cmp);
256
257 /* Computes result = in << c, returning carry. Can modify in place
258 * (if result == in). 0 < shift < 64.
259 */
260 static u64 vli_lshift(u64 *result, const u64 *in, unsigned int shift,
261 unsigned int ndigits)
262 {
263 u64 carry = 0;
264 int i;
265
266 for (i = 0; i < ndigits; i++) {
267 u64 temp = in[i];
268
269 result[i] = (temp << shift) | carry;
270 carry = temp >> (64 - shift);
271 }
272
273 return carry;
274 }
275
276 /* Computes vli = vli >> 1. */
277 static void vli_rshift1(u64 *vli, unsigned int ndigits)
278 {
279 u64 *end = vli;
280 u64 carry = 0;
281
282 vli += ndigits;
283
284 while (vli-- > end) {
285 u64 temp = *vli;
286 *vli = (temp >> 1) | carry;
287 carry = temp << 63;
288 }
289 }
290
291 /* Computes result = left + right, returning carry. Can modify in place. */
292 static u64 vli_add(u64 *result, const u64 *left, const u64 *right,
293 unsigned int ndigits)
294 {
295 u64 carry = 0;
296 int i;
297
298 for (i = 0; i < ndigits; i++) {
299 u64 sum;
300
301 sum = left[i] + right[i] + carry;
302 if (sum != left[i])
303 carry = (sum < left[i]);
304
305 result[i] = sum;
306 }
307
308 return carry;
309 }
310
311 /* Computes result = left + right, returning carry. Can modify in place. */
312 static u64 vli_uadd(u64 *result, const u64 *left, u64 right,
313 unsigned int ndigits)
314 {
315 u64 carry = right;
316 int i;
317
318 for (i = 0; i < ndigits; i++) {
319 u64 sum;
320
321 sum = left[i] + carry;
322 if (sum != left[i])
323 carry = (sum < left[i]);
324 else
325 carry = !!carry;
326
327 result[i] = sum;
328 }
329
330 return carry;
331 }
332
333 /* Computes result = left - right, returning borrow. Can modify in place. */
334 u64 vli_sub(u64 *result, const u64 *left, const u64 *right,
335 unsigned int ndigits)
336 {
337 u64 borrow = 0;
338 int i;
339
340 for (i = 0; i < ndigits; i++) {
341 u64 diff;
342
343 diff = left[i] - right[i] - borrow;
344 if (diff != left[i])
345 borrow = (diff > left[i]);
346
347 result[i] = diff;
348 }
349
350 return borrow;
351 }
352 EXPORT_SYMBOL(vli_sub);
353
354 /* Computes result = left - right, returning borrow. Can modify in place. */
355 static u64 vli_usub(u64 *result, const u64 *left, u64 right,
356 unsigned int ndigits)
357 {
358 u64 borrow = right;
359 int i;
360
361 for (i = 0; i < ndigits; i++) {
362 u64 diff;
363
364 diff = left[i] - borrow;
365 if (diff != left[i])
366 borrow = (diff > left[i]);
367
368 result[i] = diff;
369 }
370
371 return borrow;
372 }
373
374 static uint128_t mul_64_64(u64 left, u64 right)
375 {
376 uint128_t result;
377 #if defined(CONFIG_ARCH_SUPPORTS_INT128)
378 unsigned __int128 m = (unsigned __int128)left * right;
379
380 result.m_low = m;
381 result.m_high = m >> 64;
382 #else
383 u64 a0 = left & 0xffffffffull;
384 u64 a1 = left >> 32;
385 u64 b0 = right & 0xffffffffull;
386 u64 b1 = right >> 32;
387 u64 m0 = a0 * b0;
388 u64 m1 = a0 * b1;
389 u64 m2 = a1 * b0;
390 u64 m3 = a1 * b1;
391
392 m2 += (m0 >> 32);
393 m2 += m1;
394
395 /* Overflow */
396 if (m2 < m1)
397 m3 += 0x100000000ull;
398
399 result.m_low = (m0 & 0xffffffffull) | (m2 << 32);
400 result.m_high = m3 + (m2 >> 32);
401 #endif
402 return result;
403 }
404
405 static uint128_t add_128_128(uint128_t a, uint128_t b)
406 {
407 uint128_t result;
408
409 result.m_low = a.m_low + b.m_low;
410 result.m_high = a.m_high + b.m_high + (result.m_low < a.m_low);
411
412 return result;
413 }
414
415 static void vli_mult(u64 *result, const u64 *left, const u64 *right,
416 unsigned int ndigits)
417 {
418 uint128_t r01 = { 0, 0 };
419 u64 r2 = 0;
420 unsigned int i, k;
421
422 /* Compute each digit of result in sequence, maintaining the
423 * carries.
424 */
425 for (k = 0; k < ndigits * 2 - 1; k++) {
426 unsigned int min;
427
428 if (k < ndigits)
429 min = 0;
430 else
431 min = (k + 1) - ndigits;
432
433 for (i = min; i <= k && i < ndigits; i++) {
434 uint128_t product;
435
436 product = mul_64_64(left[i], right[k - i]);
437
438 r01 = add_128_128(r01, product);
439 r2 += (r01.m_high < product.m_high);
440 }
441
442 result[k] = r01.m_low;
443 r01.m_low = r01.m_high;
444 r01.m_high = r2;
445 r2 = 0;
446 }
447
448 result[ndigits * 2 - 1] = r01.m_low;
449 }
450
451 /* Compute product = left * right, for a small right value. */
452 static void vli_umult(u64 *result, const u64 *left, u32 right,
453 unsigned int ndigits)
454 {
455 uint128_t r01 = { 0 };
456 unsigned int k;
457
458 for (k = 0; k < ndigits; k++) {
459 uint128_t product;
460
461 product = mul_64_64(left[k], right);
462 r01 = add_128_128(r01, product);
463 /* no carry */
464 result[k] = r01.m_low;
465 r01.m_low = r01.m_high;
466 r01.m_high = 0;
467 }
468 result[k] = r01.m_low;
469 for (++k; k < ndigits * 2; k++)
470 result[k] = 0;
471 }
472
473 static void vli_square(u64 *result, const u64 *left, unsigned int ndigits)
474 {
475 uint128_t r01 = { 0, 0 };
476 u64 r2 = 0;
477 int i, k;
478
479 for (k = 0; k < ndigits * 2 - 1; k++) {
480 unsigned int min;
481
482 if (k < ndigits)
483 min = 0;
484 else
485 min = (k + 1) - ndigits;
486
487 for (i = min; i <= k && i <= k - i; i++) {
488 uint128_t product;
489
490 product = mul_64_64(left[i], left[k - i]);
491
492 if (i < k - i) {
493 r2 += product.m_high >> 63;
494 product.m_high = (product.m_high << 1) |
495 (product.m_low >> 63);
496 product.m_low <<= 1;
497 }
498
499 r01 = add_128_128(r01, product);
500 r2 += (r01.m_high < product.m_high);
501 }
502
503 result[k] = r01.m_low;
504 r01.m_low = r01.m_high;
505 r01.m_high = r2;
506 r2 = 0;
507 }
508
509 result[ndigits * 2 - 1] = r01.m_low;
510 }
511
512 /* Computes result = (left + right) % mod.
513 * Assumes that left < mod and right < mod, result != mod.
