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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 <linux/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 case ECC_CURVE_NIST_P521:
64 return &nist_p521;
65 default:
66 return NULL;
67 }
68}
69EXPORT_SYMBOL(ecc_get_curve);
70
71void 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}
91EXPORT_SYMBOL(ecc_digits_from_bytes);
92
93static 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
103static void ecc_free_digits_space(u64 *space)
104{
105 kfree_sensitive(space);
106}
107
108struct 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
127err_alloc_y:
128 ecc_free_digits_space(p->x);
129err_alloc_x:
130 kfree(p);
131 return NULL;
132}
133EXPORT_SYMBOL(ecc_alloc_point);
134
135void 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}
144EXPORT_SYMBOL(ecc_free_point);
145
146static 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. */
155bool 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}
166EXPORT_SYMBOL(vli_is_zero);
167
168/* Returns nonzero if bit of vli is set. */
169static u64 vli_test_bit(const u64 *vli, unsigned int bit)
170{
171 return (vli[bit / 64] & ((u64)1 << (bit % 64)));
172}
173
174static 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. */
180static 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. */
194unsigned 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}
209EXPORT_SYMBOL(vli_num_bits);
210
211/* Set dest from unaligned bit string src. */
212void 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}
220EXPORT_SYMBOL(vli_from_be64);
221
222void 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}
230EXPORT_SYMBOL(vli_from_le64);
231
232/* Sets dest = src. */
233static 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. */
242int 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}
255EXPORT_SYMBOL(vli_cmp);
256
257/* Computes result = in << c, returning carry. Can modify in place
258 * (if result == in). 0 < shift < 64.
259 */
260static 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. */
277static 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. */
292static 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. */
312static 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. */
334u64 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}
352EXPORT_SYMBOL(vli_sub);
353
354/* Computes result = left - right, returning borrow. Can modify in place. */
355static 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
374static 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
405static 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
415static 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. */
452static 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
473static 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 */
515static 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 */
532static 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 */
554static 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 */
588static 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 */
637static 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 */
687static 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 */
713static 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 */
740static 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 */
823static 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 */
934static 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 */
956static 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 */
1004void 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}
1012EXPORT_SYMBOL(vli_mod_mult_slow);
1013
1014/* Computes result = (left * right) % curve_prime. */
1015static 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. */
1025static 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 */
1039void 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}
1112EXPORT_SYMBOL(vli_mod_inv);
1113
1114/* ------ Point operations ------ */
1115
1116/* Returns true if p_point is the point at infinity, false otherwise. */
1117bool 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}
1122EXPORT_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 */
1129static 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) */
1194static 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' */
1205static 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 */
1231static 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 */
1274static 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
1329static 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 */
1392static 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 */
1414void 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}
1469EXPORT_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 */
1477static 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
1500int 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}
1513EXPORT_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 */
1522int 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}
1564EXPORT_SYMBOL(ecc_gen_privkey);
1565
1566int 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
1595err_free_point:
1596 ecc_free_point(pk);
1597out:
1598 return ret;
1599}
1600EXPORT_SYMBOL(ecc_make_pub_key);
1601
1602/* SP800-56A section 5.6.2.3.4 partial verification: ephemeral keys only */
1603int 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}
1633EXPORT_SYMBOL(ecc_is_pubkey_valid_partial);
1634
1635/* SP800-56A section 5.6.2.3.3 full verification */
1636int 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}
1660EXPORT_SYMBOL(ecc_is_pubkey_valid_full);
1661
1662int 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
1708err_validity:
1709 memzero_explicit(rand_z, sizeof(rand_z));
1710 ecc_free_point(product);
1711err_alloc_product:
1712 ecc_free_point(pk);
1713out:
1714 return ret;
1715}
1716EXPORT_SYMBOL(crypto_ecdh_shared_secret);
1717
1718MODULE_DESCRIPTION("core elliptic curve module");
1719MODULE_LICENSE("Dual BSD/GPL");
1/*
2 * Copyright (c) 2013, Kenneth MacKay
3 * All rights reserved.
