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1/*
2 * Copyright (c) 2013, 2014 Kenneth MacKay. All rights reserved.
3 * Copyright (c) 2019 Vitaly Chikunov <[email protected]>
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_POW2(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
93struct ecc_point *ecc_alloc_point(unsigned int ndigits)
94{
95 struct ecc_point *p;
96 size_t ndigits_sz;
97
98 if (!ndigits)
99 return NULL;
100
101 p = kmalloc_obj(*p);
102 if (!p)
103 return NULL;
104
105 ndigits_sz = ndigits * sizeof(u64);
106 p->x = kmalloc(ndigits_sz, GFP_KERNEL);
107 if (!p->x)
108 goto err_alloc_x;
109
110 p->y = kmalloc(ndigits_sz, GFP_KERNEL);
111 if (!p->y)
112 goto err_alloc_y;
113
114 p->ndigits = ndigits;
115
116 return p;
117
118err_alloc_y:
119 kfree(p->x);
120err_alloc_x:
121 kfree(p);
122 return NULL;
123}
124EXPORT_SYMBOL(ecc_alloc_point);
125
126void ecc_free_point(struct ecc_point *p)
127{
128 if (!p)
129 return;
130
131 kfree_sensitive(p->x);
132 kfree_sensitive(p->y);
133 kfree_sensitive(p);
134}
135EXPORT_SYMBOL(ecc_free_point);
136
137static void vli_clear(u64 *vli, unsigned int ndigits)
138{
139 int i;
140
141 for (i = 0; i < ndigits; i++)
142 vli[i] = 0;
143}
144
145/* Returns true if vli == 0, false otherwise. */
146bool vli_is_zero(const u64 *vli, unsigned int ndigits)
147{
148 int i;
149
150 for (i = 0; i < ndigits; i++) {
151 if (vli[i])
152 return false;
153 }
154
155 return true;
156}
157EXPORT_SYMBOL(vli_is_zero);
158
159/* Returns nonzero if bit of vli is set. */
160static u64 vli_test_bit(const u64 *vli, unsigned int bit)
161{
162 return (vli[bit / 64] & ((u64)1 << (bit % 64)));
163}
164
165static bool vli_is_negative(const u64 *vli, unsigned int ndigits)
166{
167 return vli_test_bit(vli, ndigits * 64 - 1);
168}
169
170/* Counts the number of 64-bit "digits" in vli. */
171static unsigned int vli_num_digits(const u64 *vli, unsigned int ndigits)
172{
173 int i;
174
175 /* Search from the end until we find a non-zero digit.
176 * We do it in reverse because we expect that most digits will
177 * be nonzero.
178 */
179 for (i = ndigits - 1; i >= 0 && vli[i] == 0; i--);
180
181 return (i + 1);
182}
183
184/* Counts the number of bits required for vli. */
185unsigned int vli_num_bits(const u64 *vli, unsigned int ndigits)
186{
187 unsigned int i, num_digits;
188 u64 digit;
189
190 num_digits = vli_num_digits(vli, ndigits);
191 if (num_digits == 0)
192 return 0;
193
194 digit = vli[num_digits - 1];
195 for (i = 0; digit; i++)
196 digit >>= 1;
197
198 return ((num_digits - 1) * 64 + i);
199}
200EXPORT_SYMBOL(vli_num_bits);
201
202/* Set dest from unaligned bit string src. */
203void vli_from_be64(u64 *dest, const void *src, unsigned int ndigits)
204{
205 int i;
206 const u64 *from = src;
207
208 for (i = 0; i < ndigits; i++)
209 dest[i] = get_unaligned_be64(&from[ndigits - 1 - i]);
210}
211EXPORT_SYMBOL(vli_from_be64);
212
213void vli_from_le64(u64 *dest, const void *src, unsigned int ndigits)
214{
215 int i;
216 const u64 *from = src;
217
218 for (i = 0; i < ndigits; i++)
219 dest[i] = get_unaligned_le64(&from[i]);
220}
221EXPORT_SYMBOL(vli_from_le64);
222
223/* Sets dest = src. */
224static void vli_set(u64 *dest, const u64 *src, unsigned int ndigits)
225{
226 int i;
227
228 for (i = 0; i < ndigits; i++)
229 dest[i] = src[i];
230}
231
232/* Returns sign of left - right. */
233int vli_cmp(const u64 *left, const u64 *right, unsigned int ndigits)
234{
235 int i;
236
237 for (i = ndigits - 1; i >= 0; i--) {
238 if (left[i] > right[i])
239 return 1;
240 else if (left[i] < right[i])
241 return -1;
242 }
243
244 return 0;
245}
246EXPORT_SYMBOL(vli_cmp);
247
248/* Computes result = in << c, returning carry. Can modify in place
249 * (if result == in). 0 < shift < 64.