514 */
515 static void vli_mod_add(u64 *result, const u64 *left, const u64 *right,
516 const u64 *mod, unsigned int ndigits)
517 {
518 u64 carry;
519
520 carry = vli_add(result, left, right, ndigits);
521
522 /* result > mod (result = mod + remainder), so subtract mod to
523 * get remainder.
524 */
525 if (carry || vli_cmp(result, mod, ndigits) >= 0)
526 vli_sub(result, result, mod, ndigits);
527 }
528
529 /* Computes result = (left - right) % mod.
530 * Assumes that left < mod and right < mod, result != mod.
531 */
532 static void vli_mod_sub(u64 *result, const u64 *left, const u64 *right,
533 const u64 *mod, unsigned int ndigits)
534 {
535 u64 borrow = vli_sub(result, left, right, ndigits);
536
537 /* In this case, p_result == -diff == (max int) - diff.
538 * Since -x % d == d - x, we can get the correct result from
539 * result + mod (with overflow).
540 */
541 if (borrow)
542 vli_add(result, result, mod, ndigits);
543 }
544
545 /*
546 * Computes result = product % mod
547 * for special form moduli: p = 2^k-c, for small c (note the minus sign)
548 *
549 * References:
550 * R. Crandall, C. Pomerance. Prime Numbers: A Computational Perspective.
551 * 9 Fast Algorithms for Large-Integer Arithmetic. 9.2.3 Moduli of special form
552 * Algorithm 9.2.13 (Fast mod operation for special-form moduli).
553 */
554 static void vli_mmod_special(u64 *result, const u64 *product,
555 const u64 *mod, unsigned int ndigits)
556 {
557 u64 c = -mod[0];
558 u64 t[ECC_MAX_DIGITS * 2];
559 u64 r[ECC_MAX_DIGITS * 2];
560
561 vli_set(r, product, ndigits * 2);
562 while (!vli_is_zero(r + ndigits, ndigits)) {
563 vli_umult(t, r + ndigits, c, ndigits);
564 vli_clear(r + ndigits, ndigits);
565 vli_add(r, r, t, ndigits * 2);
566 }
567 vli_set(t, mod, ndigits);
568 vli_clear(t + ndigits, ndigits);
569 while (vli_cmp(r, t, ndigits * 2) >= 0)
570 vli_sub(r, r, t, ndigits * 2);
571 vli_set(result, r, ndigits);
572 }
573
574 /*
575 * Computes result = product % mod
576 * for special form moduli: p = 2^{k-1}+c, for small c (note the plus sign)
577 * where k-1 does not fit into qword boundary by -1 bit (such as 255).
578
579 * References (loosely based on):
580 * A. Menezes, P. van Oorschot, S. Vanstone. Handbook of Applied Cryptography.
581 * 14.3.4 Reduction methods for moduli of special form. Algorithm 14.47.
582 * URL: http://cacr.uwaterloo.ca/hac/about/chap14.pdf
583 *
584 * H. Cohen, G. Frey, R. Avanzi, C. Doche, T. Lange, K. Nguyen, F. Vercauteren.
585 * Handbook of Elliptic and Hyperelliptic Curve Cryptography.
586 * Algorithm 10.25 Fast reduction for special form moduli
587 */
588 static void vli_mmod_special2(u64 *result, const u64 *product,
589 const u64 *mod, unsigned int ndigits)
590 {
591 u64 c2 = mod[0] * 2;
592 u64 q[ECC_MAX_DIGITS];
593 u64 r[ECC_MAX_DIGITS * 2];
594 u64 m[ECC_MAX_DIGITS * 2]; /* expanded mod */
595 int carry; /* last bit that doesn't fit into q */
596 int i;
597
598 vli_set(m, mod, ndigits);
599 vli_clear(m + ndigits, ndigits);
600
601 vli_set(r, product, ndigits);
602 /* q and carry are top bits */
603 vli_set(q, product + ndigits, ndigits);
604 vli_clear(r + ndigits, ndigits);
605 carry = vli_is_negative(r, ndigits);
606 if (carry)
607 r[ndigits - 1] &= (1ull << 63) - 1;
608 for (i = 1; carry || !vli_is_zero(q, ndigits); i++) {
609 u64 qc[ECC_MAX_DIGITS * 2];
610
611 vli_umult(qc, q, c2, ndigits);
612 if (carry)
613 vli_uadd(qc, qc, mod[0], ndigits * 2);
614 vli_set(q, qc + ndigits, ndigits);
615 vli_clear(qc + ndigits, ndigits);
616 carry = vli_is_negative(qc, ndigits);
617 if (carry)
618 qc[ndigits - 1] &= (1ull << 63) - 1;
619 if (i & 1)
620 vli_sub(r, r, qc, ndigits * 2);
621 else
622 vli_add(r, r, qc, ndigits * 2);
623 }
624 while (vli_is_negative(r, ndigits * 2))
625 vli_add(r, r, m, ndigits * 2);
626 while (vli_cmp(r, m, ndigits * 2) >= 0)
627 vli_sub(r, r, m, ndigits * 2);
628
629 vli_set(result, r, ndigits);
630 }
631
632 /*
633 * Computes result = product % mod, where product is 2N words long.
634 * Reference: Ken MacKay's micro-ecc.
635 * Currently only designed to work for curve_p or curve_n.
636 */
637 static void vli_mmod_slow(u64 *result, u64 *product, const u64 *mod,
638 unsigned int ndigits)
639 {
640 u64 mod_m[2 * ECC_MAX_DIGITS];
641 u64 tmp[2 * ECC_MAX_DIGITS];
642 u64 *v[2] = { tmp, product };
643 u64 carry = 0;
644 unsigned int i;
645 /* Shift mod so its highest set bit is at the maximum position. */
646 int shift = (ndigits * 2 * 64) - vli_num_bits(mod, ndigits);
647 int word_shift = shift / 64;
648 int bit_shift = shift % 64;
649
650 vli_clear(mod_m, word_shift);
651 if (bit_shift > 0) {
652 for (i = 0; i < ndigits; ++i) {
653 mod_m[word_shift + i] = (mod[i] << bit_shift) | carry;
654 carry = mod[i] >> (64 - bit_shift);
655 }
656 } else
657 vli_set(mod_m + word_shift, mod, ndigits);
658
659 for (i = 1; shift >= 0; --shift) {
660 u64 borrow = 0;
661 unsigned int j;
662
663 for (j = 0; j < ndigits * 2; ++j) {
664 u64 diff = v[i][j] - mod_m[j] - borrow;
665
666 if (diff != v[i][j])
667 borrow = (diff > v[i][j]);
668 v[1 - i][j] = diff;
669 }
670 i = !(i ^ borrow); /* Swap the index if there was no borrow */
671 vli_rshift1(mod_m, ndigits);
672 mod_m[ndigits - 1] |= mod_m[ndigits] << (64 - 1);
673 vli_rshift1(mod_m + ndigits, ndigits);
674 }
675 vli_set(result, v[i], ndigits);
676 }
677
678 /* Computes result = product % mod using Barrett's reduction with precomputed
679 * value mu appended to the mod after ndigits, mu = (2^{2w} / mod) and have
680 * length ndigits + 1, where mu * (2^w - 1) should not overflow ndigits
681 * boundary.
682 *
683 * Reference:
684 * R. Brent, P. Zimmermann. Modern Computer Arithmetic. 2010.
685 * 2.4.1 Barrett's algorithm. Algorithm 2.5.