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 <linux/random.h>
28#include <linux/slab.h>
29#include <linux/swab.h>
30#include <linux/fips.h>
31#include <crypto/ecdh.h>
32
33#include "ecc.h"
34#include "ecc_curve_defs.h"
35
36typedef struct {
37 u64 m_low;
38 u64 m_high;
39} uint128_t;
40
41static inline const struct ecc_curve *ecc_get_curve(unsigned int curve_id)
42{
43 switch (curve_id) {
44 /* In FIPS mode only allow P256 and higher */
45 case ECC_CURVE_NIST_P192:
46 return fips_enabled ? NULL : &nist_p192;
47 case ECC_CURVE_NIST_P256:
48 return &nist_p256;
49 default:
50 return NULL;
51 }
52}
53
54static u64 *ecc_alloc_digits_space(unsigned int ndigits)
55{
56 size_t len = ndigits * sizeof(u64);
57
58 if (!len)
59 return NULL;
60
61 return kmalloc(len, GFP_KERNEL);
62}
63
64static void ecc_free_digits_space(u64 *space)
65{
66 kzfree(space);
67}
68
69static struct ecc_point *ecc_alloc_point(unsigned int ndigits)
70{
71 struct ecc_point *p = kmalloc(sizeof(*p), GFP_KERNEL);
72
73 if (!p)
74 return NULL;
75
76 p->x = ecc_alloc_digits_space(ndigits);
77 if (!p->x)
78 goto err_alloc_x;
79
80 p->y = ecc_alloc_digits_space(ndigits);
81 if (!p->y)
82 goto err_alloc_y;
83
84 p->ndigits = ndigits;
85
86 return p;
87
88err_alloc_y:
89 ecc_free_digits_space(p->x);
90err_alloc_x:
91 kfree(p);
92 return NULL;
93}
94
95static void ecc_free_point(struct ecc_point *p)
96{
97 if (!p)
98 return;
99
100 kzfree(p->x);
101 kzfree(p->y);
102 kzfree(p);
103}
104
105static void vli_clear(u64 *vli, unsigned int ndigits)
106{
107 int i;
108
109 for (i = 0; i < ndigits; i++)
110 vli[i] = 0;
111}
112
113/* Returns true if vli == 0, false otherwise. */
114static bool vli_is_zero(const u64 *vli, unsigned int ndigits)
115{
116 int i;
117
118 for (i = 0; i < ndigits; i++) {
119 if (vli[i])
120 return false;
121 }
122
123 return true;
124}
125
126/* Returns nonzero if bit bit of vli is set. */
127static u64 vli_test_bit(const u64 *vli, unsigned int bit)
128{
129 return (vli[bit / 64] & ((u64)1 << (bit % 64)));
130}
131
132/* Counts the number of 64-bit "digits" in vli. */
133static unsigned int vli_num_digits(const u64 *vli, unsigned int ndigits)
134{
135 int i;
136
137 /* Search from the end until we find a non-zero digit.
138 * We do it in reverse because we expect that most digits will
139 * be nonzero.
140 */
141 for (i = ndigits - 1; i >= 0 && vli[i] == 0; i--);
142
143 return (i + 1);
144}
145
146/* Counts the number of bits required for vli. */
147static unsigned int vli_num_bits(const u64 *vli, unsigned int ndigits)
148{
149 unsigned int i, num_digits;
150 u64 digit;
151
152 num_digits = vli_num_digits(vli, ndigits);
153 if (num_digits == 0)
154 return 0;
155
156 digit = vli[num_digits - 1];
157 for (i = 0; digit; i++)
158 digit >>= 1;
159
160 return ((num_digits - 1) * 64 + i);
161}
162
163/* Sets dest = src. */
164static void vli_set(u64 *dest, const u64 *src, unsigned int ndigits)
165{
166 int i;
167
168 for (i = 0; i < ndigits; i++)
169 dest[i] = src[i];
170}
171
172/* Returns sign of left - right. */
173static int vli_cmp(const u64 *left, const u64 *right, unsigned int ndigits)
174{
175 int i;
176
177 for (i = ndigits - 1; i >= 0; i--) {
178 if (left[i] > right[i])
179 return 1;
180 else if (left[i] < right[i])
181 return -1;
182 }
183
184 return 0;
185}
186
187/* Computes result = in << c, returning carry. Can modify in place
188 * (if result == in). 0 < shift < 64.
