Loading...
Note: File does not exist in v3.1.
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
41typedef struct {
42 u64 m_low;
43 u64 m_high;
44} uint128_t;
45
46/* Returns curv25519 curve param */
47const struct ecc_curve *ecc_get_curve25519(void)
48{
49 return &ecc_25519;
50}
51EXPORT_SYMBOL(ecc_get_curve25519);
52
53const 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 default:
64 return NULL;
65 }
66}
67EXPORT_SYMBOL(ecc_get_curve);
68
69static u64 *ecc_alloc_digits_space(unsigned int ndigits)
70{
71 size_t len = ndigits * sizeof(u64);
72
73 if (!len)
74 return NULL;
75
76 return kmalloc(len, GFP_KERNEL);
77}
78
79static void ecc_free_digits_space(u64 *space)
80{
81 kfree_sensitive(space);
82}
83
84struct ecc_point *ecc_alloc_point(unsigned int ndigits)
85{
86 struct ecc_point *p = kmalloc(sizeof(*p), GFP_KERNEL);
87
88 if (!p)
89 return NULL;
90
91 p->x = ecc_alloc_digits_space(ndigits);
92 if (!p->x)
93 goto err_alloc_x;
94
95 p->y = ecc_alloc_digits_space(ndigits);
96 if (!p->y)
97 goto err_alloc_y;
98
99 p->ndigits = ndigits;
100
101 return p;
102
103err_alloc_y:
104 ecc_free_digits_space(p->x);
105err_alloc_x:
106 kfree(p);
107 return NULL;
108}
109EXPORT_SYMBOL(ecc_alloc_point);
110
111void ecc_free_point(struct ecc_point *p)
112{
113 if (!p)
114 return;
115
116 kfree_sensitive(p->x);
117 kfree_sensitive(p->y);
118 kfree_sensitive(p);
119}
120EXPORT_SYMBOL(ecc_free_point);
121
122static void vli_clear(u64 *vli, unsigned int ndigits)
123{
124 int i;
125
126 for (i = 0; i < ndigits; i++)
127 vli[i] = 0;
128}
129
130/* Returns true if vli == 0, false otherwise. */
131bool vli_is_zero(const u64 *vli, unsigned int ndigits)
132{
133 int i;
134
135 for (i = 0; i < ndigits; i++) {
136 if (vli[i])
137 return false;
138 }
139
140 return true;
141}
142EXPORT_SYMBOL(vli_is_zero);
143
144/* Returns nonzero if bit of vli is set. */
145static u64 vli_test_bit(const u64 *vli, unsigned int bit)
146{
147 return (vli[bit / 64] & ((u64)1 << (bit % 64)));
148}
149
150static bool vli_is_negative(const u64 *vli, unsigned int ndigits)
151{
152 return vli_test_bit(vli, ndigits * 64 - 1);
153}
154
155/* Counts the number of 64-bit "digits" in vli. */
156static unsigned int vli_num_digits(const u64 *vli, unsigned int ndigits)
157{
158 int i;
159
160 /* Search from the end until we find a non-zero digit.
161 * We do it in reverse because we expect that most digits will
162 * be nonzero.
163 */
164 for (i = ndigits - 1; i >= 0 && vli[i] == 0; i--);
165
166 return (i + 1);
167}
168
169/* Counts the number of bits required for vli. */
170unsigned int vli_num_bits(const u64 *vli, unsigned int ndigits)
171{
172 unsigned int i, num_digits;
173 u64 digit;
174
175 num_digits = vli_num_digits(vli, ndigits);
176 if (num_digits == 0)
177 return 0;
178
179 digit = vli[num_digits - 1];
180 for (i = 0; digit; i++)
181 digit >>= 1;
182
183 return ((num_digits - 1) * 64 + i);
184}
185EXPORT_SYMBOL(vli_num_bits);
186
187/* Set dest from unaligned bit string src. */
188void vli_from_be64(u64 *dest, const void *src, unsigned int ndigits)
189{
190 int i;
191 const u64 *from = src;
192
193 for (i = 0; i < ndigits; i++)
194 dest[i] = get_unaligned_be64(&from[ndigits - 1 - i]);
195}
196EXPORT_SYMBOL(vli_from_be64);
197
198void vli_from_le64(u64 *dest, const void *src, unsigned int ndigits)
199{
200 int i;
201 const u64 *from = src;
202
203 for (i = 0; i < ndigits; i++)
204 dest[i] = get_unaligned_le64(&from[i]);
205}
206EXPORT_SYMBOL(vli_from_le64);
207
208/* Sets dest = src. */
209static void vli_set(u64 *dest, const u64 *src, unsigned int ndigits)
210{
211 int i;
212
213 for (i = 0; i < ndigits; i++)
214 dest[i] = src[i];
215}
216
217/* Returns sign of left - right. */
218int vli_cmp(const u64 *left, const u64 *right, unsigned int ndigits)
219{
220 int i;
221
222 for (i = ndigits - 1; i >= 0; i--) {
223 if (left[i] > right[i])
224 return 1;
225 else if (left[i] < right[i])
226 return -1;
227 }
228
229 return 0;
230}
231EXPORT_SYMBOL(vli_cmp);
232
233/* Computes result = in << c, returning carry. Can modify in place
234 * (if result == in). 0 < shift < 64.
235 */
236static u64 vli_lshift(u64 *result, const u64 *in, unsigned int shift,
237 unsigned int ndigits)
238{
239 u64 carry = 0;
240 int i;
241
242 for (i = 0; i < ndigits; i++) {
243 u64 temp = in[i];
244
245 result[i] = (temp << shift) | carry;
246 carry = temp >> (64 - shift);
247 }
248
249 return carry;
250}
251
252/* Computes vli = vli >> 1. */
253static void vli_rshift1(u64 *vli, unsigned int ndigits)
254{
255 u64 *end = vli;
256 u64 carry = 0;
257
258 vli += ndigits;
259
260 while (vli-- > end) {
261 u64 temp = *vli;
262 *vli = (temp >> 1) | carry;
263 carry = temp << 63;
264 }
265}
266
267/* Computes result = left + right, returning carry. Can modify in place. */
268static u64 vli_add(u64 *result, const u64 *left, const u64 *right,
269 unsigned int ndigits)
270{
271 u64 carry = 0;
272 int i;
273
274 for (i = 0; i < ndigits; i++) {
275 u64 sum;
276
277 sum = left[i] + right[i] + carry;
278 if (sum != left[i])
279 carry = (sum < left[i]);
280
281 result[i] = sum;
282 }
283
284 return carry;
285}
286
287/* Computes result = left + right, returning carry. Can modify in place. */
288static u64 vli_uadd(u64 *result, const u64 *left, u64 right,
289 unsigned int ndigits)
290{
291 u64 carry = right;
292 int i;
293
294 for (i = 0; i < ndigits; i++) {
295 u64 sum;
296
297 sum = left[i] + carry;
298 if (sum != left[i])
299 carry = (sum < left[i]);
300 else
301 carry = !!carry;
302
303 result[i] = sum;
304 }
305
306 return carry;
307}
308
309/* Computes result = left - right, returning borrow. Can modify in place. */
310u64 vli_sub(u64 *result, const u64 *left, const u64 *right,
311 unsigned int ndigits)
312{
313 u64 borrow = 0;
314 int i;
315
316 for (i = 0; i < ndigits; i++) {
317 u64 diff;
318
319 diff = left[i] - right[i] - borrow;
320 if (diff != left[i])
321 borrow = (diff > left[i]);
322
323 result[i] = diff;
324 }
325
326 return borrow;
327}
328EXPORT_SYMBOL(vli_sub);
329
330/* Computes result = left - right, returning borrow. Can modify in place. */
331static u64 vli_usub(u64 *result, const u64 *left, u64 right,
332 unsigned int ndigits)
333{
334 u64 borrow = right;
335 int i;
336
337 for (i = 0; i < ndigits; i++) {
338 u64 diff;
339
340 diff = left[i] - borrow;
341 if (diff != left[i])
342 borrow = (diff > left[i]);
343
344 result[i] = diff;
345 }
346
347 return borrow;
348}
349
350static uint128_t mul_64_64(u64 left, u64 right)
351{
352 uint128_t result;
353#if defined(CONFIG_ARCH_SUPPORTS_INT128)
354 unsigned __int128 m = (unsigned __int128)left * right;
355
356 result.m_low = m;
357 result.m_high = m >> 64;
358#else
359 u64 a0 = left & 0xffffffffull;
360 u64 a1 = left >> 32;
361 u64 b0 = right & 0xffffffffull;
362 u64 b1 = right >> 32;
363 u64 m0 = a0 * b0;
364 u64 m1 = a0 * b1;
365 u64 m2 = a1 * b0;
366 u64 m3 = a1 * b1;
367
368 m2 += (m0 >> 32);
369 m2 += m1;
370
371 /* Overflow */
372 if (m2 < m1)
373 m3 += 0x100000000ull;
374
375 result.m_low = (m0 & 0xffffffffull) | (m2 << 32);
376 result.m_high = m3 + (m2 >> 32);
377#endif
378 return result;
379}
380
381static uint128_t add_128_128(uint128_t a, uint128_t b)
382{
383 uint128_t result;
384
385 result.m_low = a.m_low + b.m_low;
386 result.m_high = a.m_high + b.m_high + (result.m_low < a.m_low);
387
388 return result;
389}
390
391static void vli_mult(u64 *result, const u64 *left, const u64 *right,
392 unsigned int ndigits)
393{
394 uint128_t r01 = { 0, 0 };
395 u64 r2 = 0;
396 unsigned int i, k;
397
398 /* Compute each digit of result in sequence, maintaining the
399 * carries.