686 */
687 static void vli_mmod_barrett(u64 *result, u64 *product, const u64 *mod,
688 unsigned int ndigits)
689 {
690 u64 q[ECC_MAX_DIGITS * 2];
691 u64 r[ECC_MAX_DIGITS * 2];
692 const u64 *mu = mod + ndigits;
693
694 vli_mult(q, product + ndigits, mu, ndigits);
695 if (mu[ndigits])
696 vli_add(q + ndigits, q + ndigits, product + ndigits, ndigits);
697 vli_mult(r, mod, q + ndigits, ndigits);
698 vli_sub(r, product, r, ndigits * 2);
699 while (!vli_is_zero(r + ndigits, ndigits) ||
700 vli_cmp(r, mod, ndigits) != -1) {
701 u64 carry;
702
703 carry = vli_sub(r, r, mod, ndigits);
704 vli_usub(r + ndigits, r + ndigits, carry, ndigits);
705 }
706 vli_set(result, r, ndigits);
707 }
708
709 /* Computes p_result = p_product % curve_p.
710 * See algorithm 5 and 6 from
711 * http://www.isys.uni-klu.ac.at/PDF/2001-0126-MT.pdf
712 */
713 static void vli_mmod_fast_192(u64 *result, const u64 *product,
714 const u64 *curve_prime, u64 *tmp)
715 {
716 const unsigned int ndigits = ECC_CURVE_NIST_P192_DIGITS;
717 int carry;
718
719 vli_set(result, product, ndigits);
720
721 vli_set(tmp, &product[3], ndigits);
722 carry = vli_add(result, result, tmp, ndigits);
723
724 tmp[0] = 0;
725 tmp[1] = product[3];
726 tmp[2] = product[4];
727 carry += vli_add(result, result, tmp, ndigits);
728
729 tmp[0] = tmp[1] = product[5];
730 tmp[2] = 0;
731 carry += vli_add(result, result, tmp, ndigits);
732
733 while (carry || vli_cmp(curve_prime, result, ndigits) != 1)
734 carry -= vli_sub(result, result, curve_prime, ndigits);
735 }
736
737 /* Computes result = product % curve_prime
738 * from http://www.nsa.gov/ia/_files/nist-routines.pdf
739 */
740 static void vli_mmod_fast_256(u64 *result, const u64 *product,
741 const u64 *curve_prime, u64 *tmp)
742 {
743 int carry;
744 const unsigned int ndigits = ECC_CURVE_NIST_P256_DIGITS;
745
746 /* t */
747 vli_set(result, product, ndigits);
748
749 /* s1 */
750 tmp[0] = 0;
751 tmp[1] = product[5] & 0xffffffff00000000ull;
752 tmp[2] = product[6];
753 tmp[3] = product[7];
754 carry = vli_lshift(tmp, tmp, 1, ndigits);
755 carry += vli_add(result, result, tmp, ndigits);
756
757 /* s2 */
758 tmp[1] = product[6] << 32;
759 tmp[2] = (product[6] >> 32) | (product[7] << 32);
760 tmp[3] = product[7] >> 32;
761 carry += vli_lshift(tmp, tmp, 1, ndigits);
762 carry += vli_add(result, result, tmp, ndigits);
763
764 /* s3 */
765 tmp[0] = product[4];
766 tmp[1] = product[5] & 0xffffffff;
767 tmp[2] = 0;
768 tmp[3] = product[7];
769 carry += vli_add(result, result, tmp, ndigits);
770
771 /* s4 */
772 tmp[0] = (product[4] >> 32) | (product[5] << 32);
773 tmp[1] = (product[5] >> 32) | (product[6] & 0xffffffff00000000ull);
774 tmp[2] = product[7];
775 tmp[3] = (product[6] >> 32) | (product[4] << 32);
776 carry += vli_add(result, result, tmp, ndigits);
777
778 /* d1 */
779 tmp[0] = (product[5] >> 32) | (product[6] << 32);
780 tmp[1] = (product[6] >> 32);
781 tmp[2] = 0;
782 tmp[3] = (product[4] & 0xffffffff) | (product[5] << 32);
783 carry -= vli_sub(result, result, tmp, ndigits);
784
785 /* d2 */
786 tmp[0] = product[6];
787 tmp[1] = product[7];
788 tmp[2] = 0;
789 tmp[3] = (product[4] >> 32) | (product[5] & 0xffffffff00000000ull);
790 carry -= vli_sub(result, result, tmp, ndigits);
791
792 /* d3 */
793 tmp[0] = (product[6] >> 32) | (product[7] << 32);
794 tmp[1] = (product[7] >> 32) | (product[4] << 32);
795 tmp[2] = (product[4] >> 32) | (product[5] << 32);
796 tmp[3] = (product[6] << 32);
797 carry -= vli_sub(result, result, tmp, ndigits);
798
799 /* d4 */
800 tmp[0] = product[7];
801 tmp[1] = product[4] & 0xffffffff00000000ull;
802 tmp[2] = product[5];
803 tmp[3] = product[6] & 0xffffffff00000000ull;
804 carry -= vli_sub(result, result, tmp, ndigits);
805
806 if (carry < 0) {
807 do {
808 carry += vli_add(result, result, curve_prime, ndigits);
809 } while (carry < 0);
810 } else {
811 while (carry || vli_cmp(curve_prime, result, ndigits) != 1)
812 carry -= vli_sub(result, result, curve_prime, ndigits);
813 }
814 }
815
816 #define SL32OR32(x32, y32) (((u64)x32 << 32) | y32)
817 #define AND64H(x64) (x64 & 0xffFFffFF00000000ull)
818 #define AND64L(x64) (x64 & 0x00000000ffFFffFFull)
819
820 /* Computes result = product % curve_prime
821 * from "Mathematical routines for the NIST prime elliptic curves"
822 */
823 static void vli_mmod_fast_384(u64 *result, const u64 *product,
824 const u64 *curve_prime, u64 *tmp)
825 {
826 int carry;
827 const unsigned int ndigits = ECC_CURVE_NIST_P384_DIGITS;
828
829 /* t */
830 vli_set(result, product, ndigits);
831
832 /* s1 */
833 tmp[0] = 0; // 0 || 0
834 tmp[1] = 0; // 0 || 0
835 tmp[2] = SL32OR32(product[11], (product[10]>>32)); //a22||a21
836 tmp[3] = product[11]>>32; // 0 ||a23
837 tmp[4] = 0; // 0 || 0
838 tmp[5] = 0; // 0 || 0
839 carry = vli_lshift(tmp, tmp, 1, ndigits);
840 carry += vli_add(result, result, tmp, ndigits);
841
842 /* s2 */
843 tmp[0] = product[6]; //a13||a12
844 tmp[1] = product[7]; //a15||a14
845 tmp[2] = product[8]; //a17||a16
846 tmp[3] = product[9]; //a19||a18
847 tmp[4] = product[10]; //a21||a20
848 tmp[5] = product[11]; //a23||a22
849 carry += vli_add(result, result, tmp, ndigits);
850
851 /* s3 */
852 tmp[0] = SL32OR32(product[11], (product[10]>>32)); //a22||a21
853 tmp[1] = SL32OR32(product[6], (product[11]>>32)); //a12||a23
854 tmp[2] = SL32OR32(product[7], (product[6])>>32); //a14||a13
855 tmp[3] = SL32OR32(product[8], (product[7]>>32)); //a16||a15
856 tmp[4] = SL32OR32(product[9], (product[8]>>32)); //a18||a17
857 tmp[5] = SL32OR32(product[10], (product[9]>>32)); //a20||a19
858 carry += vli_add(result, result, tmp, ndigits);
859