189 */
190static u64 vli_lshift(u64 *result, const u64 *in, unsigned int shift,
191 unsigned int ndigits)
192{
193 u64 carry = 0;
194 int i;
195
196 for (i = 0; i < ndigits; i++) {
197 u64 temp = in[i];
198
199 result[i] = (temp << shift) | carry;
200 carry = temp >> (64 - shift);
201 }
202
203 return carry;
204}
205
206/* Computes vli = vli >> 1. */
207static void vli_rshift1(u64 *vli, unsigned int ndigits)
208{
209 u64 *end = vli;
210 u64 carry = 0;
211
212 vli += ndigits;
213
214 while (vli-- > end) {
215 u64 temp = *vli;
216 *vli = (temp >> 1) | carry;
217 carry = temp << 63;
218 }
219}
220
221/* Computes result = left + right, returning carry. Can modify in place. */
222static u64 vli_add(u64 *result, const u64 *left, const u64 *right,
223 unsigned int ndigits)
224{
225 u64 carry = 0;
226 int i;
227
228 for (i = 0; i < ndigits; i++) {
229 u64 sum;
230
231 sum = left[i] + right[i] + carry;
232 if (sum != left[i])
233 carry = (sum < left[i]);
234
235 result[i] = sum;
236 }
237
238 return carry;
239}
240
241/* Computes result = left - right, returning borrow. Can modify in place. */
242static u64 vli_sub(u64 *result, const u64 *left, const u64 *right,
243 unsigned int ndigits)
244{
245 u64 borrow = 0;
246 int i;
247
248 for (i = 0; i < ndigits; i++) {
249 u64 diff;
250
251 diff = left[i] - right[i] - borrow;
252 if (diff != left[i])
253 borrow = (diff > left[i]);
254
255 result[i] = diff;
256 }
257
258 return borrow;
259}
260
261static uint128_t mul_64_64(u64 left, u64 right)
262{
263 u64 a0 = left & 0xffffffffull;
264 u64 a1 = left >> 32;
265 u64 b0 = right & 0xffffffffull;
266 u64 b1 = right >> 32;
267 u64 m0 = a0 * b0;
268 u64 m1 = a0 * b1;
269 u64 m2 = a1 * b0;
270 u64 m3 = a1 * b1;
271 uint128_t result;
272
273 m2 += (m0 >> 32);
274 m2 += m1;
275
276 /* Overflow */
277 if (m2 < m1)
278 m3 += 0x100000000ull;
279
280 result.m_low = (m0 & 0xffffffffull) | (m2 << 32);
281 result.m_high = m3 + (m2 >> 32);
282
283 return result;
284}
285
286static uint128_t add_128_128(uint128_t a, uint128_t b)
287{
288 uint128_t result;
289
290 result.m_low = a.m_low + b.m_low;
291 result.m_high = a.m_high + b.m_high + (result.m_low < a.m_low);
292
293 return result;
294}
295
296static void vli_mult(u64 *result, const u64 *left, const u64 *right,
297 unsigned int ndigits)
298{
299 uint128_t r01 = { 0, 0 };
300 u64 r2 = 0;
301 unsigned int i, k;
302
303 /* Compute each digit of result in sequence, maintaining the
304 * carries.
305 */
306 for (k = 0; k < ndigits * 2 - 1; k++) {
307 unsigned int min;
308
309 if (k < ndigits)
310 min = 0;
311 else
312 min = (k + 1) - ndigits;
313
314 for (i = min; i <= k && i < ndigits; i++) {
315 uint128_t product;
316
317 product = mul_64_64(left[i], right[k - i]);
318
319 r01 = add_128_128(r01, product);
320 r2 += (r01.m_high < product.m_high);
321 }
322
323 result[k] = r01.m_low;
324 r01.m_low = r01.m_high;
325 r01.m_high = r2;
326 r2 = 0;
327 }
328
329 result[ndigits * 2 - 1] = r01.m_low;
330}
331
332static void vli_square(u64 *result, const u64 *left, unsigned int ndigits)
333{
334 uint128_t r01 = { 0, 0 };
335 u64 r2 = 0;
336 int i, k;
337
338 for (k = 0; k < ndigits * 2 - 1; k++) {
339 unsigned int min;
340
341 if (k < ndigits)
342 min = 0;
343 else
344 min = (k + 1) - ndigits;
345
346 for (i = min; i <= k && i <= k - i; i++) {
347 uint128_t product;
348
349 product = mul_64_64(left[i], left[k - i]);
350
351 if (i < k - i) {
352 r2 += product.m_high >> 63;
353 product.m_high = (product.m_high << 1) |
354 (product.m_low >> 63);
355 product.m_low <<= 1;
356 }
357
358 r01 = add_128_128(r01, product);
359 r2 += (r01.m_high < product.m_high);
360 }
361
362 result[k] = r01.m_low;
363 r01.m_low = r01.m_high;
364 r01.m_high = r2;
365 r2 = 0;
366 }
367
368 result[ndigits * 2 - 1] = r01.m_low;
369}
370
371/* Computes result = (left + right) % mod.
372 * Assumes that left < mod and right < mod, result != mod.
373 */
374static void vli_mod_add(u64 *result, const u64 *left, const u64 *right,
375 const u64 *mod, unsigned int ndigits)
376{
377 u64 carry;
378
379 carry = vli_add(result, left, right, ndigits);
380
381 /* result > mod (result = mod + remainder), so subtract mod to
382 * get remainder.
383 */
384 if (carry || vli_cmp(result, mod, ndigits) >= 0)
385 vli_sub(result, result, mod, ndigits);
386}
387
388/* Computes result = (left - right) % mod.
389 * Assumes that left < mod and right < mod, result != mod.
390 */
391static void vli_mod_sub(u64 *result, const u64 *left, const u64 *right,
392 const u64 *mod, unsigned int ndigits)
393{
394 u64 borrow = vli_sub(result, left, right, ndigits);
395
396 /* In this case, p_result == -diff == (max int) - diff.
397 * Since -x % d == d - x, we can get the correct result from
398 * result + mod (with overflow).
399 */
400 if (borrow)
401 vli_add(result, result, mod, ndigits);
402}
403
404/* Computes p_result = p_product % curve_p.