400 */
401 for (k = 0; k < ndigits * 2 - 1; k++) {
402 unsigned int min;
403
404 if (k < ndigits)
405 min = 0;
406 else
407 min = (k + 1) - ndigits;
408
409 for (i = min; i <= k && i < ndigits; i++) {
410 uint128_t product;
411
412 product = mul_64_64(left[i], right[k - i]);
413
414 r01 = add_128_128(r01, product);
415 r2 += (r01.m_high < product.m_high);
416 }
417
418 result[k] = r01.m_low;
419 r01.m_low = r01.m_high;
420 r01.m_high = r2;
421 r2 = 0;
422 }
423
424 result[ndigits * 2 - 1] = r01.m_low;
425}
426
427/* Compute product = left * right, for a small right value. */
428static void vli_umult(u64 *result, const u64 *left, u32 right,
429 unsigned int ndigits)
430{
431 uint128_t r01 = { 0 };
432 unsigned int k;
433
434 for (k = 0; k < ndigits; k++) {
435 uint128_t product;
436
437 product = mul_64_64(left[k], right);
438 r01 = add_128_128(r01, product);
439 /* no carry */
440 result[k] = r01.m_low;
441 r01.m_low = r01.m_high;
442 r01.m_high = 0;
443 }
444 result[k] = r01.m_low;
445 for (++k; k < ndigits * 2; k++)
446 result[k] = 0;
447}
448
449static void vli_square(u64 *result, const u64 *left, unsigned int ndigits)
450{
451 uint128_t r01 = { 0, 0 };
452 u64 r2 = 0;
453 int i, k;
454
455 for (k = 0; k < ndigits * 2 - 1; k++) {
456 unsigned int min;
457
458 if (k < ndigits)
459 min = 0;
460 else
461 min = (k + 1) - ndigits;
462
463 for (i = min; i <= k && i <= k - i; i++) {
464 uint128_t product;
465
466 product = mul_64_64(left[i], left[k - i]);
467
468 if (i < k - i) {
469 r2 += product.m_high >> 63;
470 product.m_high = (product.m_high << 1) |
471 (product.m_low >> 63);
472 product.m_low <<= 1;
473 }
474
475 r01 = add_128_128(r01, product);
476 r2 += (r01.m_high < product.m_high);
477 }
478
479 result[k] = r01.m_low;
480 r01.m_low = r01.m_high;
481 r01.m_high = r2;
482 r2 = 0;
483 }
484
485 result[ndigits * 2 - 1] = r01.m_low;
486}
487
488/* Computes result = (left + right) % mod.
489 * Assumes that left < mod and right < mod, result != mod.
490 */
491static void vli_mod_add(u64 *result, const u64 *left, const u64 *right,
492 const u64 *mod, unsigned int ndigits)
493{
494 u64 carry;
495
496 carry = vli_add(result, left, right, ndigits);
497
498 /* result > mod (result = mod + remainder), so subtract mod to
499 * get remainder.
500 */
501 if (carry || vli_cmp(result, mod, ndigits) >= 0)
502 vli_sub(result, result, mod, ndigits);
503}
504
505/* Computes result = (left - right) % mod.
506 * Assumes that left < mod and right < mod, result != mod.
507 */
508static void vli_mod_sub(u64 *result, const u64 *left, const u64 *right,
509 const u64 *mod, unsigned int ndigits)
510{
511 u64 borrow = vli_sub(result, left, right, ndigits);
512
513 /* In this case, p_result == -diff == (max int) - diff.
514 * Since -x % d == d - x, we can get the correct result from
515 * result + mod (with overflow).
516 */
517 if (borrow)
518 vli_add(result, result, mod, ndigits);
519}
520
521/*
522 * Computes result = product % mod
523 * for special form moduli: p = 2^k-c, for small c (note the minus sign)
524 *
525 * References:
526 * R. Crandall, C. Pomerance. Prime Numbers: A Computational Perspective.
527 * 9 Fast Algorithms for Large-Integer Arithmetic. 9.2.3 Moduli of special form
528 * Algorithm 9.2.13 (Fast mod operation for special-form moduli).
529 */
530static void vli_mmod_special(u64 *result, const u64 *product,
531 const u64 *mod, unsigned int ndigits)
532{
533 u64 c = -mod[0];
534 u64 t[ECC_MAX_DIGITS * 2];
535 u64 r[ECC_MAX_DIGITS * 2];
536
537 vli_set(r, product, ndigits * 2);
538 while (!vli_is_zero(r + ndigits, ndigits)) {
539 vli_umult(t, r + ndigits, c, ndigits);
540 vli_clear(r + ndigits, ndigits);
541 vli_add(r, r, t, ndigits * 2);
542 }
543 vli_set(t, mod, ndigits);
544 vli_clear(t + ndigits, ndigits);
545 while (vli_cmp(r, t, ndigits * 2) >= 0)
546 vli_sub(r, r, t, ndigits * 2);
547 vli_set(result, r, ndigits);
548}
549
550/*
551 * Computes result = product % mod
552 * for special form moduli: p = 2^{k-1}+c, for small c (note the plus sign)
553 * where k-1 does not fit into qword boundary by -1 bit (such as 255).
554
555 * References (loosely based on):
556 * A. Menezes, P. van Oorschot, S. Vanstone. Handbook of Applied Cryptography.
557 * 14.3.4 Reduction methods for moduli of special form. Algorithm 14.47.
558 * URL: http://cacr.uwaterloo.ca/hac/about/chap14.pdf
559 *
560 * H. Cohen, G. Frey, R. Avanzi, C. Doche, T. Lange, K. Nguyen, F. Vercauteren.
561 * Handbook of Elliptic and Hyperelliptic Curve Cryptography.