250 */
251static u64 vli_lshift(u64 *result, const u64 *in, unsigned int shift,
252 unsigned int ndigits)
253{
254 u64 carry = 0;
255 int i;
256
257 for (i = 0; i < ndigits; i++) {
258 u64 temp = in[i];
259
260 result[i] = (temp << shift) | carry;
261 carry = temp >> (64 - shift);
262 }
263
264 return carry;
265}
266
267/* Computes vli = vli >> 1. */
268static void vli_rshift1(u64 *vli, unsigned int ndigits)
269{
270 u64 *end = vli;
271 u64 carry = 0;
272
273 vli += ndigits;
274
275 while (vli-- > end) {
276 u64 temp = *vli;
277 *vli = (temp >> 1) | carry;
278 carry = temp << 63;
279 }
280}
281
282#ifdef __has_builtin
283#if __has_builtin(__builtin_addcll)
284#define USE_BUILTIN_ADDC
285#endif
286#endif
287
288/* Computes result = left + right + carry_in and updates carry_out */
289static inline void add_carry(u64 left, u64 right, u64 *result, u64 carry_in,
290 u64 *carry_out)
291{
292#ifdef USE_BUILTIN_ADDC
293 *result = __builtin_addcll(left, right, carry_in, carry_out);
294#else
295 u64 sum1, sum2;
296 u64 c1 = __builtin_uaddll_overflow(left, right, &sum1);
297 u64 c2 = __builtin_uaddll_overflow(sum1, carry_in, &sum2);
298 *result = sum2;
299 *carry_out = c1 | c2;
300#endif
301}
302
303#ifdef __has_builtin
304#if __has_builtin(__builtin_subcll)
305#define USE_BUILTIN_SUBC
306#endif
307#endif
308
309/* Computes result = left - right - borrow_in and updates borrow_out */
310static inline void sub_borrow(u64 left, u64 right, u64 *result, u64 borrow_in,
311 u64 *borrow_out)
312{
313#ifdef USE_BUILTIN_SUBC
314 *result = __builtin_subcll(left, right, borrow_in, borrow_out);
315#else
316 u64 diff1, diff2;
317 u64 b1 = __builtin_usubll_overflow(left, right, &diff1);
318 u64 b2 = __builtin_usubll_overflow(diff1, borrow_in, &diff2);
319 *result = diff2;
320 *borrow_out = b1 | b2;
321#endif
322}
323
324/* Computes result = left + right, returning carry. Can modify in place. */
325static u64 vli_add(u64 *result, const u64 *left, const u64 *right,
326 unsigned int ndigits)
327{
328 u64 carry = 0;
329 int i;
330
331 for (i = 0; i < ndigits; i++)
332 add_carry(left[i], right[i], &result[i], carry, &carry);
333
334 return carry;
335}
336
337/* Computes result = left + right, returning carry. Can modify in place. */
338static u64 vli_uadd(u64 *result, const u64 *left, u64 right,
339 unsigned int ndigits)
340{
341 u64 carry;
342 int i;
343
344 if (ndigits == 0)
345 return right;
346
347 carry = __builtin_uaddll_overflow(left[0], right, &result[0]);
348
349 for (i = 1; i < ndigits; i++)
350 carry = __builtin_uaddll_overflow(left[i], carry, &result[i]);
351
352 return carry;
353}
354
355/* Computes result = left - right, returning borrow. Can modify in place. */
356u64 vli_sub(u64 *result, const u64 *left, const u64 *right,
357 unsigned int ndigits)
358{
359 u64 borrow = 0;
360 int i;
361
362 for (i = 0; i < ndigits; i++)
363 sub_borrow(left[i], right[i], &result[i], borrow, &borrow);
364
365 return borrow;
366}
367EXPORT_SYMBOL(vli_sub);
368
369/* Computes result = left - right, returning borrow. Can modify in place. */
370static u64 vli_usub(u64 *result, const u64 *left, u64 right,
371 unsigned int ndigits)
372{
373 u64 borrow;
374 int i;
375
376 if (ndigits == 0)
377 return right;
378
379 borrow = __builtin_usubll_overflow(left[0], right, &result[0]);
380
381 for (i = 1; i < ndigits; i++)
382 borrow = __builtin_usubll_overflow(left[i], borrow, &result[i]);
383
384 return borrow;