405 * See algorithm 5 and 6 from
406 * http://www.isys.uni-klu.ac.at/PDF/2001-0126-MT.pdf
407 */
408static void vli_mmod_fast_192(u64 *result, const u64 *product,
409 const u64 *curve_prime, u64 *tmp)
410{
411 const unsigned int ndigits = 3;
412 int carry;
413
414 vli_set(result, product, ndigits);
415
416 vli_set(tmp, &product[3], ndigits);
417 carry = vli_add(result, result, tmp, ndigits);
418
419 tmp[0] = 0;
420 tmp[1] = product[3];
421 tmp[2] = product[4];
422 carry += vli_add(result, result, tmp, ndigits);
423
424 tmp[0] = tmp[1] = product[5];
425 tmp[2] = 0;
426 carry += vli_add(result, result, tmp, ndigits);
427
428 while (carry || vli_cmp(curve_prime, result, ndigits) != 1)
429 carry -= vli_sub(result, result, curve_prime, ndigits);
430}
431
432/* Computes result = product % curve_prime
433 * from http://www.nsa.gov/ia/_files/nist-routines.pdf
434 */
435static void vli_mmod_fast_256(u64 *result, const u64 *product,
436 const u64 *curve_prime, u64 *tmp)
437{
438 int carry;
439 const unsigned int ndigits = 4;
440
441 /* t */
442 vli_set(result, product, ndigits);
443
444 /* s1 */
445 tmp[0] = 0;
446 tmp[1] = product[5] & 0xffffffff00000000ull;
447 tmp[2] = product[6];
448 tmp[3] = product[7];
449 carry = vli_lshift(tmp, tmp, 1, ndigits);
450 carry += vli_add(result, result, tmp, ndigits);
451
452 /* s2 */
453 tmp[1] = product[6] << 32;
454 tmp[2] = (product[6] >> 32) | (product[7] << 32);
455 tmp[3] = product[7] >> 32;
456 carry += vli_lshift(tmp, tmp, 1, ndigits);
457 carry += vli_add(result, result, tmp, ndigits);
458
459 /* s3 */
460 tmp[0] = product[4];
461 tmp[1] = product[5] & 0xffffffff;
462 tmp[2] = 0;
463 tmp[3] = product[7];
464 carry += vli_add(result, result, tmp, ndigits);
465
466 /* s4 */
467 tmp[0] = (product[4] >> 32) | (product[5] << 32);
468 tmp[1] = (product[5] >> 32) | (product[6] & 0xffffffff00000000ull);
469 tmp[2] = product[7];
470 tmp[3] = (product[6] >> 32) | (product[4] << 32);
471 carry += vli_add(result, result, tmp, ndigits);
472
473 /* d1 */
474 tmp[0] = (product[5] >> 32) | (product[6] << 32);
475 tmp[1] = (product[6] >> 32);
476 tmp[2] = 0;
477 tmp[3] = (product[4] & 0xffffffff) | (product[5] << 32);
478 carry -= vli_sub(result, result, tmp, ndigits);
479
480 /* d2 */
481 tmp[0] = product[6];
482 tmp[1] = product[7];
483 tmp[2] = 0;
484 tmp[3] = (product[4] >> 32) | (product[5] & 0xffffffff00000000ull);
485 carry -= vli_sub(result, result, tmp, ndigits);
486
487 /* d3 */
488 tmp[0] = (product[6] >> 32) | (product[7] << 32);
489 tmp[1] = (product[7] >> 32) | (product[4] << 32);
490 tmp[2] = (product[4] >> 32) | (product[5] << 32);
491 tmp[3] = (product[6] << 32);
492 carry -= vli_sub(result, result, tmp, ndigits);
493
494 /* d4 */
495 tmp[0] = product[7];
496 tmp[1] = product[4] & 0xffffffff00000000ull;
497 tmp[2] = product[5];
498 tmp[3] = product[6] & 0xffffffff00000000ull;
499 carry -= vli_sub(result, result, tmp, ndigits);
500
501 if (carry < 0) {
502 do {
503 carry += vli_add(result, result, curve_prime, ndigits);
504 } while (carry < 0);
505 } else {
506 while (carry || vli_cmp(curve_prime, result, ndigits) != 1)
507 carry -= vli_sub(result, result, curve_prime, ndigits);
508 }
509}
510
511/* Computes result = product % curve_prime
512 * from http://www.nsa.gov/ia/_files/nist-routines.pdf
513*/
514static bool vli_mmod_fast(u64 *result, u64 *product,
515 const u64 *curve_prime, unsigned int ndigits)
516{
517 u64 tmp[2 * ndigits];
518
519 switch (ndigits) {
520 case 3:
521 vli_mmod_fast_192(result, product, curve_prime, tmp);
522 break;
523 case 4:
524 vli_mmod_fast_256(result, product, curve_prime, tmp);
525 break;
526 default:
527 pr_err("unsupports digits size!\n");
528 return false;
529 }
530
531 return true;
532}
533
534/* Computes result = (left * right) % curve_prime. */
535static void vli_mod_mult_fast(u64 *result, const u64 *left, const u64 *right,
536 const u64 *curve_prime, unsigned int ndigits)
537{
538 u64 product[2 * ndigits];
539
540 vli_mult(product, left, right, ndigits);
541 vli_mmod_fast(result, product, curve_prime, ndigits);
542}
543
544/* Computes result = left^2 % curve_prime. */
545static void vli_mod_square_fast(u64 *result, const u64 *left,
546 const u64 *curve_prime, unsigned int ndigits)
547{
548 u64 product[2 * ndigits];
549
550 vli_square(product, left, ndigits);
551 vli_mmod_fast(result, product, curve_prime, ndigits);
552}
553
554#define EVEN(vli) (!(vli[0] & 1))
555/* Computes result = (1 / p_input) % mod. All VLIs are the same size.