562 * Algorithm 10.25 Fast reduction for special form moduli
563 */
564static void vli_mmod_special2(u64 *result, const u64 *product,
565 const u64 *mod, unsigned int ndigits)
566{
567 u64 c2 = mod[0] * 2;
568 u64 q[ECC_MAX_DIGITS];
569 u64 r[ECC_MAX_DIGITS * 2];
570 u64 m[ECC_MAX_DIGITS * 2]; /* expanded mod */
571 int carry; /* last bit that doesn't fit into q */
572 int i;
573
574 vli_set(m, mod, ndigits);
575 vli_clear(m + ndigits, ndigits);
576
577 vli_set(r, product, ndigits);
578 /* q and carry are top bits */
579 vli_set(q, product + ndigits, ndigits);
580 vli_clear(r + ndigits, ndigits);
581 carry = vli_is_negative(r, ndigits);
582 if (carry)
583 r[ndigits - 1] &= (1ull << 63) - 1;
584 for (i = 1; carry || !vli_is_zero(q, ndigits); i++) {
585 u64 qc[ECC_MAX_DIGITS * 2];
586
587 vli_umult(qc, q, c2, ndigits);
588 if (carry)
589 vli_uadd(qc, qc, mod[0], ndigits * 2);
590 vli_set(q, qc + ndigits, ndigits);
591 vli_clear(qc + ndigits, ndigits);
592 carry = vli_is_negative(qc, ndigits);
593 if (carry)
594 qc[ndigits - 1] &= (1ull << 63) - 1;
595 if (i & 1)
596 vli_sub(r, r, qc, ndigits * 2);
597 else
598 vli_add(r, r, qc, ndigits * 2);
599 }
600 while (vli_is_negative(r, ndigits * 2))
601 vli_add(r, r, m, ndigits * 2);
602 while (vli_cmp(r, m, ndigits * 2) >= 0)
603 vli_sub(r, r, m, ndigits * 2);
604
605 vli_set(result, r, ndigits);
606}
607
608/*
609 * Computes result = product % mod, where product is 2N words long.
610 * Reference: Ken MacKay's micro-ecc.
611 * Currently only designed to work for curve_p or curve_n.
612 */
613static void vli_mmod_slow(u64 *result, u64 *product, const u64 *mod,
614 unsigned int ndigits)
615{
616 u64 mod_m[2 * ECC_MAX_DIGITS];
617 u64 tmp[2 * ECC_MAX_DIGITS];
618 u64 *v[2] = { tmp, product };
619 u64 carry = 0;
620 unsigned int i;
621 /* Shift mod so its highest set bit is at the maximum position. */
622 int shift = (ndigits * 2 * 64) - vli_num_bits(mod, ndigits);
623 int word_shift = shift / 64;
624 int bit_shift = shift % 64;
625
626 vli_clear(mod_m, word_shift);
627 if (bit_shift > 0) {
628 for (i = 0; i < ndigits; ++i) {
629 mod_m[word_shift + i] = (mod[i] << bit_shift) | carry;
630 carry = mod[i] >> (64 - bit_shift);
631 }
632 } else
633 vli_set(mod_m + word_shift, mod, ndigits);
634
635 for (i = 1; shift >= 0; --shift) {
636 u64 borrow = 0;
637 unsigned int j;
638
639 for (j = 0; j < ndigits * 2; ++j) {
640 u64 diff = v[i][j] - mod_m[j] - borrow;
641
642 if (diff != v[i][j])
643 borrow = (diff > v[i][j]);
644 v[1 - i][j] = diff;
645 }
646 i = !(i ^ borrow); /* Swap the index if there was no borrow */
647 vli_rshift1(mod_m, ndigits);
648 mod_m[ndigits - 1] |= mod_m[ndigits] << (64 - 1);
649 vli_rshift1(mod_m + ndigits, ndigits);
650 }
651 vli_set(result, v[i], ndigits);
652}
653
654/* Computes result = product % mod using Barrett's reduction with precomputed
655 * value mu appended to the mod after ndigits, mu = (2^{2w} / mod) and have
656 * length ndigits + 1, where mu * (2^w - 1) should not overflow ndigits
657 * boundary.
658 *
659 * Reference:
660 * R. Brent, P. Zimmermann. Modern Computer Arithmetic. 2010.
661 * 2.4.1 Barrett's algorithm. Algorithm 2.5.
662 */
663static void vli_mmod_barrett(u64 *result, u64 *product, const u64 *mod,
664 unsigned int ndigits)
665{
666 u64 q[ECC_MAX_DIGITS * 2];
667 u64 r[ECC_MAX_DIGITS * 2];
668 const u64 *mu = mod + ndigits;
669
670 vli_mult(q, product + ndigits, mu, ndigits);
671 if (mu[ndigits])
672 vli_add(q + ndigits, q + ndigits, product + ndigits, ndigits);
673 vli_mult(r, mod, q + ndigits, ndigits);
674 vli_sub(r, product, r, ndigits * 2);
675 while (!vli_is_zero(r + ndigits, ndigits) ||
676 vli_cmp(r, mod, ndigits) != -1) {
677 u64 carry;
678
679 carry = vli_sub(r, r, mod, ndigits);
680 vli_usub(r + ndigits, r + ndigits, carry, ndigits);
681 }
682 vli_set(result, r, ndigits);
683}
684
685/* Computes p_result = p_product % curve_p.
686 * See algorithm 5 and 6 from
687 * http://www.isys.uni-klu.ac.at/PDF/2001-0126-MT.pdf
688 */
689static void vli_mmod_fast_192(u64 *result, const u64 *product,
690 const u64 *curve_prime, u64 *tmp)
691{
692 const unsigned int ndigits = 3;
693 int carry;
694
695 vli_set(result, product, ndigits);
696
697 vli_set(tmp, &product[3], ndigits);
698 carry = vli_add(result, result, tmp, ndigits);
699
700 tmp[0] = 0;
701 tmp[1] = product[3];
702 tmp[2] = product[4];
703 carry += vli_add(result, result, tmp, ndigits);
704
705 tmp[0] = tmp[1] = product[5];
706 tmp[2] = 0;
707 carry += vli_add(result, result, tmp, ndigits);
708
709 while (carry || vli_cmp(curve_prime, result, ndigits) != 1)
710 carry -= vli_sub(result, result, curve_prime, ndigits);
711}
712
713/* Computes result = product % curve_prime
714 * from http://www.nsa.gov/ia/_files/nist-routines.pdf
715 */
716static void vli_mmod_fast_256(u64 *result, const u64 *product,
717 const u64 *curve_prime, u64 *tmp)
718{
719 int carry;
720 const unsigned int ndigits = 4;
721
722 /* t */
723 vli_set(result, product, ndigits);
724
725 /* s1 */
726 tmp[0] = 0;
727 tmp[1] = product[5] & 0xffffffff00000000ull;
728 tmp[2] = product[6];
729 tmp[3] = product[7];
730 carry = vli_lshift(tmp, tmp, 1, ndigits);
731 carry += vli_add(result, result, tmp, ndigits);
732
733 /* s2 */
734 tmp[1] = product[6] << 32;
735 tmp[2] = (product[6] >> 32) | (product[7] << 32);
736 tmp[3] = product[7] >> 32;
737 carry += vli_lshift(tmp, tmp, 1, ndigits);
738 carry += vli_add(result, result, tmp, ndigits);
739
740 /* s3 */
741 tmp[0] = product[4];
742 tmp[1] = product[5] & 0xffffffff;
743 tmp[2] = 0;
744 tmp[3] = product[7];
745 carry += vli_add(result, result, tmp, ndigits);
746
747 /* s4 */
748 tmp[0] = (product[4] >> 32) | (product[5] << 32);
749 tmp[1] = (product[5] >> 32) | (product[6] & 0xffffffff00000000ull);
750 tmp[2] = product[7];
751 tmp[3] = (product[6] >> 32) | (product[4] << 32);
752 carry += vli_add(result, result, tmp, ndigits);
753
754 /* d1 */
755 tmp[0] = (product[5] >> 32) | (product[6] << 32);
756 tmp[1] = (product[6] >> 32);
757 tmp[2] = 0;
758 tmp[3] = (product[4] & 0xffffffff) | (product[5] << 32);
759 carry -= vli_sub(result, result, tmp, ndigits);