385}
386
387static uint128_t mul_64_64(u64 left, u64 right)
388{
389 uint128_t result;
390#if defined(CONFIG_ARCH_SUPPORTS_INT128)
391 unsigned __int128 m = (unsigned __int128)left * right;
392
393 result.m_low = m;
394 result.m_high = m >> 64;
395#else
396 u64 a0 = left & 0xffffffffull;
397 u64 a1 = left >> 32;
398 u64 b0 = right & 0xffffffffull;
399 u64 b1 = right >> 32;
400 u64 m0 = a0 * b0;
401 u64 m1 = a0 * b1;
402 u64 m2 = a1 * b0;
403 u64 m3 = a1 * b1;
404
405 m2 += (m0 >> 32);
406 m2 += m1;
407
408 /* Overflow */
409 if (m2 < m1)
410 m3 += 0x100000000ull;
411
412 result.m_low = (m0 & 0xffffffffull) | (m2 << 32);
413 result.m_high = m3 + (m2 >> 32);
414#endif
415 return result;
416}
417
418/* Calculate addition with overflow checking. Returns true on wrap-around,
419 * false otherwise.
420 */
421static bool check_add_128_128_overflow(uint128_t *result, uint128_t a,
422 uint128_t b)
423{
424 bool carry;
425
426 result->m_low = a.m_low + b.m_low;
427 carry = (result->m_low < a.m_low);
428
429 result->m_high = a.m_high + b.m_high + carry;
430
431 /* Using constant-time bitwise arithmetic to prevent timing
432 * side-channels.
433 */
434 carry = (result->m_high < a.m_high) |
435 ((result->m_high == a.m_high) & carry);
436
437 return carry;
438}
439
440static void vli_mult(u64 *result, const u64 *left, const u64 *right,
441 unsigned int ndigits)
442{
443 uint128_t r01 = { 0, 0 };
444 u64 r2 = 0;
445 unsigned int i, k;
446
447 /* Compute each digit of result in sequence, maintaining the
448 * carries.
449 */
450 for (k = 0; k < ndigits * 2 - 1; k++) {
451 unsigned int min;
452
453 if (k < ndigits)
454 min = 0;
455 else
456 min = (k + 1) - ndigits;
457
458 for (i = min; i <= k && i < ndigits; i++) {
459 uint128_t product;
460
461 product = mul_64_64(left[i], right[k - i]);
462 r2 += check_add_128_128_overflow(&r01, r01, product);
463 }
464
465 result[k] = r01.m_low;
466 r01.m_low = r01.m_high;
467 r01.m_high = r2;
468 r2 = 0;
469 }
470
471 result[ndigits * 2 - 1] = r01.m_low;
472}
473
474/* Compute product = left * right, for a small right value. */
475static void vli_umult(u64 *result, const u64 *left, u32 right,
476 unsigned int ndigits)
477{
478 uint128_t r01 = { 0 };
479 unsigned int k;
480
481 for (k = 0; k < ndigits; k++) {
482 uint128_t product;
483
484 product = mul_64_64(left[k], right);
485 check_add_128_128_overflow(&r01, r01, product);
486 /* no carry */
487 result[k] = r01.m_low;
488 r01.m_low = r01.m_high;
489 r01.m_high = 0;
490 }
491 result[k] = r01.m_low;
492 for (++k; k < ndigits * 2; k++)
493 result[k] = 0;
494}
495
496static void vli_square(u64 *result, const u64 *left, unsigned int ndigits)
497{
498 uint128_t r01 = { 0, 0 };
499 u64 r2 = 0;
500 int i, k;
501
502 for (k = 0; k < ndigits * 2 - 1; k++) {
503 unsigned int min;
504
505 if (k < ndigits)
506 min = 0;
507 else
508 min = (k + 1) - ndigits;
509
510 for (i = min; i <= k && i <= k - i; i++) {
511 uint128_t product;
512
513 product = mul_64_64(left[i], left[k - i]);
514
515 if (i < k - i) {
516 r2 += product.m_high >> 63;
517 product.m_high = (product.m_high << 1) |
518 (product.m_low >> 63);
519 product.m_low <<= 1;
520 }
521
522 r2 += check_add_128_128_overflow(&r01, r01, product);
523 }
524
525 result[k] = r01.m_low;
526 r01.m_low = r01.m_high;
527 r01.m_high = r2;
528 r2 = 0;
529 }
530
531 result[ndigits * 2 - 1] = r01.m_low;
532}
533
534/* Computes result = (left + right) % mod.