556 * See "From Euclid's GCD to Montgomery Multiplication to the Great Divide"
557 * https://labs.oracle.com/techrep/2001/smli_tr-2001-95.pdf
558 */
559static void vli_mod_inv(u64 *result, const u64 *input, const u64 *mod,
560 unsigned int ndigits)
561{
562 u64 a[ndigits], b[ndigits];
563 u64 u[ndigits], v[ndigits];
564 u64 carry;
565 int cmp_result;
566
567 if (vli_is_zero(input, ndigits)) {
568 vli_clear(result, ndigits);
569 return;
570 }
571
572 vli_set(a, input, ndigits);
573 vli_set(b, mod, ndigits);
574 vli_clear(u, ndigits);
575 u[0] = 1;
576 vli_clear(v, ndigits);
577
578 while ((cmp_result = vli_cmp(a, b, ndigits)) != 0) {
579 carry = 0;
580
581 if (EVEN(a)) {
582 vli_rshift1(a, ndigits);
583
584 if (!EVEN(u))
585 carry = vli_add(u, u, mod, ndigits);
586
587 vli_rshift1(u, ndigits);
588 if (carry)
589 u[ndigits - 1] |= 0x8000000000000000ull;
590 } else if (EVEN(b)) {
591 vli_rshift1(b, ndigits);
592
593 if (!EVEN(v))
594 carry = vli_add(v, v, mod, ndigits);
595
596 vli_rshift1(v, ndigits);
597 if (carry)
598 v[ndigits - 1] |= 0x8000000000000000ull;
599 } else if (cmp_result > 0) {
600 vli_sub(a, a, b, ndigits);
601 vli_rshift1(a, ndigits);
602
603 if (vli_cmp(u, v, ndigits) < 0)
604 vli_add(u, u, mod, ndigits);
605
606 vli_sub(u, u, v, ndigits);
607 if (!EVEN(u))
608 carry = vli_add(u, u, mod, ndigits);
609
610 vli_rshift1(u, ndigits);
611 if (carry)
612 u[ndigits - 1] |= 0x8000000000000000ull;
613 } else {
614 vli_sub(b, b, a, ndigits);
615 vli_rshift1(b, ndigits);
616
617 if (vli_cmp(v, u, ndigits) < 0)
618 vli_add(v, v, mod, ndigits);
619
620 vli_sub(v, v, u, ndigits);
621 if (!EVEN(v))
622 carry = vli_add(v, v, mod, ndigits);
623
624 vli_rshift1(v, ndigits);
625 if (carry)
626 v[ndigits - 1] |= 0x8000000000000000ull;
627 }
628 }
629
630 vli_set(result, u, ndigits);
631}
632
633/* ------ Point operations ------ */
634
635/* Returns true if p_point is the point at infinity, false otherwise. */
636static bool ecc_point_is_zero(const struct ecc_point *point)
637{
638 return (vli_is_zero(point->x, point->ndigits) &&
639 vli_is_zero(point->y, point->ndigits));
640}
641
642/* Point multiplication algorithm using Montgomery's ladder with co-Z
643 * coordinates. From http://eprint.iacr.org/2011/338.pdf
644 */
645
646/* Double in place */
647static void ecc_point_double_jacobian(u64 *x1, u64 *y1, u64 *z1,
648 u64 *curve_prime, unsigned int ndigits)
649{
650 /* t1 = x, t2 = y, t3 = z */
651 u64 t4[ndigits];
652 u64 t5[ndigits];
653
654 if (vli_is_zero(z1, ndigits))
655 return;
656
657 /* t4 = y1^2 */
658 vli_mod_square_fast(t4, y1, curve_prime, ndigits);
659 /* t5 = x1*y1^2 = A */
660 vli_mod_mult_fast(t5, x1, t4, curve_prime, ndigits);
661 /* t4 = y1^4 */
662 vli_mod_square_fast(t4, t4, curve_prime, ndigits);
663 /* t2 = y1*z1 = z3 */
664 vli_mod_mult_fast(y1, y1, z1, curve_prime, ndigits);
665 /* t3 = z1^2 */
666 vli_mod_square_fast(z1, z1, curve_prime, ndigits);
667
668 /* t1 = x1 + z1^2 */
669 vli_mod_add(x1, x1, z1, curve_prime, ndigits);
670 /* t3 = 2*z1^2 */
671 vli_mod_add(z1, z1, z1, curve_prime, ndigits);
672 /* t3 = x1 - z1^2 */
673 vli_mod_sub(z1, x1, z1, curve_prime, ndigits);
674 /* t1 = x1^2 - z1^4 */
675 vli_mod_mult_fast(x1, x1, z1, curve_prime, ndigits);
676
677 /* t3 = 2*(x1^2 - z1^4) */
678 vli_mod_add(z1, x1, x1, curve_prime, ndigits);
679 /* t1 = 3*(x1^2 - z1^4) */