760
761 /* d2 */
762 tmp[0] = product[6];
763 tmp[1] = product[7];
764 tmp[2] = 0;
765 tmp[3] = (product[4] >> 32) | (product[5] & 0xffffffff00000000ull);
766 carry -= vli_sub(result, result, tmp, ndigits);
767
768 /* d3 */
769 tmp[0] = (product[6] >> 32) | (product[7] << 32);
770 tmp[1] = (product[7] >> 32) | (product[4] << 32);
771 tmp[2] = (product[4] >> 32) | (product[5] << 32);
772 tmp[3] = (product[6] << 32);
773 carry -= vli_sub(result, result, tmp, ndigits);
774
775 /* d4 */
776 tmp[0] = product[7];
777 tmp[1] = product[4] & 0xffffffff00000000ull;
778 tmp[2] = product[5];
779 tmp[3] = product[6] & 0xffffffff00000000ull;
780 carry -= vli_sub(result, result, tmp, ndigits);
781
782 if (carry < 0) {
783 do {
784 carry += vli_add(result, result, curve_prime, ndigits);
785 } while (carry < 0);
786 } else {
787 while (carry || vli_cmp(curve_prime, result, ndigits) != 1)
788 carry -= vli_sub(result, result, curve_prime, ndigits);
789 }
790}
791
792#define SL32OR32(x32, y32) (((u64)x32 << 32) | y32)
793#define AND64H(x64) (x64 & 0xffFFffFF00000000ull)
794#define AND64L(x64) (x64 & 0x00000000ffFFffFFull)
795
796/* Computes result = product % curve_prime
797 * from "Mathematical routines for the NIST prime elliptic curves"
798 */
799static void vli_mmod_fast_384(u64 *result, const u64 *product,
800 const u64 *curve_prime, u64 *tmp)
801{
802 int carry;
803 const unsigned int ndigits = 6;
804
805 /* t */
806 vli_set(result, product, ndigits);
807
808 /* s1 */
809 tmp[0] = 0; // 0 || 0
810 tmp[1] = 0; // 0 || 0
811 tmp[2] = SL32OR32(product[11], (product[10]>>32)); //a22||a21
812 tmp[3] = product[11]>>32; // 0 ||a23
813 tmp[4] = 0; // 0 || 0
814 tmp[5] = 0; // 0 || 0
815 carry = vli_lshift(tmp, tmp, 1, ndigits);
816 carry += vli_add(result, result, tmp, ndigits);
817
818 /* s2 */
819 tmp[0] = product[6]; //a13||a12
820 tmp[1] = product[7]; //a15||a14
821 tmp[2] = product[8]; //a17||a16
822 tmp[3] = product[9]; //a19||a18
823 tmp[4] = product[10]; //a21||a20
824 tmp[5] = product[11]; //a23||a22
825 carry += vli_add(result, result, tmp, ndigits);
826
827 /* s3 */
828 tmp[0] = SL32OR32(product[11], (product[10]>>32)); //a22||a21
829 tmp[1] = SL32OR32(product[6], (product[11]>>32)); //a12||a23
830 tmp[2] = SL32OR32(product[7], (product[6])>>32); //a14||a13
831 tmp[3] = SL32OR32(product[8], (product[7]>>32)); //a16||a15
832 tmp[4] = SL32OR32(product[9], (product[8]>>32)); //a18||a17
833 tmp[5] = SL32OR32(product[10], (product[9]>>32)); //a20||a19
834 carry += vli_add(result, result, tmp, ndigits);
835
836 /* s4 */
837 tmp[0] = AND64H(product[11]); //a23|| 0
838 tmp[1] = (product[10]<<32); //a20|| 0
839 tmp[2] = product[6]; //a13||a12
840 tmp[3] = product[7]; //a15||a14
841 tmp[4] = product[8]; //a17||a16
842 tmp[5] = product[9]; //a19||a18
843 carry += vli_add(result, result, tmp, ndigits);
844
845 /* s5 */
846 tmp[0] = 0; // 0|| 0
847 tmp[1] = 0; // 0|| 0
848 tmp[2] = product[10]; //a21||a20
849 tmp[3] = product[11]; //a23||a22
850 tmp[4] = 0; // 0|| 0
851 tmp[5] = 0; // 0|| 0
852 carry += vli_add(result, result, tmp, ndigits);
853
854 /* s6 */
855 tmp[0] = AND64L(product[10]); // 0 ||a20
856 tmp[1] = AND64H(product[10]); //a21|| 0
857 tmp[2] = product[11]; //a23||a22
858 tmp[3] = 0; // 0 || 0
859 tmp[4] = 0; // 0 || 0
860 tmp[5] = 0; // 0 || 0
861 carry += vli_add(result, result, tmp, ndigits);
862
863 /* d1 */
864 tmp[0] = SL32OR32(product[6], (product[11]>>32)); //a12||a23
865 tmp[1] = SL32OR32(product[7], (product[6]>>32)); //a14||a13
866 tmp[2] = SL32OR32(product[8], (product[7]>>32)); //a16||a15
867 tmp[3] = SL32OR32(product[9], (product[8]>>32)); //a18||a17
868 tmp[4] = SL32OR32(product[10], (product[9]>>32)); //a20||a19
869 tmp[5] = SL32OR32(product[11], (product[10]>>32)); //a22||a21
870 carry -= vli_sub(result, result, tmp, ndigits);
871
872 /* d2 */
873 tmp[0] = (product[10]<<32); //a20|| 0
874 tmp[1] = SL32OR32(product[11], (product[10]>>32)); //a22||a21
875 tmp[2] = (product[11]>>32); // 0 ||a23
876 tmp[3] = 0; // 0 || 0
877 tmp[4] = 0; // 0 || 0
878 tmp[5] = 0; // 0 || 0
879 carry -= vli_sub(result, result, tmp, ndigits);
880
881 /* d3 */
882 tmp[0] = 0; // 0 || 0
883 tmp[1] = AND64H(product[11]); //a23|| 0
884 tmp[2] = product[11]>>32; // 0 ||a23
885 tmp[3] = 0; // 0 || 0
886 tmp[4] = 0; // 0 || 0
887 tmp[5] = 0; // 0 || 0
888 carry -= vli_sub(result, result, tmp, ndigits);
889
890 if (carry < 0) {
891 do {
892 carry += vli_add(result, result, curve_prime, ndigits);
893 } while (carry < 0);
894 } else {
895 while (carry || vli_cmp(curve_prime, result, ndigits) != 1)
896 carry -= vli_sub(result, result, curve_prime, ndigits);
897 }
898
899}
900
901#undef SL32OR32
902#undef AND64H
903#undef AND64L
904
905/* Computes result = product % curve_prime for different curve_primes.
906 *
907 * Note that curve_primes are distinguished just by heuristic check and
908 * not by complete conformance check.
909 */
910static bool vli_mmod_fast(u64 *result, u64 *product,
911 const struct ecc_curve *curve)
912{
913 u64 tmp[2 * ECC_MAX_DIGITS];
914 const u64 *curve_prime = curve->p;
915 const unsigned int ndigits = curve->g.ndigits;
916
917 /* All NIST curves have name prefix 'nist_' */
918 if (strncmp(curve->name, "nist_", 5) != 0) {
919 /* Try to handle Pseudo-Marsenne primes. */
920 if (curve_prime[ndigits - 1] == -1ull) {
921 vli_mmod_special(result, product, curve_prime,
922 ndigits);
923 return true;
924 } else if (curve_prime[ndigits - 1] == 1ull << 63 &&
925 curve_prime[ndigits - 2] == 0) {
926 vli_mmod_special2(result, product, curve_prime,
927 ndigits);
928 return true;
929 }
930 vli_mmod_barrett(result, product, curve_prime, ndigits);
931 return true;
932 }
933
934 switch (ndigits) {
935 case 3:
936 vli_mmod_fast_192(result, product, curve_prime, tmp);
937 break;
938 case 4:
939 vli_mmod_fast_256(result, product, curve_prime, tmp);
940 break;
941 case 6:
942 vli_mmod_fast_384(result, product, curve_prime, tmp);
943 break;
944 default:
945 pr_err_ratelimited("ecc: unsupported digits size!\n");
946 return false;
947 }
948
949 return true;
950}
951
952/* Computes result = (left * right) % mod.