860 /* s4 */
861 tmp[0] = AND64H(product[11]); //a23|| 0
862 tmp[1] = (product[10]<<32); //a20|| 0
863 tmp[2] = product[6]; //a13||a12
864 tmp[3] = product[7]; //a15||a14
865 tmp[4] = product[8]; //a17||a16
866 tmp[5] = product[9]; //a19||a18
867 carry += vli_add(result, result, tmp, ndigits);
868
869 /* s5 */
870 tmp[0] = 0; // 0|| 0
871 tmp[1] = 0; // 0|| 0
872 tmp[2] = product[10]; //a21||a20
873 tmp[3] = product[11]; //a23||a22
874 tmp[4] = 0; // 0|| 0
875 tmp[5] = 0; // 0|| 0
876 carry += vli_add(result, result, tmp, ndigits);
877
878 /* s6 */
879 tmp[0] = AND64L(product[10]); // 0 ||a20
880 tmp[1] = AND64H(product[10]); //a21|| 0
881 tmp[2] = product[11]; //a23||a22
882 tmp[3] = 0; // 0 || 0
883 tmp[4] = 0; // 0 || 0
884 tmp[5] = 0; // 0 || 0
885 carry += vli_add(result, result, tmp, ndigits);
886
887 /* d1 */
888 tmp[0] = SL32OR32(product[6], (product[11]>>32)); //a12||a23
889 tmp[1] = SL32OR32(product[7], (product[6]>>32)); //a14||a13
890 tmp[2] = SL32OR32(product[8], (product[7]>>32)); //a16||a15
891 tmp[3] = SL32OR32(product[9], (product[8]>>32)); //a18||a17
892 tmp[4] = SL32OR32(product[10], (product[9]>>32)); //a20||a19
893 tmp[5] = SL32OR32(product[11], (product[10]>>32)); //a22||a21
894 carry -= vli_sub(result, result, tmp, ndigits);
895
896 /* d2 */
897 tmp[0] = (product[10]<<32); //a20|| 0
898 tmp[1] = SL32OR32(product[11], (product[10]>>32)); //a22||a21
899 tmp[2] = (product[11]>>32); // 0 ||a23
900 tmp[3] = 0; // 0 || 0
901 tmp[4] = 0; // 0 || 0
902 tmp[5] = 0; // 0 || 0
903 carry -= vli_sub(result, result, tmp, ndigits);
904
905 /* d3 */
906 tmp[0] = 0; // 0 || 0
907 tmp[1] = AND64H(product[11]); //a23|| 0
908 tmp[2] = product[11]>>32; // 0 ||a23
909 tmp[3] = 0; // 0 || 0
910 tmp[4] = 0; // 0 || 0
911 tmp[5] = 0; // 0 || 0
912 carry -= vli_sub(result, result, tmp, ndigits);
913
914 if (carry < 0) {
915 do {
916 carry += vli_add(result, result, curve_prime, ndigits);
917 } while (carry < 0);
918 } else {
919 while (carry || vli_cmp(curve_prime, result, ndigits) != 1)
920 carry -= vli_sub(result, result, curve_prime, ndigits);
921 }
922
923 }
924
925 #undef SL32OR32
926 #undef AND64H
927 #undef AND64L
928
929 /*
930 * Computes result = product % curve_prime
931 * from "Recommendations for Discrete Logarithm-Based Cryptography:
932 * Elliptic Curve Domain Parameters" section G.1.4
933 */
934 static void vli_mmod_fast_521(u64 *result, const u64 *product,
935 const u64 *curve_prime, u64 *tmp)
936 {
937 const unsigned int ndigits = ECC_CURVE_NIST_P521_DIGITS;
938 size_t i;
939
940 /* Initialize result with lowest 521 bits from product */
941 vli_set(result, product, ndigits);
942 result[8] &= 0x1ff;
943
944 for (i = 0; i < ndigits; i++)
945 tmp[i] = (product[8 + i] >> 9) | (product[9 + i] << 55);
946 tmp[8] &= 0x1ff;
947
948 vli_mod_add(result, result, tmp, curve_prime, ndigits);
949 }
950
951 /* Computes result = product % curve_prime for different curve_primes.
952 *
953 * Note that curve_primes are distinguished just by heuristic check and
954 * not by complete conformance check.
955 */
956 static bool vli_mmod_fast(u64 *result, u64 *product,
957 const struct ecc_curve *curve)
958 {
959 u64 tmp[2 * ECC_MAX_DIGITS];
960 const u64 *curve_prime = curve->p;
961 const unsigned int ndigits = curve->g.ndigits;
962
963 /* All NIST curves have name prefix 'nist_' */
964 if (strncmp(curve->name, "nist_", 5) != 0) {
965 /* Try to handle Pseudo-Marsenne primes. */
966 if (curve_prime[ndigits - 1] == -1ull) {
967 vli_mmod_special(result, product, curve_prime,
968 ndigits);
969 return true;
970 } else if (curve_prime[ndigits - 1] == 1ull << 63 &&
971 curve_prime[ndigits - 2] == 0) {
972 vli_mmod_special2(result, product, curve_prime,
973 ndigits);
974 return true;
975 }
976 vli_mmod_barrett(result, product, curve_prime, ndigits);
977 return true;
978 }
979
980 switch (ndigits) {
981 case ECC_CURVE_NIST_P192_DIGITS:
982 vli_mmod_fast_192(result, product, curve_prime, tmp);
983 break;
984 case ECC_CURVE_NIST_P256_DIGITS:
985 vli_mmod_fast_256(result, product, curve_prime, tmp);
986 break;
987 case ECC_CURVE_NIST_P384_DIGITS:
988 vli_mmod_fast_384(result, product, curve_prime, tmp);
989 break;
990 case ECC_CURVE_NIST_P521_DIGITS:
991 vli_mmod_fast_521(result, product, curve_prime, tmp);
992 break;
993 default:
994 pr_err_ratelimited("ecc: unsupported digits size!\n");
995 return false;
996 }
997
998 return true;
999 }
1000
1001 /* Computes result = (left * right) % mod.
1002 * Assumes that mod is big enough curve order.
1003 */
1004 void vli_mod_mult_slow(u64 *result, const u64 *left, const u64 *right,
1005 const u64 *mod, unsigned int ndigits)
1006 {
1007 u64 product[ECC_MAX_DIGITS * 2];
1008
1009 vli_mult(product, left, right, ndigits);
1010 vli_mmod_slow(result, product, mod, ndigits);
1011 }
1012 EXPORT_SYMBOL(vli_mod_mult_slow);
1013
1014 /* Computes result = (left * right) % curve_prime. */
1015 static void vli_mod_mult_fast(u64 *result, const u64 *left, const u64 *right,
1016 const struct ecc_curve *curve)
1017 {
1018 u64 product[2 * ECC_MAX_DIGITS];
1019
1020 vli_mult(product, left, right, curve->g.ndigits);
1021 vli_mmod_fast(result, product, curve);
1022 }
1023
1024 /* Computes result = left^2 % curve_prime. */
1025 static void vli_mod_square_fast(u64 *result, const u64 *left,
1026 const struct ecc_curve *curve)
1027 {
1028 u64 product[2 * ECC_MAX_DIGITS];
1029
1030 vli_square(product, left, curve->g.ndigits);
1031 vli_mmod_fast(result, product, curve);
1032 }
1033
1034 #define EVEN(vli) (!(vli[0] & 1))
1035 /* Computes result = (1 / p_input) % mod. All VLIs are the same size.