680 vli_mod_add(x1, x1, z1, curve_prime, ndigits);
681 if (vli_test_bit(x1, 0)) {
682 u64 carry = vli_add(x1, x1, curve_prime, ndigits);
683
684 vli_rshift1(x1, ndigits);
685 x1[ndigits - 1] |= carry << 63;
686 } else {
687 vli_rshift1(x1, ndigits);
688 }
689 /* t1 = 3/2*(x1^2 - z1^4) = B */
690
691 /* t3 = B^2 */
692 vli_mod_square_fast(z1, x1, curve_prime, ndigits);
693 /* t3 = B^2 - A */
694 vli_mod_sub(z1, z1, t5, curve_prime, ndigits);
695 /* t3 = B^2 - 2A = x3 */
696 vli_mod_sub(z1, z1, t5, curve_prime, ndigits);
697 /* t5 = A - x3 */
698 vli_mod_sub(t5, t5, z1, curve_prime, ndigits);
699 /* t1 = B * (A - x3) */
700 vli_mod_mult_fast(x1, x1, t5, curve_prime, ndigits);
701 /* t4 = B * (A - x3) - y1^4 = y3 */
702 vli_mod_sub(t4, x1, t4, curve_prime, ndigits);
703
704 vli_set(x1, z1, ndigits);
705 vli_set(z1, y1, ndigits);
706 vli_set(y1, t4, ndigits);
707}
708
709/* Modify (x1, y1) => (x1 * z^2, y1 * z^3) */
710static void apply_z(u64 *x1, u64 *y1, u64 *z, u64 *curve_prime,
711 unsigned int ndigits)
712{
713 u64 t1[ndigits];
714
715 vli_mod_square_fast(t1, z, curve_prime, ndigits); /* z^2 */
716 vli_mod_mult_fast(x1, x1, t1, curve_prime, ndigits); /* x1 * z^2 */
717 vli_mod_mult_fast(t1, t1, z, curve_prime, ndigits); /* z^3 */
718 vli_mod_mult_fast(y1, y1, t1, curve_prime, ndigits); /* y1 * z^3 */
719}
720
721/* P = (x1, y1) => 2P, (x2, y2) => P' */
722static void xycz_initial_double(u64 *x1, u64 *y1, u64 *x2, u64 *y2,
723 u64 *p_initial_z, u64 *curve_prime,
724 unsigned int ndigits)
725{
726 u64 z[ndigits];
727
728 vli_set(x2, x1, ndigits);
729 vli_set(y2, y1, ndigits);
730
731 vli_clear(z, ndigits);
732 z[0] = 1;
733
734 if (p_initial_z)
735 vli_set(z, p_initial_z, ndigits);
736
737 apply_z(x1, y1, z, curve_prime, ndigits);
738
739 ecc_point_double_jacobian(x1, y1, z, curve_prime, ndigits);
740
741 apply_z(x2, y2, z, curve_prime, ndigits);
742}
743
744/* Input P = (x1, y1, Z), Q = (x2, y2, Z)
745 * Output P' = (x1', y1', Z3), P + Q = (x3, y3, Z3)
746 * or P => P', Q => P + Q
747 */
748static void xycz_add(u64 *x1, u64 *y1, u64 *x2, u64 *y2, u64 *curve_prime,
749 unsigned int ndigits)
750{
751 /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
752 u64 t5[ndigits];
753
754 /* t5 = x2 - x1 */
755 vli_mod_sub(t5, x2, x1, curve_prime, ndigits);
756 /* t5 = (x2 - x1)^2 = A */
757 vli_mod_square_fast(t5, t5, curve_prime, ndigits);
758 /* t1 = x1*A = B */
759 vli_mod_mult_fast(x1, x1, t5, curve_prime, ndigits);
760 /* t3 = x2*A = C */
761 vli_mod_mult_fast(x2, x2, t5, curve_prime, ndigits);
762 /* t4 = y2 - y1 */
763 vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
764 /* t5 = (y2 - y1)^2 = D */
765 vli_mod_square_fast(t5, y2, curve_prime, ndigits);
766
767 /* t5 = D - B */
768 vli_mod_sub(t5, t5, x1, curve_prime, ndigits);
769 /* t5 = D - B - C = x3 */
770 vli_mod_sub(t5, t5, x2, curve_prime, ndigits);
771 /* t3 = C - B */
772 vli_mod_sub(x2, x2, x1, curve_prime, ndigits);
773 /* t2 = y1*(C - B) */
774 vli_mod_mult_fast(y1, y1, x2, curve_prime, ndigits);
775 /* t3 = B - x3 */
776 vli_mod_sub(x2, x1, t5, curve_prime, ndigits);
777 /* t4 = (y2 - y1)*(B - x3) */
778 vli_mod_mult_fast(y2, y2, x2, curve_prime, ndigits);
779 /* t4 = y3 */
780 vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
781
782 vli_set(x2, t5, ndigits);
783}
784
785/* Input P = (x1, y1, Z), Q = (x2, y2, Z)
786 * Output P + Q = (x3, y3, Z3), P - Q = (x3', y3', Z3)