953 * Assumes that mod is big enough curve order.
954 */
955void vli_mod_mult_slow(u64 *result, const u64 *left, const u64 *right,
956 const u64 *mod, unsigned int ndigits)
957{
958 u64 product[ECC_MAX_DIGITS * 2];
959
960 vli_mult(product, left, right, ndigits);
961 vli_mmod_slow(result, product, mod, ndigits);
962}
963EXPORT_SYMBOL(vli_mod_mult_slow);
964
965/* Computes result = (left * right) % curve_prime. */
966static void vli_mod_mult_fast(u64 *result, const u64 *left, const u64 *right,
967 const struct ecc_curve *curve)
968{
969 u64 product[2 * ECC_MAX_DIGITS];
970
971 vli_mult(product, left, right, curve->g.ndigits);
972 vli_mmod_fast(result, product, curve);
973}
974
975/* Computes result = left^2 % curve_prime. */
976static void vli_mod_square_fast(u64 *result, const u64 *left,
977 const struct ecc_curve *curve)
978{
979 u64 product[2 * ECC_MAX_DIGITS];
980
981 vli_square(product, left, curve->g.ndigits);
982 vli_mmod_fast(result, product, curve);
983}
984
985#define EVEN(vli) (!(vli[0] & 1))
986/* Computes result = (1 / p_input) % mod. All VLIs are the same size.
987 * See "From Euclid's GCD to Montgomery Multiplication to the Great Divide"
988 * https://labs.oracle.com/techrep/2001/smli_tr-2001-95.pdf
989 */
990void vli_mod_inv(u64 *result, const u64 *input, const u64 *mod,
991 unsigned int ndigits)
992{
993 u64 a[ECC_MAX_DIGITS], b[ECC_MAX_DIGITS];
994 u64 u[ECC_MAX_DIGITS], v[ECC_MAX_DIGITS];
995 u64 carry;
996 int cmp_result;
997
998 if (vli_is_zero(input, ndigits)) {
999 vli_clear(result, ndigits);
1000 return;
1001 }
1002
1003 vli_set(a, input, ndigits);
1004 vli_set(b, mod, ndigits);
1005 vli_clear(u, ndigits);
1006 u[0] = 1;
1007 vli_clear(v, ndigits);
1008
1009 while ((cmp_result = vli_cmp(a, b, ndigits)) != 0) {
1010 carry = 0;
1011
1012 if (EVEN(a)) {
1013 vli_rshift1(a, ndigits);
1014
1015 if (!EVEN(u))
1016 carry = vli_add(u, u, mod, ndigits);
1017
1018 vli_rshift1(u, ndigits);
1019 if (carry)
1020 u[ndigits - 1] |= 0x8000000000000000ull;
1021 } else if (EVEN(b)) {
1022 vli_rshift1(b, ndigits);
1023
1024 if (!EVEN(v))
1025 carry = vli_add(v, v, mod, ndigits);
1026
1027 vli_rshift1(v, ndigits);
1028 if (carry)
1029 v[ndigits - 1] |= 0x8000000000000000ull;
1030 } else if (cmp_result > 0) {
1031 vli_sub(a, a, b, ndigits);
1032 vli_rshift1(a, ndigits);
1033
1034 if (vli_cmp(u, v, ndigits) < 0)
1035 vli_add(u, u, mod, ndigits);
1036
1037 vli_sub(u, u, v, ndigits);
1038 if (!EVEN(u))
1039 carry = vli_add(u, u, mod, ndigits);
1040
1041 vli_rshift1(u, ndigits);
1042 if (carry)
1043 u[ndigits - 1] |= 0x8000000000000000ull;
1044 } else {
1045 vli_sub(b, b, a, ndigits);
1046 vli_rshift1(b, ndigits);
1047
1048 if (vli_cmp(v, u, ndigits) < 0)
1049 vli_add(v, v, mod, ndigits);
1050
1051 vli_sub(v, v, u, ndigits);
1052 if (!EVEN(v))
1053 carry = vli_add(v, v, mod, ndigits);
1054
1055 vli_rshift1(v, ndigits);
1056 if (carry)
1057 v[ndigits - 1] |= 0x8000000000000000ull;
1058 }
1059 }
1060
1061 vli_set(result, u, ndigits);
1062}
1063EXPORT_SYMBOL(vli_mod_inv);
1064
1065/* ------ Point operations ------ */
1066
1067/* Returns true if p_point is the point at infinity, false otherwise. */
1068bool ecc_point_is_zero(const struct ecc_point *point)
1069{
1070 return (vli_is_zero(point->x, point->ndigits) &&
1071 vli_is_zero(point->y, point->ndigits));
1072}
1073EXPORT_SYMBOL(ecc_point_is_zero);
1074
1075/* Point multiplication algorithm using Montgomery's ladder with co-Z
1076 * coordinates. From https://eprint.iacr.org/2011/338.pdf
1077 */
1078
1079/* Double in place */
1080static void ecc_point_double_jacobian(u64 *x1, u64 *y1, u64 *z1,
1081 const struct ecc_curve *curve)
1082{
1083 /* t1 = x, t2 = y, t3 = z */
1084 u64 t4[ECC_MAX_DIGITS];
1085 u64 t5[ECC_MAX_DIGITS];
1086 const u64 *curve_prime = curve->p;
1087 const unsigned int ndigits = curve->g.ndigits;
1088
1089 if (vli_is_zero(z1, ndigits))
1090 return;
1091
1092 /* t4 = y1^2 */
1093 vli_mod_square_fast(t4, y1, curve);
1094 /* t5 = x1*y1^2 = A */
1095 vli_mod_mult_fast(t5, x1, t4, curve);
1096 /* t4 = y1^4 */
1097 vli_mod_square_fast(t4, t4, curve);
1098 /* t2 = y1*z1 = z3 */
1099 vli_mod_mult_fast(y1, y1, z1, curve);
1100 /* t3 = z1^2 */
1101 vli_mod_square_fast(z1, z1, curve);
1102
1103 /* t1 = x1 + z1^2 */
1104 vli_mod_add(x1, x1, z1, curve_prime, ndigits);
1105 /* t3 = 2*z1^2 */
1106 vli_mod_add(z1, z1, z1, curve_prime, ndigits);
1107 /* t3 = x1 - z1^2 */
1108 vli_mod_sub(z1, x1, z1, curve_prime, ndigits);
1109 /* t1 = x1^2 - z1^4 */
1110 vli_mod_mult_fast(x1, x1, z1, curve);
1111
1112 /* t3 = 2*(x1^2 - z1^4) */
1113 vli_mod_add(z1, x1, x1, curve_prime, ndigits);
1114 /* t1 = 3*(x1^2 - z1^4) */
1115 vli_mod_add(x1, x1, z1, curve_prime, ndigits);
1116 if (vli_test_bit(x1, 0)) {
1117 u64 carry = vli_add(x1, x1, curve_prime, ndigits);
1118
1119 vli_rshift1(x1, ndigits);
1120 x1[ndigits - 1] |= carry << 63;
1121 } else {
1122 vli_rshift1(x1, ndigits);
1123 }
1124 /* t1 = 3/2*(x1^2 - z1^4) = B */
1125
1126 /* t3 = B^2 */
1127 vli_mod_square_fast(z1, x1, curve);
1128 /* t3 = B^2 - A */
1129 vli_mod_sub(z1, z1, t5, curve_prime, ndigits);
1130 /* t3 = B^2 - 2A = x3 */
1131 vli_mod_sub(z1, z1, t5, curve_prime, ndigits);
1132 /* t5 = A - x3 */
1133 vli_mod_sub(t5, t5, z1, curve_prime, ndigits);
1134 /* t1 = B * (A - x3) */