1036 * See "From Euclid's GCD to Montgomery Multiplication to the Great Divide"
1037 * https://labs.oracle.com/techrep/2001/smli_tr-2001-95.pdf
1038 */
1039 void vli_mod_inv(u64 *result, const u64 *input, const u64 *mod,
1040 unsigned int ndigits)
1041 {
1042 u64 a[ECC_MAX_DIGITS], b[ECC_MAX_DIGITS];
1043 u64 u[ECC_MAX_DIGITS], v[ECC_MAX_DIGITS];
1044 u64 carry;
1045 int cmp_result;
1046
1047 if (vli_is_zero(input, ndigits)) {
1048 vli_clear(result, ndigits);
1049 return;
1050 }
1051
1052 vli_set(a, input, ndigits);
1053 vli_set(b, mod, ndigits);
1054 vli_clear(u, ndigits);
1055 u[0] = 1;
1056 vli_clear(v, ndigits);
1057
1058 while ((cmp_result = vli_cmp(a, b, ndigits)) != 0) {
1059 carry = 0;
1060
1061 if (EVEN(a)) {
1062 vli_rshift1(a, ndigits);
1063
1064 if (!EVEN(u))
1065 carry = vli_add(u, u, mod, ndigits);
1066
1067 vli_rshift1(u, ndigits);
1068 if (carry)
1069 u[ndigits - 1] |= 0x8000000000000000ull;
1070 } else if (EVEN(b)) {
1071 vli_rshift1(b, ndigits);
1072
1073 if (!EVEN(v))
1074 carry = vli_add(v, v, mod, ndigits);
1075
1076 vli_rshift1(v, ndigits);
1077 if (carry)
1078 v[ndigits - 1] |= 0x8000000000000000ull;
1079 } else if (cmp_result > 0) {
1080 vli_sub(a, a, b, ndigits);
1081 vli_rshift1(a, ndigits);
1082
1083 if (vli_cmp(u, v, ndigits) < 0)
1084 vli_add(u, u, mod, ndigits);
1085
1086 vli_sub(u, u, v, ndigits);
1087 if (!EVEN(u))
1088 carry = vli_add(u, u, mod, ndigits);
1089
1090 vli_rshift1(u, ndigits);
1091 if (carry)
1092 u[ndigits - 1] |= 0x8000000000000000ull;
1093 } else {
1094 vli_sub(b, b, a, ndigits);
1095 vli_rshift1(b, ndigits);
1096
1097 if (vli_cmp(v, u, ndigits) < 0)
1098 vli_add(v, v, mod, ndigits);
1099
1100 vli_sub(v, v, u, ndigits);
1101 if (!EVEN(v))
1102 carry = vli_add(v, v, mod, ndigits);
1103
1104 vli_rshift1(v, ndigits);
1105 if (carry)
1106 v[ndigits - 1] |= 0x8000000000000000ull;
1107 }
1108 }
1109
1110 vli_set(result, u, ndigits);
1111 }
1112 EXPORT_SYMBOL(vli_mod_inv);
1113
1114 /* ------ Point operations ------ */
1115
1116 /* Returns true if p_point is the point at infinity, false otherwise. */
1117 bool ecc_point_is_zero(const struct ecc_point *point)
1118 {
1119 return (vli_is_zero(point->x, point->ndigits) &&
1120 vli_is_zero(point->y, point->ndigits));
1121 }
1122 EXPORT_SYMBOL(ecc_point_is_zero);
1123
1124 /* Point multiplication algorithm using Montgomery's ladder with co-Z
1125 * coordinates. From https://eprint.iacr.org/2011/338.pdf
1126 */
1127
1128 /* Double in place */
1129 static void ecc_point_double_jacobian(u64 *x1, u64 *y1, u64 *z1,
1130 const struct ecc_curve *curve)
1131 {
1132 /* t1 = x, t2 = y, t3 = z */
1133 u64 t4[ECC_MAX_DIGITS];
1134 u64 t5[ECC_MAX_DIGITS];
1135 const u64 *curve_prime = curve->p;
1136 const unsigned int ndigits = curve->g.ndigits;
1137
1138 if (vli_is_zero(z1, ndigits))
1139 return;
1140
1141 /* t4 = y1^2 */
1142 vli_mod_square_fast(t4, y1, curve);
1143 /* t5 = x1*y1^2 = A */
1144 vli_mod_mult_fast(t5, x1, t4, curve);
1145 /* t4 = y1^4 */
1146 vli_mod_square_fast(t4, t4, curve);
1147 /* t2 = y1*z1 = z3 */
1148 vli_mod_mult_fast(y1, y1, z1, curve);
1149 /* t3 = z1^2 */
1150 vli_mod_square_fast(z1, z1, curve);
1151
1152 /* t1 = x1 + z1^2 */
1153 vli_mod_add(x1, x1, z1, curve_prime, ndigits);
1154 /* t3 = 2*z1^2 */
1155 vli_mod_add(z1, z1, z1, curve_prime, ndigits);
1156 /* t3 = x1 - z1^2 */
1157 vli_mod_sub(z1, x1, z1, curve_prime, ndigits);
1158 /* t1 = x1^2 - z1^4 */
1159 vli_mod_mult_fast(x1, x1, z1, curve);
1160
1161 /* t3 = 2*(x1^2 - z1^4) */
1162 vli_mod_add(z1, x1, x1, curve_prime, ndigits);
1163 /* t1 = 3*(x1^2 - z1^4) */
1164 vli_mod_add(x1, x1, z1, curve_prime, ndigits);
1165 if (vli_test_bit(x1, 0)) {
1166 u64 carry = vli_add(x1, x1, curve_prime, ndigits);
1167
1168 vli_rshift1(x1, ndigits);
1169 x1[ndigits - 1] |= carry << 63;
1170 } else {
1171 vli_rshift1(x1, ndigits);
1172 }
1173 /* t1 = 3/2*(x1^2 - z1^4) = B */
1174
1175 /* t3 = B^2 */
1176 vli_mod_square_fast(z1, x1, curve);
1177 /* t3 = B^2 - A */
1178 vli_mod_sub(z1, z1, t5, curve_prime, ndigits);
1179 /* t3 = B^2 - 2A = x3 */
1180 vli_mod_sub(z1, z1, t5, curve_prime, ndigits);
1181 /* t5 = A - x3 */
1182 vli_mod_sub(t5, t5, z1, curve_prime, ndigits);
1183 /* t1 = B * (A - x3) */
1184 vli_mod_mult_fast(x1, x1, t5, curve);
1185 /* t4 = B * (A - x3) - y1^4 = y3 */
1186 vli_mod_sub(t4, x1, t4, curve_prime, ndigits);
1187
1188 vli_set(x1, z1, ndigits);
1189 vli_set(z1, y1, ndigits);
1190 vli_set(y1, t4, ndigits);
1191 }
1192
1193 /* Modify (x1, y1) => (x1 * z^2, y1 * z^3) */
1194 static void apply_z(u64 *x1, u64 *y1, u64 *z, const struct ecc_curve *curve)
1195 {
1196 u64 t1[ECC_MAX_DIGITS];
1197
1198 vli_mod_square_fast(t1, z, curve); /* z^2 */
1199 vli_mod_mult_fast(x1, x1, t1, curve); /* x1 * z^2 */
1200 vli_mod_mult_fast(t1, t1, z, curve); /* z^3 */
1201 vli_mod_mult_fast(y1, y1, t1, curve); /* y1 * z^3 */
1202 }
1203
1204 /* P = (x1, y1) => 2P, (x2, y2) => P' */
1205 static void xycz_initial_double(u64 *x1, u64 *y1, u64 *x2, u64 *y2,
1206 u64 *p_initial_z, const struct ecc_curve *curve)
1207 {
1208 u64 z[ECC_MAX_DIGITS];
1209 const unsigned int ndigits = curve->g.ndigits;
1210
1211 vli_set(x2, x1, ndigits);