535 * Assumes that left < mod and right < mod, result != mod.
536 */
537static void vli_mod_add(u64 *result, const u64 *left, const u64 *right,
538 const u64 *mod, unsigned int ndigits)
539{
540 u64 carry;
541
542 carry = vli_add(result, left, right, ndigits);
543
544 /* result > mod (result = mod + remainder), so subtract mod to
545 * get remainder.
546 */
547 if (carry || vli_cmp(result, mod, ndigits) >= 0)
548 vli_sub(result, result, mod, ndigits);
549}
550
551/* Computes result = (left - right) % mod.
552 * Assumes that left < mod and right < mod, result != mod.
553 */
554static void vli_mod_sub(u64 *result, const u64 *left, const u64 *right,
555 const u64 *mod, unsigned int ndigits)
556{
557 u64 borrow = vli_sub(result, left, right, ndigits);
558
559 /* In this case, p_result == -diff == (max int) - diff.
560 * Since -x % d == d - x, we can get the correct result from
561 * result + mod (with overflow).
562 */
563 if (borrow)
564 vli_add(result, result, mod, ndigits);
565}
566
567/*
568 * Computes result = product % mod
569 * for special form moduli: p = 2^k-c, for small c (note the minus sign)
570 *
571 * References:
572 * R. Crandall, C. Pomerance. Prime Numbers: A Computational Perspective.
573 * 9 Fast Algorithms for Large-Integer Arithmetic. 9.2.3 Moduli of special form
574 * Algorithm 9.2.13 (Fast mod operation for special-form moduli).
575 */
576static void vli_mmod_special(u64 *result, const u64 *product,
577 const u64 *mod, unsigned int ndigits)
578{
579 u64 c = -mod[0];
580 u64 t[ECC_MAX_DIGITS * 2];
581 u64 r[ECC_MAX_DIGITS * 2];
582
583 vli_set(r, product, ndigits * 2);
584 while (!vli_is_zero(r + ndigits, ndigits)) {
585 vli_umult(t, r + ndigits, c, ndigits);
586 vli_clear(r + ndigits, ndigits);
587 vli_add(r, r, t, ndigits * 2);
588 }
589 vli_set(t, mod, ndigits);
590 vli_clear(t + ndigits, ndigits);
591 while (vli_cmp(r, t, ndigits * 2) >= 0)
592 vli_sub(r, r, t, ndigits * 2);
593 vli_set(result, r, ndigits);
594}
595
596/*
597 * Computes result = product % mod
598 * for special form moduli: p = 2^{k-1}+c, for small c (note the plus sign)
599 * where k-1 does not fit into qword boundary by -1 bit (such as 255).
600
601 * References (loosely based on):
602 * A. Menezes, P. van Oorschot, S. Vanstone. Handbook of Applied Cryptography.
603 * 14.3.4 Reduction methods for moduli of special form. Algorithm 14.47.
604 * URL: http://cacr.uwaterloo.ca/hac/about/chap14.pdf
605 *
606 * H. Cohen, G. Frey, R. Avanzi, C. Doche, T. Lange, K. Nguyen, F. Vercauteren.
607 * Handbook of Elliptic and Hyperelliptic Curve Cryptography.