787 * or P => P - Q, Q => P + Q
788 */
789static void xycz_add_c(u64 *x1, u64 *y1, u64 *x2, u64 *y2, u64 *curve_prime,
790 unsigned int ndigits)
791{
792 /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
793 u64 t5[ndigits];
794 u64 t6[ndigits];
795 u64 t7[ndigits];
796
797 /* t5 = x2 - x1 */
798 vli_mod_sub(t5, x2, x1, curve_prime, ndigits);
799 /* t5 = (x2 - x1)^2 = A */
800 vli_mod_square_fast(t5, t5, curve_prime, ndigits);
801 /* t1 = x1*A = B */
802 vli_mod_mult_fast(x1, x1, t5, curve_prime, ndigits);
803 /* t3 = x2*A = C */
804 vli_mod_mult_fast(x2, x2, t5, curve_prime, ndigits);
805 /* t4 = y2 + y1 */
806 vli_mod_add(t5, y2, y1, curve_prime, ndigits);
807 /* t4 = y2 - y1 */
808 vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
809
810 /* t6 = C - B */
811 vli_mod_sub(t6, x2, x1, curve_prime, ndigits);
812 /* t2 = y1 * (C - B) */
813 vli_mod_mult_fast(y1, y1, t6, curve_prime, ndigits);
814 /* t6 = B + C */
815 vli_mod_add(t6, x1, x2, curve_prime, ndigits);
816 /* t3 = (y2 - y1)^2 */
817 vli_mod_square_fast(x2, y2, curve_prime, ndigits);
818 /* t3 = x3 */
819 vli_mod_sub(x2, x2, t6, curve_prime, ndigits);
820
821 /* t7 = B - x3 */
822 vli_mod_sub(t7, x1, x2, curve_prime, ndigits);
823 /* t4 = (y2 - y1)*(B - x3) */
824 vli_mod_mult_fast(y2, y2, t7, curve_prime, ndigits);
825 /* t4 = y3 */
826 vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
827
828 /* t7 = (y2 + y1)^2 = F */
829 vli_mod_square_fast(t7, t5, curve_prime, ndigits);
830 /* t7 = x3' */
831 vli_mod_sub(t7, t7, t6, curve_prime, ndigits);
832 /* t6 = x3' - B */
833 vli_mod_sub(t6, t7, x1, curve_prime, ndigits);
834 /* t6 = (y2 + y1)*(x3' - B) */
835 vli_mod_mult_fast(t6, t6, t5, curve_prime, ndigits);
836 /* t2 = y3' */
837 vli_mod_sub(y1, t6, y1, curve_prime, ndigits);
838
839 vli_set(x1, t7, ndigits);
840}
841
842static void ecc_point_mult(struct ecc_point *result,
843 const struct ecc_point *point, const u64 *scalar,
844 u64 *initial_z, u64 *curve_prime,
845 unsigned int ndigits)
846{
847 /* R0 and R1 */
848 u64 rx[2][ndigits];
849 u64 ry[2][ndigits];
850 u64 z[ndigits];
851 int i, nb;
852 int num_bits = vli_num_bits(scalar, ndigits);
853
854 vli_set(rx[1], point->x, ndigits);
855 vli_set(ry[1], point->y, ndigits);
856
857 xycz_initial_double(rx[1], ry[1], rx[0], ry[0], initial_z, curve_prime,
858 ndigits);
859
860 for (i = num_bits - 2; i > 0; i--) {
861 nb = !vli_test_bit(scalar, i);
862 xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb], curve_prime,
863 ndigits);
864 xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve_prime,
865 ndigits);
866 }
867
868 nb = !vli_test_bit(scalar, 0);
869 xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb], curve_prime,
870 ndigits);
871
872 /* Find final 1/Z value. */
873 /* X1 - X0 */
874 vli_mod_sub(z, rx[1], rx[0], curve_prime, ndigits);
875 /* Yb * (X1 - X0) */
876 vli_mod_mult_fast(z, z, ry[1 - nb], curve_prime, ndigits);
877 /* xP * Yb * (X1 - X0) */
878 vli_mod_mult_fast(z, z, point->x, curve_prime, ndigits);
879
880 /* 1 / (xP * Yb * (X1 - X0)) */
881 vli_mod_inv(z, z, curve_prime, point->ndigits);
882
883 /* yP / (xP * Yb * (X1 - X0)) */
884 vli_mod_mult_fast(z, z, point->y, curve_prime, ndigits);
885 /* Xb * yP / (xP * Yb * (X1 - X0)) */
886 vli_mod_mult_fast(z, z, rx[1 - nb], curve_prime, ndigits);
887 /* End 1/Z calculation */
888