1212 vli_set(y2, y1, ndigits);
1213
1214 vli_clear(z, ndigits);
1215 z[0] = 1;
1216
1217 if (p_initial_z)
1218 vli_set(z, p_initial_z, ndigits);
1219
1220 apply_z(x1, y1, z, curve);
1221
1222 ecc_point_double_jacobian(x1, y1, z, curve);
1223
1224 apply_z(x2, y2, z, curve);
1225 }
1226
1227 /* Input P = (x1, y1, Z), Q = (x2, y2, Z)
1228 * Output P' = (x1', y1', Z3), P + Q = (x3, y3, Z3)
1229 * or P => P', Q => P + Q
1230 */
1231 static void xycz_add(u64 *x1, u64 *y1, u64 *x2, u64 *y2,
1232 const struct ecc_curve *curve)
1233 {
1234 /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
1235 u64 t5[ECC_MAX_DIGITS];
1236 const u64 *curve_prime = curve->p;
1237 const unsigned int ndigits = curve->g.ndigits;
1238
1239 /* t5 = x2 - x1 */
1240 vli_mod_sub(t5, x2, x1, curve_prime, ndigits);
1241 /* t5 = (x2 - x1)^2 = A */
1242 vli_mod_square_fast(t5, t5, curve);
1243 /* t1 = x1*A = B */
1244 vli_mod_mult_fast(x1, x1, t5, curve);
1245 /* t3 = x2*A = C */
1246 vli_mod_mult_fast(x2, x2, t5, curve);
1247 /* t4 = y2 - y1 */
1248 vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
1249 /* t5 = (y2 - y1)^2 = D */
1250 vli_mod_square_fast(t5, y2, curve);
1251
1252 /* t5 = D - B */
1253 vli_mod_sub(t5, t5, x1, curve_prime, ndigits);
1254 /* t5 = D - B - C = x3 */
1255 vli_mod_sub(t5, t5, x2, curve_prime, ndigits);
1256 /* t3 = C - B */
1257 vli_mod_sub(x2, x2, x1, curve_prime, ndigits);
1258 /* t2 = y1*(C - B) */
1259 vli_mod_mult_fast(y1, y1, x2, curve);
1260 /* t3 = B - x3 */
1261 vli_mod_sub(x2, x1, t5, curve_prime, ndigits);
1262 /* t4 = (y2 - y1)*(B - x3) */
1263 vli_mod_mult_fast(y2, y2, x2, curve);
1264 /* t4 = y3 */
1265 vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
1266
1267 vli_set(x2, t5, ndigits);
1268 }
1269
1270 /* Input P = (x1, y1, Z), Q = (x2, y2, Z)
1271 * Output P + Q = (x3, y3, Z3), P - Q = (x3', y3', Z3)
1272 * or P => P - Q, Q => P + Q
1273 */
1274 static void xycz_add_c(u64 *x1, u64 *y1, u64 *x2, u64 *y2,
1275 const struct ecc_curve *curve)
1276 {
1277 /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
1278 u64 t5[ECC_MAX_DIGITS];
1279 u64 t6[ECC_MAX_DIGITS];
1280 u64 t7[ECC_MAX_DIGITS];
1281 const u64 *curve_prime = curve->p;
1282 const unsigned int ndigits = curve->g.ndigits;
1283
1284 /* t5 = x2 - x1 */
1285 vli_mod_sub(t5, x2, x1, curve_prime, ndigits);
1286 /* t5 = (x2 - x1)^2 = A */
1287 vli_mod_square_fast(t5, t5, curve);
1288 /* t1 = x1*A = B */
1289 vli_mod_mult_fast(x1, x1, t5, curve);
1290 /* t3 = x2*A = C */
1291 vli_mod_mult_fast(x2, x2, t5, curve);
1292 /* t4 = y2 + y1 */
1293 vli_mod_add(t5, y2, y1, curve_prime, ndigits);
1294 /* t4 = y2 - y1 */
1295 vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
1296
1297 /* t6 = C - B */
1298 vli_mod_sub(t6, x2, x1, curve_prime, ndigits);
1299 /* t2 = y1 * (C - B) */
1300 vli_mod_mult_fast(y1, y1, t6, curve);
1301 /* t6 = B + C */
1302 vli_mod_add(t6, x1, x2, curve_prime, ndigits);
1303 /* t3 = (y2 - y1)^2 */
1304 vli_mod_square_fast(x2, y2, curve);
1305 /* t3 = x3 */
1306 vli_mod_sub(x2, x2, t6, curve_prime, ndigits);
1307
1308 /* t7 = B - x3 */
1309 vli_mod_sub(t7, x1, x2, curve_prime, ndigits);
1310 /* t4 = (y2 - y1)*(B - x3) */
1311 vli_mod_mult_fast(y2, y2, t7, curve);
1312 /* t4 = y3 */
1313 vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
1314
1315 /* t7 = (y2 + y1)^2 = F */
1316 vli_mod_square_fast(t7, t5, curve);
1317 /* t7 = x3' */
1318 vli_mod_sub(t7, t7, t6, curve_prime, ndigits);
1319 /* t6 = x3' - B */
1320 vli_mod_sub(t6, t7, x1, curve_prime, ndigits);
1321 /* t6 = (y2 + y1)*(x3' - B) */
1322 vli_mod_mult_fast(t6, t6, t5, curve);
1323 /* t2 = y3' */
1324 vli_mod_sub(y1, t6, y1, curve_prime, ndigits);
1325
1326 vli_set(x1, t7, ndigits);
1327 }
1328
1329 static void ecc_point_mult(struct ecc_point *result,
1330 const struct ecc_point *point, const u64 *scalar,
1331 u64 *initial_z, const struct ecc_curve *curve,
1332 unsigned int ndigits)
1333 {
1334 /* R0 and R1 */
1335 u64 rx[2][ECC_MAX_DIGITS];
1336 u64 ry[2][ECC_MAX_DIGITS];
1337 u64 z[ECC_MAX_DIGITS];
1338 u64 sk[2][ECC_MAX_DIGITS];
1339 u64 *curve_prime = curve->p;
1340 int i, nb;
1341 int num_bits;
1342 int carry;
1343
1344 carry = vli_add(sk[0], scalar, curve->n, ndigits);
1345 vli_add(sk[1], sk[0], curve->n, ndigits);
1346 scalar = sk[!carry];
1347 if (curve->nbits == 521) /* NIST P521 */
1348 num_bits = curve->nbits + 2;
1349 else
1350 num_bits = sizeof(u64) * ndigits * 8 + 1;
1351
1352 vli_set(rx[1], point->x, ndigits);
1353 vli_set(ry[1], point->y, ndigits);
1354
1355 xycz_initial_double(rx[1], ry[1], rx[0], ry[0], initial_z, curve);
1356
1357 for (i = num_bits - 2; i > 0; i--) {
1358 nb = !vli_test_bit(scalar, i);
1359 xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb], curve);
1360 xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve);
1361 }
1362
1363 nb = !vli_test_bit(scalar, 0);
1364 xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb], curve);
1365
1366 /* Find final 1/Z value. */
1367 /* X1 - X0 */
1368 vli_mod_sub(z, rx[1], rx[0], curve_prime, ndigits);
1369 /* Yb * (X1 - X0) */
1370 vli_mod_mult_fast(z, z, ry[1 - nb], curve);
1371 /* xP * Yb * (X1 - X0) */
1372 vli_mod_mult_fast(z, z, point->x, curve);