608 * Algorithm 10.25 Fast reduction for special form moduli
609 */
610static void vli_mmod_special2(u64 *result, const u64 *product,
611 const u64 *mod, unsigned int ndigits)
612{
613 u64 c2 = mod[0] * 2;
614 u64 q[ECC_MAX_DIGITS];
615 u64 r[ECC_MAX_DIGITS * 2];
616 u64 m[ECC_MAX_DIGITS * 2]; /* expanded mod */
617 int carry; /* last bit that doesn't fit into q */
618 int i;
619
620 vli_set(m, mod, ndigits);
621 vli_clear(m + ndigits, ndigits);
622
623 vli_set(r, product, ndigits);
624 /* q and carry are top bits */
625 vli_set(q, product + ndigits, ndigits);
626 vli_clear(r + ndigits, ndigits);
627 carry = vli_is_negative(r, ndigits);
628 if (carry)
629 r[ndigits - 1] &= (1ull << 63) - 1;
630 for (i = 1; carry || !vli_is_zero(q, ndigits); i++) {
631 u64 qc[ECC_MAX_DIGITS * 2];
632
633 vli_umult(qc, q, c2, ndigits);
634 if (carry)
635 vli_uadd(qc, qc, mod[0], ndigits * 2);
636 vli_set(q, qc + ndigits, ndigits);
637 vli_clear(qc + ndigits, ndigits);
638 carry = vli_is_negative(qc, ndigits);
639 if (carry)
640 qc[ndigits - 1] &= (1ull << 63) - 1;
641 if (i & 1)
642 vli_sub(r, r, qc, ndigits * 2);
643 else
644 vli_add(r, r, qc, ndigits * 2);
645 }
646 while (vli_is_negative(r, ndigits * 2))
647 vli_add(r, r, m, ndigits * 2);
648 while (vli_cmp(r, m, ndigits * 2) >= 0)
649 vli_sub(r, r, m, ndigits * 2);
650
651 vli_set(result, r, ndigits);
652}
653
654/*
655 * Computes result = product % mod, where product is 2N words long.
656 * Reference: Ken MacKay's micro-ecc.
657 * Currently only designed to work for curve_p or curve_n.
658 */
659static void vli_mmod_slow(u64 *result, u64 *product, const u64 *mod,
660 unsigned int ndigits)
661{
662 u64 mod_m[2 * ECC_MAX_DIGITS];
663 u64 tmp[2 * ECC_MAX_DIGITS];
664 u64 *v[2] = { tmp, product };
665 u64 carry = 0;
666 unsigned int i;
667 /* Shift mod so its highest set bit is at the maximum position. */
668 int shift = (ndigits * 2 * 64) - vli_num_bits(mod, ndigits);
669 int word_shift = shift / 64;
670 int bit_shift = shift % 64;
671
672 vli_clear(mod_m, word_shift);
673 if (bit_shift > 0) {
674 for (i = 0; i < ndigits; ++i) {
675 mod_m[word_shift + i] = (mod[i] << bit_shift) | carry;
676 carry = mod[i] >> (64 - bit_shift);
677 }
678 } else
679 vli_set(mod_m + word_shift, mod, ndigits);
680
681 for (i = 1; shift >= 0; --shift) {
682 u64 borrow = 0;
683 unsigned int j;
684
685 for (j = 0; j < ndigits * 2; ++j) {
686 u64 diff = v[i][j] - mod_m[j] - borrow;
687
688 if (diff != v[i][j])
689 borrow = (diff > v[i][j]);
690 v[1 - i][j] = diff;
691 }
692 i = !(i ^ borrow); /* Swap the index if there was no borrow */
693 vli_rshift1(mod_m, ndigits);
694 mod_m[ndigits - 1] |= mod_m[ndigits] << (64 - 1);
695 vli_rshift1(mod_m + ndigits, ndigits);
696 }
697 vli_set(result, v[i], ndigits);
698}
699
700/* Computes result = product % mod using Barrett's reduction with precomputed
701 * value mu appended to the mod after ndigits, mu = (2^{2w} / mod) and have
702 * length ndigits + 1, where mu * (2^w - 1) should not overflow ndigits
703 * boundary.
704 *
705 * Reference:
706 * R. Brent, P. Zimmermann. Modern Computer Arithmetic. 2010.
707 * 2.4.1 Barrett's algorithm. Algorithm 2.5.
708 */
709static void vli_mmod_barrett(u64 *result, u64 *product, const u64 *mod,
710 unsigned int ndigits)
711{
712 u64 q[ECC_MAX_DIGITS * 2];
713 u64 r[ECC_MAX_DIGITS * 2];
714 const u64 *mu = mod + ndigits;
715
716 vli_mult(q, product + ndigits, mu, ndigits);
717 if (mu[ndigits])
718 vli_add(q + ndigits, q + ndigits, product + ndigits, ndigits);
719 vli_mult(r, mod, q + ndigits, ndigits);
720 vli_sub(r, product, r, ndigits * 2);
721 while (!vli_is_zero(r + ndigits, ndigits) ||
722 vli_cmp(r, mod, ndigits) != -1) {
723 u64 carry;
724
725 carry = vli_sub(r, r, mod, ndigits);
726 vli_usub(r + ndigits, r + ndigits, carry, ndigits);
727 }
728 vli_set(result, r, ndigits);
729}
730
731/* Computes p_result = p_product % curve_p.