889 xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve_prime, ndigits);
890
891 apply_z(rx[0], ry[0], z, curve_prime, ndigits);
892
893 vli_set(result->x, rx[0], ndigits);
894 vli_set(result->y, ry[0], ndigits);
895}
896
897static inline void ecc_swap_digits(const u64 *in, u64 *out,
898 unsigned int ndigits)
899{
900 int i;
901
902 for (i = 0; i < ndigits; i++)
903 out[i] = __swab64(in[ndigits - 1 - i]);
904}
905
906int ecc_is_key_valid(unsigned int curve_id, unsigned int ndigits,
907 const u8 *private_key, unsigned int private_key_len)
908{
909 int nbytes;
910 const struct ecc_curve *curve = ecc_get_curve(curve_id);
911
912 if (!private_key)
913 return -EINVAL;
914
915 nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT;
916
917 if (private_key_len != nbytes)
918 return -EINVAL;
919
920 if (vli_is_zero((const u64 *)&private_key[0], ndigits))
921 return -EINVAL;
922
923 /* Make sure the private key is in the range [1, n-1]. */
924 if (vli_cmp(curve->n, (const u64 *)&private_key[0], ndigits) != 1)
925 return -EINVAL;
926
927 return 0;
928}
929
930int ecdh_make_pub_key(unsigned int curve_id, unsigned int ndigits,
931 const u8 *private_key, unsigned int private_key_len,
932 u8 *public_key, unsigned int public_key_len)
933{
934 int ret = 0;
935 struct ecc_point *pk;
936 u64 priv[ndigits];
937 unsigned int nbytes;
938 const struct ecc_curve *curve = ecc_get_curve(curve_id);
939
940 if (!private_key || !curve) {
941 ret = -EINVAL;
942 goto out;
943 }
944
945 ecc_swap_digits((const u64 *)private_key, priv, ndigits);
946
947 pk = ecc_alloc_point(ndigits);
948 if (!pk) {
949 ret = -ENOMEM;
950 goto out;
951 }
952
953 ecc_point_mult(pk, &curve->g, priv, NULL, curve->p, ndigits);
954 if (ecc_point_is_zero(pk)) {
955 ret = -EAGAIN;
956 goto err_free_point;
957 }
958
959 nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT;
960 ecc_swap_digits(pk->x, (u64 *)public_key, ndigits);
961 ecc_swap_digits(pk->y, (u64 *)&public_key[nbytes], ndigits);
962
963err_free_point:
964 ecc_free_point(pk);
965out:
966 return ret;
967}
968
969int crypto_ecdh_shared_secret(unsigned int curve_id, unsigned int ndigits,
970 const u8 *private_key, unsigned int private_key_len,
971 const u8 *public_key, unsigned int public_key_len,
972 u8 *secret, unsigned int secret_len)
973{
974 int ret = 0;
975 struct ecc_point *product, *pk;
976 u64 priv[ndigits];
977 u64 rand_z[ndigits];
978 unsigned int nbytes;
979 const struct ecc_curve *curve = ecc_get_curve(curve_id);
980
981 if (!private_key || !public_key || !curve) {
982 ret = -EINVAL;
983 goto out;
984 }
985
986 nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT;
987
988 get_random_bytes(rand_z, nbytes);
989
990 pk = ecc_alloc_point(ndigits);
991 if (!pk) {
992 ret = -ENOMEM;
993 goto out;
994 }
995
996 product = ecc_alloc_point(ndigits);
997 if (!product) {
998 ret = -ENOMEM;
999 goto err_alloc_product;
1000 }
1001
1002 ecc_swap_digits((const u64 *)public_key, pk->x, ndigits);
1003 ecc_swap_digits((const u64 *)&public_key[nbytes], pk->y, ndigits);
1004 ecc_swap_digits((const u64 *)private_key, priv, ndigits);
1005
1006 ecc_point_mult(product, pk, priv, rand_z, curve->p, ndigits);
1007
1008 ecc_swap_digits(product->x, (u64 *)secret, ndigits);
1009
1010 if (ecc_point_is_zero(product))
1011 ret = -EFAULT;
1012
1013 ecc_free_point(product);
1014err_alloc_product:
1015 ecc_free_point(pk);
1016out:
1017 return ret;
1018}