1135 vli_mod_mult_fast(x1, x1, t5, curve);
1136 /* t4 = B * (A - x3) - y1^4 = y3 */
1137 vli_mod_sub(t4, x1, t4, curve_prime, ndigits);
1138
1139 vli_set(x1, z1, ndigits);
1140 vli_set(z1, y1, ndigits);
1141 vli_set(y1, t4, ndigits);
1142}
1143
1144/* Modify (x1, y1) => (x1 * z^2, y1 * z^3) */
1145static void apply_z(u64 *x1, u64 *y1, u64 *z, const struct ecc_curve *curve)
1146{
1147 u64 t1[ECC_MAX_DIGITS];
1148
1149 vli_mod_square_fast(t1, z, curve); /* z^2 */
1150 vli_mod_mult_fast(x1, x1, t1, curve); /* x1 * z^2 */
1151 vli_mod_mult_fast(t1, t1, z, curve); /* z^3 */
1152 vli_mod_mult_fast(y1, y1, t1, curve); /* y1 * z^3 */
1153}
1154
1155/* P = (x1, y1) => 2P, (x2, y2) => P' */
1156static void xycz_initial_double(u64 *x1, u64 *y1, u64 *x2, u64 *y2,
1157 u64 *p_initial_z, const struct ecc_curve *curve)
1158{
1159 u64 z[ECC_MAX_DIGITS];
1160 const unsigned int ndigits = curve->g.ndigits;
1161
1162 vli_set(x2, x1, ndigits);
1163 vli_set(y2, y1, ndigits);
1164
1165 vli_clear(z, ndigits);
1166 z[0] = 1;
1167
1168 if (p_initial_z)
1169 vli_set(z, p_initial_z, ndigits);
1170
1171 apply_z(x1, y1, z, curve);
1172
1173 ecc_point_double_jacobian(x1, y1, z, curve);
1174
1175 apply_z(x2, y2, z, curve);
1176}
1177
1178/* Input P = (x1, y1, Z), Q = (x2, y2, Z)
1179 * Output P' = (x1', y1', Z3), P + Q = (x3, y3, Z3)
1180 * or P => P', Q => P + Q
1181 */
1182static void xycz_add(u64 *x1, u64 *y1, u64 *x2, u64 *y2,
1183 const struct ecc_curve *curve)
1184{
1185 /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
1186 u64 t5[ECC_MAX_DIGITS];
1187 const u64 *curve_prime = curve->p;
1188 const unsigned int ndigits = curve->g.ndigits;
1189
1190 /* t5 = x2 - x1 */
1191 vli_mod_sub(t5, x2, x1, curve_prime, ndigits);
1192 /* t5 = (x2 - x1)^2 = A */
1193 vli_mod_square_fast(t5, t5, curve);
1194 /* t1 = x1*A = B */
1195 vli_mod_mult_fast(x1, x1, t5, curve);
1196 /* t3 = x2*A = C */
1197 vli_mod_mult_fast(x2, x2, t5, curve);
1198 /* t4 = y2 - y1 */
1199 vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
1200 /* t5 = (y2 - y1)^2 = D */
1201 vli_mod_square_fast(t5, y2, curve);
1202
1203 /* t5 = D - B */
1204 vli_mod_sub(t5, t5, x1, curve_prime, ndigits);
1205 /* t5 = D - B - C = x3 */
1206 vli_mod_sub(t5, t5, x2, curve_prime, ndigits);
1207 /* t3 = C - B */
1208 vli_mod_sub(x2, x2, x1, curve_prime, ndigits);
1209 /* t2 = y1*(C - B) */
1210 vli_mod_mult_fast(y1, y1, x2, curve);
1211 /* t3 = B - x3 */
1212 vli_mod_sub(x2, x1, t5, curve_prime, ndigits);
1213 /* t4 = (y2 - y1)*(B - x3) */
1214 vli_mod_mult_fast(y2, y2, x2, curve);
1215 /* t4 = y3 */
1216 vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
1217
1218 vli_set(x2, t5, ndigits);
1219}
1220
1221/* Input P = (x1, y1, Z), Q = (x2, y2, Z)
1222 * Output P + Q = (x3, y3, Z3), P - Q = (x3', y3', Z3)
1223 * or P => P - Q, Q => P + Q
1224 */
1225static void xycz_add_c(u64 *x1, u64 *y1, u64 *x2, u64 *y2,
1226 const struct ecc_curve *curve)
1227{
1228 /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
1229 u64 t5[ECC_MAX_DIGITS];
1230 u64 t6[ECC_MAX_DIGITS];
1231 u64 t7[ECC_MAX_DIGITS];
1232 const u64 *curve_prime = curve->p;
1233 const unsigned int ndigits = curve->g.ndigits;
1234
1235 /* t5 = x2 - x1 */
1236 vli_mod_sub(t5, x2, x1, curve_prime, ndigits);
1237 /* t5 = (x2 - x1)^2 = A */
1238 vli_mod_square_fast(t5, t5, curve);
1239 /* t1 = x1*A = B */
1240 vli_mod_mult_fast(x1, x1, t5, curve);
1241 /* t3 = x2*A = C */
1242 vli_mod_mult_fast(x2, x2, t5, curve);
1243 /* t4 = y2 + y1 */
1244 vli_mod_add(t5, y2, y1, curve_prime, ndigits);
1245 /* t4 = y2 - y1 */
1246 vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
1247
1248 /* t6 = C - B */
1249 vli_mod_sub(t6, x2, x1, curve_prime, ndigits);
1250 /* t2 = y1 * (C - B) */
1251 vli_mod_mult_fast(y1, y1, t6, curve);
1252 /* t6 = B + C */
1253 vli_mod_add(t6, x1, x2, curve_prime, ndigits);
1254 /* t3 = (y2 - y1)^2 */
1255 vli_mod_square_fast(x2, y2, curve);
1256 /* t3 = x3 */
1257 vli_mod_sub(x2, x2, t6, curve_prime, ndigits);
1258
1259 /* t7 = B - x3 */
1260 vli_mod_sub(t7, x1, x2, curve_prime, ndigits);
1261 /* t4 = (y2 - y1)*(B - x3) */
1262 vli_mod_mult_fast(y2, y2, t7, curve);
1263 /* t4 = y3 */
1264 vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
1265
1266 /* t7 = (y2 + y1)^2 = F */
1267 vli_mod_square_fast(t7, t5, curve);
1268 /* t7 = x3' */
1269 vli_mod_sub(t7, t7, t6, curve_prime, ndigits);
1270 /* t6 = x3' - B */
1271 vli_mod_sub(t6, t7, x1, curve_prime, ndigits);
1272 /* t6 = (y2 + y1)*(x3' - B) */
1273 vli_mod_mult_fast(t6, t6, t5, curve);
1274 /* t2 = y3' */
1275 vli_mod_sub(y1, t6, y1, curve_prime, ndigits);
1276
1277 vli_set(x1, t7, ndigits);
1278}
1279
1280static void ecc_point_mult(struct ecc_point *result,
1281 const struct ecc_point *point, const u64 *scalar,
1282 u64 *initial_z, const struct ecc_curve *curve,
1283 unsigned int ndigits)
1284{
1285 /* R0 and R1 */
1286 u64 rx[2][ECC_MAX_DIGITS];
1287 u64 ry[2][ECC_MAX_DIGITS];
1288 u64 z[ECC_MAX_DIGITS];
1289 u64 sk[2][ECC_MAX_DIGITS];
1290 u64 *curve_prime = curve->p;
1291 int i, nb;
1292 int num_bits;
1293 int carry;
1294
1295 carry = vli_add(sk[0], scalar, curve->n, ndigits);
1296 vli_add(sk[1], sk[0], curve->n, ndigits);
1297 scalar = sk[!carry];
1298 num_bits = sizeof(u64) * ndigits * 8 + 1;
1299