1373
1374 /* 1 / (xP * Yb * (X1 - X0)) */
1375 vli_mod_inv(z, z, curve_prime, point->ndigits);
1376
1377 /* yP / (xP * Yb * (X1 - X0)) */
1378 vli_mod_mult_fast(z, z, point->y, curve);
1379 /* Xb * yP / (xP * Yb * (X1 - X0)) */
1380 vli_mod_mult_fast(z, z, rx[1 - nb], curve);
1381 /* End 1/Z calculation */
1382
1383 xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve);
1384
1385 apply_z(rx[0], ry[0], z, curve);
1386
1387 vli_set(result->x, rx[0], ndigits);
1388 vli_set(result->y, ry[0], ndigits);
1389 }
1390
1391 /* Computes R = P + Q mod p */
1392 static void ecc_point_add(const struct ecc_point *result,
1393 const struct ecc_point *p, const struct ecc_point *q,
1394 const struct ecc_curve *curve)
1395 {
1396 u64 z[ECC_MAX_DIGITS];
1397 u64 px[ECC_MAX_DIGITS];
1398 u64 py[ECC_MAX_DIGITS];
1399 unsigned int ndigits = curve->g.ndigits;
1400
1401 vli_set(result->x, q->x, ndigits);
1402 vli_set(result->y, q->y, ndigits);
1403 vli_mod_sub(z, result->x, p->x, curve->p, ndigits);
1404 vli_set(px, p->x, ndigits);
1405 vli_set(py, p->y, ndigits);
1406 xycz_add(px, py, result->x, result->y, curve);
1407 vli_mod_inv(z, z, curve->p, ndigits);
1408 apply_z(result->x, result->y, z, curve);
1409 }
1410
1411 /* Computes R = u1P + u2Q mod p using Shamir's trick.
1412 * Based on: Kenneth MacKay's micro-ecc (2014).
1413 */
1414 void ecc_point_mult_shamir(const struct ecc_point *result,
1415 const u64 *u1, const struct ecc_point *p,
1416 const u64 *u2, const struct ecc_point *q,
1417 const struct ecc_curve *curve)
1418 {
1419 u64 z[ECC_MAX_DIGITS];
1420 u64 sump[2][ECC_MAX_DIGITS];
1421 u64 *rx = result->x;
1422 u64 *ry = result->y;
1423 unsigned int ndigits = curve->g.ndigits;
1424 unsigned int num_bits;
1425 struct ecc_point sum = ECC_POINT_INIT(sump[0], sump[1], ndigits);
1426 const struct ecc_point *points[4];
1427 const struct ecc_point *point;
1428 unsigned int idx;
1429 int i;
1430
1431 ecc_point_add(&sum, p, q, curve);
1432 points[0] = NULL;
1433 points[1] = p;
1434 points[2] = q;
1435 points[3] = ∑
1436
1437 num_bits = max(vli_num_bits(u1, ndigits), vli_num_bits(u2, ndigits));
1438 i = num_bits - 1;
1439 idx = !!vli_test_bit(u1, i);
1440 idx |= (!!vli_test_bit(u2, i)) << 1;
1441 point = points[idx];
1442
1443 vli_set(rx, point->x, ndigits);
1444 vli_set(ry, point->y, ndigits);
1445 vli_clear(z + 1, ndigits - 1);
1446 z[0] = 1;
1447
1448 for (--i; i >= 0; i--) {
1449 ecc_point_double_jacobian(rx, ry, z, curve);
1450 idx = !!vli_test_bit(u1, i);
1451 idx |= (!!vli_test_bit(u2, i)) << 1;
1452 point = points[idx];
1453 if (point) {
1454 u64 tx[ECC_MAX_DIGITS];
1455 u64 ty[ECC_MAX_DIGITS];
1456 u64 tz[ECC_MAX_DIGITS];
1457
1458 vli_set(tx, point->x, ndigits);
1459 vli_set(ty, point->y, ndigits);
1460 apply_z(tx, ty, z, curve);
1461 vli_mod_sub(tz, rx, tx, curve->p, ndigits);
1462 xycz_add(tx, ty, rx, ry, curve);
1463 vli_mod_mult_fast(z, z, tz, curve);
1464 }
1465 }
1466 vli_mod_inv(z, z, curve->p, ndigits);
1467 apply_z(rx, ry, z, curve);
1468 }
1469 EXPORT_SYMBOL(ecc_point_mult_shamir);
1470
1471 /*
1472 * This function performs checks equivalent to Appendix A.4.2 of FIPS 186-5.
1473 * Whereas A.4.2 results in an integer in the interval [1, n-1], this function
1474 * ensures that the integer is in the range of [2, n-3]. We are slightly
1475 * stricter because of the currently used scalar multiplication algorithm.
1476 */
1477 static int __ecc_is_key_valid(const struct ecc_curve *curve,
1478 const u64 *private_key, unsigned int ndigits)
1479 {
1480 u64 one[ECC_MAX_DIGITS] = { 1, };
1481 u64 res[ECC_MAX_DIGITS];
1482
1483 if (!private_key)
1484 return -EINVAL;
1485
1486 if (curve->g.ndigits != ndigits)
1487 return -EINVAL;
1488
1489 /* Make sure the private key is in the range [2, n-3]. */
1490 if (vli_cmp(one, private_key, ndigits) != -1)
1491 return -EINVAL;
1492 vli_sub(res, curve->n, one, ndigits);
1493 vli_sub(res, res, one, ndigits);
1494 if (vli_cmp(res, private_key, ndigits) != 1)
1495 return -EINVAL;
1496
1497 return 0;
1498 }
1499
1500 int ecc_is_key_valid(unsigned int curve_id, unsigned int ndigits,
1501 const u64 *private_key, unsigned int private_key_len)
1502 {
1503 int nbytes;
1504 const struct ecc_curve *curve = ecc_get_curve(curve_id);
1505
1506 nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT;
1507
1508 if (private_key_len != nbytes)
1509 return -EINVAL;
1510
1511 return __ecc_is_key_valid(curve, private_key, ndigits);
1512 }
1513 EXPORT_SYMBOL(ecc_is_key_valid);
1514
1515 /*
1516 * ECC private keys are generated using the method of rejection sampling,
1517 * equivalent to that described in FIPS 186-5, Appendix A.2.2.
1518 *
1519 * This method generates a private key uniformly distributed in the range
1520 * [2, n-3].
1521 */
1522 int ecc_gen_privkey(unsigned int curve_id, unsigned int ndigits,
1523 u64 *private_key)
1524 {
1525 const struct ecc_curve *curve = ecc_get_curve(curve_id);
1526 unsigned int nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT;
1527 unsigned int nbits = vli_num_bits(curve->n, ndigits);
1528 int err;
1529
1530 /*
1531 * Step 1 & 2: check that N is included in Table 1 of FIPS 186-5,
1532 * section 6.1.1.