1300 vli_set(rx[1], point->x, ndigits);
1301 vli_set(ry[1], point->y, ndigits);
1302
1303 xycz_initial_double(rx[1], ry[1], rx[0], ry[0], initial_z, curve);
1304
1305 for (i = num_bits - 2; i > 0; i--) {
1306 nb = !vli_test_bit(scalar, i);
1307 xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb], curve);
1308 xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve);
1309 }
1310
1311 nb = !vli_test_bit(scalar, 0);
1312 xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb], curve);
1313
1314 /* Find final 1/Z value. */
1315 /* X1 - X0 */
1316 vli_mod_sub(z, rx[1], rx[0], curve_prime, ndigits);
1317 /* Yb * (X1 - X0) */
1318 vli_mod_mult_fast(z, z, ry[1 - nb], curve);
1319 /* xP * Yb * (X1 - X0) */
1320 vli_mod_mult_fast(z, z, point->x, curve);
1321
1322 /* 1 / (xP * Yb * (X1 - X0)) */
1323 vli_mod_inv(z, z, curve_prime, point->ndigits);
1324
1325 /* yP / (xP * Yb * (X1 - X0)) */
1326 vli_mod_mult_fast(z, z, point->y, curve);
1327 /* Xb * yP / (xP * Yb * (X1 - X0)) */
1328 vli_mod_mult_fast(z, z, rx[1 - nb], curve);
1329 /* End 1/Z calculation */
1330
1331 xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve);
1332
1333 apply_z(rx[0], ry[0], z, curve);
1334
1335 vli_set(result->x, rx[0], ndigits);
1336 vli_set(result->y, ry[0], ndigits);
1337}
1338
1339/* Computes R = P + Q mod p */
1340static void ecc_point_add(const struct ecc_point *result,
1341 const struct ecc_point *p, const struct ecc_point *q,
1342 const struct ecc_curve *curve)
1343{
1344 u64 z[ECC_MAX_DIGITS];
1345 u64 px[ECC_MAX_DIGITS];
1346 u64 py[ECC_MAX_DIGITS];
1347 unsigned int ndigits = curve->g.ndigits;
1348
1349 vli_set(result->x, q->x, ndigits);
1350 vli_set(result->y, q->y, ndigits);
1351 vli_mod_sub(z, result->x, p->x, curve->p, ndigits);
1352 vli_set(px, p->x, ndigits);
1353 vli_set(py, p->y, ndigits);
1354 xycz_add(px, py, result->x, result->y, curve);
1355 vli_mod_inv(z, z, curve->p, ndigits);
1356 apply_z(result->x, result->y, z, curve);
1357}
1358
1359/* Computes R = u1P + u2Q mod p using Shamir's trick.
1360 * Based on: Kenneth MacKay's micro-ecc (2014).
1361 */
1362void ecc_point_mult_shamir(const struct ecc_point *result,
1363 const u64 *u1, const struct ecc_point *p,
1364 const u64 *u2, const struct ecc_point *q,
1365 const struct ecc_curve *curve)
1366{
1367 u64 z[ECC_MAX_DIGITS];
1368 u64 sump[2][ECC_MAX_DIGITS];
1369 u64 *rx = result->x;
1370 u64 *ry = result->y;
1371 unsigned int ndigits = curve->g.ndigits;
1372 unsigned int num_bits;
1373 struct ecc_point sum = ECC_POINT_INIT(sump[0], sump[1], ndigits);
1374 const struct ecc_point *points[4];
1375 const struct ecc_point *point;
1376 unsigned int idx;
1377 int i;
1378
1379 ecc_point_add(&sum, p, q, curve);
1380 points[0] = NULL;
1381 points[1] = p;
1382 points[2] = q;
1383 points[3] = ∑
1384
1385 num_bits = max(vli_num_bits(u1, ndigits), vli_num_bits(u2, ndigits));
1386 i = num_bits - 1;
1387 idx = (!!vli_test_bit(u1, i)) | ((!!vli_test_bit(u2, i)) << 1);
1388 point = points[idx];
1389
1390 vli_set(rx, point->x, ndigits);
1391 vli_set(ry, point->y, ndigits);
1392 vli_clear(z + 1, ndigits - 1);
1393 z[0] = 1;
1394
1395 for (--i; i >= 0; i--) {
1396 ecc_point_double_jacobian(rx, ry, z, curve);
1397 idx = (!!vli_test_bit(u1, i)) | ((!!vli_test_bit(u2, i)) << 1);
1398 point = points[idx];
1399 if (point) {
1400 u64 tx[ECC_MAX_DIGITS];
1401 u64 ty[ECC_MAX_DIGITS];
1402 u64 tz[ECC_MAX_DIGITS];
1403
1404 vli_set(tx, point->x, ndigits);
1405 vli_set(ty, point->y, ndigits);
1406 apply_z(tx, ty, z, curve);
1407 vli_mod_sub(tz, rx, tx, curve->p, ndigits);
1408 xycz_add(tx, ty, rx, ry, curve);
1409 vli_mod_mult_fast(z, z, tz, curve);
1410 }
1411 }
1412 vli_mod_inv(z, z, curve->p, ndigits);
1413 apply_z(rx, ry, z, curve);
1414}
1415EXPORT_SYMBOL(ecc_point_mult_shamir);
1416
1417static int __ecc_is_key_valid(const struct ecc_curve *curve,
1418 const u64 *private_key, unsigned int ndigits)
1419{
1420 u64 one[ECC_MAX_DIGITS] = { 1, };
1421 u64 res[ECC_MAX_DIGITS];
1422
1423 if (!private_key)
1424 return -EINVAL;
1425
1426 if (curve->g.ndigits != ndigits)
1427 return -EINVAL;
1428
1429 /* Make sure the private key is in the range [2, n-3]. */
1430 if (vli_cmp(one, private_key, ndigits) != -1)
1431 return -EINVAL;
1432 vli_sub(res, curve->n, one, ndigits);
1433 vli_sub(res, res, one, ndigits);
1434 if (vli_cmp(res, private_key, ndigits) != 1)
1435 return -EINVAL;
1436
1437 return 0;
1438}
1439
1440int ecc_is_key_valid(unsigned int curve_id, unsigned int ndigits,
1441 const u64 *private_key, unsigned int private_key_len)
1442{
1443 int nbytes;
1444 const struct ecc_curve *curve = ecc_get_curve(curve_id);
1445
1446 nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT;
1447
1448 if (private_key_len != nbytes)
1449 return -EINVAL;
1450
1451 return __ecc_is_key_valid(curve, private_key, ndigits);
1452}
1453EXPORT_SYMBOL(ecc_is_key_valid);
1454
1455/*
1456 * ECC private keys are generated using the method of extra random bits,
1457 * equivalent to that described in FIPS 186-4, Appendix B.4.1.
1458 *
1459 * d = (c mod(n–1)) + 1 where c is a string of random bits, 64 bits longer
1460 * than requested
1461 * 0 <= c mod(n-1) <= n-2 and implies that
1462 * 1 <= d <= n-1
1463 *
1464 * This method generates a private key uniformly distributed in the range
1465 * [1, n-1].
1466 */
1467int ecc_gen_privkey(unsigned int curve_id, unsigned int ndigits, u64 *privkey)
1468{
1469 const struct ecc_curve *curve = ecc_get_curve(curve_id);
1470 u64 priv[ECC_MAX_DIGITS];
1471 unsigned int nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT;
1472 unsigned int nbits = vli_num_bits(curve->n, ndigits);
1473 int err;
1474
1475 /* Check that N is included in Table 1 of FIPS 186-4, section 6.1.1 */
1476 if (nbits < 160 || ndigits > ARRAY_SIZE(priv))
1477 return -EINVAL;
1478
1479 /*
1480 * FIPS 186-4 recommends that the private key should be obtained from a
1481 * RBG with a security strength equal to or greater than the security
1482 * strength associated with N.
1483 *
1484 * The maximum security strength identified by NIST SP800-57pt1r4 for
1485 * ECC is 256 (N >= 512).
1486 *
1487 * This condition is met by the default RNG because it selects a favored
1488 * DRBG with a security strength of 256.
1489 */
1490 if (crypto_get_default_rng())
1491 return -EFAULT;
1492
1493 err = crypto_rng_get_bytes(crypto_default_rng, (u8 *)priv, nbytes);
1494 crypto_put_default_rng();
1495 if (err)
1496 return err;
1497
1498 /* Make sure the private key is in the valid range. */
1499 if (__ecc_is_key_valid(curve, priv, ndigits))
1500 return -EINVAL;
1501
1502 ecc_swap_digits(priv, privkey, ndigits);
1503
1504 return 0;
1505}
1506EXPORT_SYMBOL(ecc_gen_privkey);
1507
1508int ecc_make_pub_key(unsigned int curve_id, unsigned int ndigits,
1509 const u64 *private_key, u64 *public_key)
1510{
1511 int ret = 0;
1512 struct ecc_point *pk;
1513 u64 priv[ECC_MAX_DIGITS];
1514 const struct ecc_curve *curve = ecc_get_curve(curve_id);
1515
1516 if (!private_key || !curve || ndigits > ARRAY_SIZE(priv)) {
1517 ret = -EINVAL;
1518 goto out;
1519 }
1520
1521 ecc_swap_digits(private_key, priv, ndigits);
1522
1523 pk = ecc_alloc_point(ndigits);
1524 if (!pk) {
1525 ret = -ENOMEM;
1526 goto out;
1527 }
1528
1529 ecc_point_mult(pk, &curve->g, priv, NULL, curve, ndigits);
1530
1531 /* SP800-56A rev 3 5.6.2.1.3 key check */
1532 if (ecc_is_pubkey_valid_full(curve, pk)) {
1533 ret = -EAGAIN;
1534 goto err_free_point;
1535 }
1536
1537 ecc_swap_digits(pk->x, public_key, ndigits);
1538 ecc_swap_digits(pk->y, &public_key[ndigits], ndigits);
1539
1540err_free_point:
1541 ecc_free_point(pk);
1542out:
1543 return ret;
1544}
1545EXPORT_SYMBOL(ecc_make_pub_key);
1546
1547/* SP800-56A section 5.6.2.3.4 partial verification: ephemeral keys only */
1548int ecc_is_pubkey_valid_partial(const struct ecc_curve *curve,
1549 struct ecc_point *pk)
1550{
1551 u64 yy[ECC_MAX_DIGITS], xxx[ECC_MAX_DIGITS], w[ECC_MAX_DIGITS];
1552
1553 if (WARN_ON(pk->ndigits != curve->g.ndigits))
1554 return -EINVAL;
1555
1556 /* Check 1: Verify key is not the zero point. */
1557 if (ecc_point_is_zero(pk))
1558 return -EINVAL;
1559
1560 /* Check 2: Verify key is in the range [1, p-1]. */
1561 if (vli_cmp(curve->p, pk->x, pk->ndigits) != 1)
1562 return -EINVAL;
1563 if (vli_cmp(curve->p, pk->y, pk->ndigits) != 1)
1564 return -EINVAL;
1565
1566 /* Check 3: Verify that y^2 == (x^3 + a·x + b) mod p */
1567 vli_mod_square_fast(yy, pk->y, curve); /* y^2 */
1568 vli_mod_square_fast(xxx, pk->x, curve); /* x^2 */
1569 vli_mod_mult_fast(xxx, xxx, pk->x, curve); /* x^3 */
1570 vli_mod_mult_fast(w, curve->a, pk->x, curve); /* a·x */
1571 vli_mod_add(w, w, curve->b, curve->p, pk->ndigits); /* a·x + b */
1572 vli_mod_add(w, w, xxx, curve->p, pk->ndigits); /* x^3 + a·x + b */
1573 if (vli_cmp(yy, w, pk->ndigits) != 0) /* Equation */
1574 return -EINVAL;
1575
1576 return 0;
1577}
1578EXPORT_SYMBOL(ecc_is_pubkey_valid_partial);
1579
1580/* SP800-56A section 5.6.2.3.3 full verification */
1581int ecc_is_pubkey_valid_full(const struct ecc_curve *curve,
1582 struct ecc_point *pk)
1583{
1584 struct ecc_point *nQ;
1585
1586 /* Checks 1 through 3 */
1587 int ret = ecc_is_pubkey_valid_partial(curve, pk);
1588
1589 if (ret)
1590 return ret;
1591
1592 /* Check 4: Verify that nQ is the zero point. */
1593 nQ = ecc_alloc_point(pk->ndigits);
1594 if (!nQ)
1595 return -ENOMEM;
1596
1597 ecc_point_mult(nQ, pk, curve->n, NULL, curve, pk->ndigits);
1598 if (!ecc_point_is_zero(nQ))
1599 ret = -EINVAL;
1600
1601 ecc_free_point(nQ);
1602
1603 return ret;
1604}
1605EXPORT_SYMBOL(ecc_is_pubkey_valid_full);
1606
1607int crypto_ecdh_shared_secret(unsigned int curve_id, unsigned int ndigits,
1608 const u64 *private_key, const u64 *public_key,
1609 u64 *secret)
1610{
1611 int ret = 0;
1612 struct ecc_point *product, *pk;
1613 u64 priv[ECC_MAX_DIGITS];
1614 u64 rand_z[ECC_MAX_DIGITS];
1615 unsigned int nbytes;
1616 const struct ecc_curve *curve = ecc_get_curve(curve_id);
1617
1618 if (!private_key || !public_key || !curve ||
1619 ndigits > ARRAY_SIZE(priv) || ndigits > ARRAY_SIZE(rand_z)) {
1620 ret = -EINVAL;
1621 goto out;
1622 }
1623
1624 nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT;
1625
1626 get_random_bytes(rand_z, nbytes);
1627
1628 pk = ecc_alloc_point(ndigits);
1629 if (!pk) {
1630 ret = -ENOMEM;
1631 goto out;
1632 }
1633
1634 ecc_swap_digits(public_key, pk->x, ndigits);
1635 ecc_swap_digits(&public_key[ndigits], pk->y, ndigits);
1636 ret = ecc_is_pubkey_valid_partial(curve, pk);
1637 if (ret)
1638 goto err_alloc_product;
1639
1640 ecc_swap_digits(private_key, priv, ndigits);
1641
1642 product = ecc_alloc_point(ndigits);
1643 if (!product) {
1644 ret = -ENOMEM;
1645 goto err_alloc_product;
1646 }
1647
1648 ecc_point_mult(product, pk, priv, rand_z, curve, ndigits);
1649
1650 if (ecc_point_is_zero(product)) {
1651 ret = -EFAULT;
1652 goto err_validity;
1653 }
1654
1655 ecc_swap_digits(product->x, secret, ndigits);
1656
1657err_validity:
1658 memzero_explicit(priv, sizeof(priv));
1659 memzero_explicit(rand_z, sizeof(rand_z));
1660 ecc_free_point(product);
1661err_alloc_product:
1662 ecc_free_point(pk);
1663out:
1664 return ret;
1665}
1666EXPORT_SYMBOL(crypto_ecdh_shared_secret);
1667
1668MODULE_LICENSE("Dual BSD/GPL");