1533 */
1534 if (nbits < 224)
1535 return -EINVAL;
1536
1537 /*
1538 * FIPS 186-5 recommends that the private key should be obtained from a
1539 * RBG with a security strength equal to or greater than the security
1540 * strength associated with N.
1541 *
1542 * The maximum security strength identified by NIST SP800-57pt1r4 for
1543 * ECC is 256 (N >= 512).
1544 *
1545 * This condition is met by the default RNG because it selects a favored
1546 * DRBG with a security strength of 256.
1547 */
1548 if (crypto_get_default_rng())
1549 return -EFAULT;
1550
1551 /* Step 3: obtain N returned_bits from the DRBG. */
1552 err = crypto_rng_get_bytes(crypto_default_rng,
1553 (u8 *)private_key, nbytes);
1554 crypto_put_default_rng();
1555 if (err)
1556 return err;
1557
1558 /* Step 4: make sure the private key is in the valid range. */
1559 if (__ecc_is_key_valid(curve, private_key, ndigits))
1560 return -EINVAL;
1561
1562 return 0;
1563 }
1564 EXPORT_SYMBOL(ecc_gen_privkey);
1565
1566 int ecc_make_pub_key(unsigned int curve_id, unsigned int ndigits,
1567 const u64 *private_key, u64 *public_key)
1568 {
1569 int ret = 0;
1570 struct ecc_point *pk;
1571 const struct ecc_curve *curve = ecc_get_curve(curve_id);
1572
1573 if (!private_key) {
1574 ret = -EINVAL;
1575 goto out;
1576 }
1577
1578 pk = ecc_alloc_point(ndigits);
1579 if (!pk) {
1580 ret = -ENOMEM;
1581 goto out;
1582 }
1583
1584 ecc_point_mult(pk, &curve->g, private_key, NULL, curve, ndigits);
1585
1586 /* SP800-56A rev 3 5.6.2.1.3 key check */
1587 if (ecc_is_pubkey_valid_full(curve, pk)) {
1588 ret = -EAGAIN;
1589 goto err_free_point;
1590 }
1591
1592 ecc_swap_digits(pk->x, public_key, ndigits);
1593 ecc_swap_digits(pk->y, &public_key[ndigits], ndigits);
1594
1595 err_free_point:
1596 ecc_free_point(pk);
1597 out:
1598 return ret;
1599 }
1600 EXPORT_SYMBOL(ecc_make_pub_key);
1601
1602 /* SP800-56A section 5.6.2.3.4 partial verification: ephemeral keys only */
1603 int ecc_is_pubkey_valid_partial(const struct ecc_curve *curve,
1604 struct ecc_point *pk)
1605 {
1606 u64 yy[ECC_MAX_DIGITS], xxx[ECC_MAX_DIGITS], w[ECC_MAX_DIGITS];
1607
1608 if (WARN_ON(pk->ndigits != curve->g.ndigits))
1609 return -EINVAL;
1610
1611 /* Check 1: Verify key is not the zero point. */
1612 if (ecc_point_is_zero(pk))
1613 return -EINVAL;
1614
1615 /* Check 2: Verify key is in the range [1, p-1]. */
1616 if (vli_cmp(curve->p, pk->x, pk->ndigits) != 1)
1617 return -EINVAL;
1618 if (vli_cmp(curve->p, pk->y, pk->ndigits) != 1)
1619 return -EINVAL;
1620
1621 /* Check 3: Verify that y^2 == (x^3 + a·x + b) mod p */
1622 vli_mod_square_fast(yy, pk->y, curve); /* y^2 */
1623 vli_mod_square_fast(xxx, pk->x, curve); /* x^2 */
1624 vli_mod_mult_fast(xxx, xxx, pk->x, curve); /* x^3 */
1625 vli_mod_mult_fast(w, curve->a, pk->x, curve); /* a·x */
1626 vli_mod_add(w, w, curve->b, curve->p, pk->ndigits); /* a·x + b */
1627 vli_mod_add(w, w, xxx, curve->p, pk->ndigits); /* x^3 + a·x + b */
1628 if (vli_cmp(yy, w, pk->ndigits) != 0) /* Equation */
1629 return -EINVAL;
1630
1631 return 0;
1632 }
1633 EXPORT_SYMBOL(ecc_is_pubkey_valid_partial);
1634
1635 /* SP800-56A section 5.6.2.3.3 full verification */
1636 int ecc_is_pubkey_valid_full(const struct ecc_curve *curve,
1637 struct ecc_point *pk)
1638 {
1639 struct ecc_point *nQ;
1640
1641 /* Checks 1 through 3 */
1642 int ret = ecc_is_pubkey_valid_partial(curve, pk);
1643
1644 if (ret)
1645 return ret;
1646
1647 /* Check 4: Verify that nQ is the zero point. */
1648 nQ = ecc_alloc_point(pk->ndigits);
1649 if (!nQ)
1650 return -ENOMEM;
1651
1652 ecc_point_mult(nQ, pk, curve->n, NULL, curve, pk->ndigits);
1653 if (!ecc_point_is_zero(nQ))
1654 ret = -EINVAL;
1655
1656 ecc_free_point(nQ);
1657
1658 return ret;
1659 }
1660 EXPORT_SYMBOL(ecc_is_pubkey_valid_full);
1661
1662 int crypto_ecdh_shared_secret(unsigned int curve_id, unsigned int ndigits,
1663 const u64 *private_key, const u64 *public_key,
1664 u64 *secret)
1665 {
1666 int ret = 0;
1667 struct ecc_point *product, *pk;
1668 u64 rand_z[ECC_MAX_DIGITS];
1669 unsigned int nbytes;
1670 const struct ecc_curve *curve = ecc_get_curve(curve_id);
1671
1672 if (!private_key || !public_key || ndigits > ARRAY_SIZE(rand_z)) {
1673 ret = -EINVAL;
1674 goto out;
1675 }
1676
1677 nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT;
1678
1679 get_random_bytes(rand_z, nbytes);
1680
1681 pk = ecc_alloc_point(ndigits);
1682 if (!pk) {
1683 ret = -ENOMEM;
1684 goto out;
1685 }
1686
1687 ecc_swap_digits(public_key, pk->x, ndigits);
1688 ecc_swap_digits(&public_key[ndigits], pk->y, ndigits);
1689 ret = ecc_is_pubkey_valid_partial(curve, pk);
1690 if (ret)
1691 goto err_alloc_product;
1692
1693 product = ecc_alloc_point(ndigits);
1694 if (!product) {
1695 ret = -ENOMEM;
1696 goto err_alloc_product;
1697 }
1698
1699 ecc_point_mult(product, pk, private_key, rand_z, curve, ndigits);
1700
1701 if (ecc_point_is_zero(product)) {
1702 ret = -EFAULT;
1703 goto err_validity;
1704 }
1705
1706 ecc_swap_digits(product->x, secret, ndigits);
1707
1708 err_validity:
1709 memzero_explicit(rand_z, sizeof(rand_z));
1710 ecc_free_point(product);
1711 err_alloc_product:
1712 ecc_free_point(pk);
1713 out:
1714 return ret;
1715 }
1716 EXPORT_SYMBOL(crypto_ecdh_shared_secret);
1717
1718 MODULE_DESCRIPTION("core elliptic curve module");
1719 MODULE_LICENSE("Dual BSD/GPL");
1720
Linux® is a registered trademark of Linus Torvalds in the United States and other countries.
TOMOYO® is a registered trademark of NTT DATA CORPORATION.