732 * See algorithm 5 and 6 from
733 * http://www.isys.uni-klu.ac.at/PDF/2001-0126-MT.pdf
734 */
735static void vli_mmod_fast_192(u64 *result, const u64 *product,
736 const u64 *curve_prime, u64 *tmp)
737{
738 const unsigned int ndigits = ECC_CURVE_NIST_P192_DIGITS;
739 int carry;
740
741 vli_set(result, product, ndigits);
742
743 vli_set(tmp, &product[3], ndigits);
744 carry = vli_add(result, result, tmp, ndigits);
745
746 tmp[0] = 0;
747 tmp[1] = product[3];
748 tmp[2] = product[4];
749 carry += vli_add(result, result, tmp, ndigits);
750
751 tmp[0] = tmp[1] = product[5];
752 tmp[2] = 0;
753 carry += vli_add(result, result, tmp, ndigits);
754
755 while (carry || vli_cmp(curve_prime, result, ndigits) != 1)
756 carry -= vli_sub(result, result, curve_prime, ndigits);
757}
758
759/* Computes result = product % curve_prime
760 * from http://www.nsa.gov/ia/_files/nist-routines.pdf
761 */
762static void vli_mmod_fast_256(u64 *result, const u64 *product,
763 const u64 *curve_prime, u64 *tmp)
764{
765 int carry;
766 const unsigned int ndigits = ECC_CURVE_NIST_P256_DIGITS;
767
768 /* t */
769 vli_set(result, product, ndigits);
770
771 /* s1 */
772 tmp[0] = 0;
773 tmp[1] = product[5] & 0xffffffff00000000ull;
774 tmp[2] = product[6];
775 tmp[3] = product[7];
776 carry = vli_lshift(tmp, tmp, 1, ndigits);
777 carry += vli_add(result, result, tmp, ndigits);
778
779 /* s2 */
780 tmp[1] = product[6] << 32;
781 tmp[2] = (product[6] >> 32) | (product[7] << 32);
782 tmp[3] = product[7] >> 32;
783 carry += vli_lshift(tmp, tmp, 1, ndigits);
784 carry += vli_add(result, result, tmp, ndigits);
785
786 /* s3 */
787 tmp[0] = product[4];
788 tmp[1] = product[5] & 0xffffffff;
789 tmp[2] = 0;
790 tmp[3] = product[7];
791 carry += vli_add(result, result, tmp, ndigits);
792
793 /* s4 */
794 tmp[0] = (product[4] >> 32) | (product[5] << 32);
795 tmp[1] = (product[5] >> 32) | (product[6] & 0xffffffff00000000ull);
796 tmp[2] = product[7];
797 tmp[3] = (product[6] >> 32) | (product[4] << 32);
798 carry += vli_add(result, result, tmp, ndigits);
799
800 /* d1 */
801 tmp[0] = (product[5] >> 32) | (product[6] << 32);
802 tmp[1] = (product[6] >> 32);
803 tmp[2] = 0;
804 tmp[3] = (product[4] & 0xffffffff) | (product[5] << 32);
805 carry -= vli_sub(result, result, tmp, ndigits);
806
807 /* d2 */
808 tmp[0] = product[6];
809 tmp[1] = product[7];
810 tmp[2] = 0;
811 tmp[3] = (product[4] >> 32) | (product[5] & 0xffffffff00000000ull);
812 carry -= vli_sub(result, result, tmp, ndigits);
813
814 /* d3 */
815 tmp[0] = (product[6] >> 32) | (product[7] << 32);
816 tmp[1] = (product[7] >> 32) | (product[4] << 32);
817 tmp[2] = (product[4] >> 32) | (product[5] << 32);
818 tmp[3] = (product[6] << 32);
819 carry -= vli_sub(result, result, tmp, ndigits);
820
821 /* d4 */
822 tmp[0] = product[7];
823 tmp[1] = product[4] & 0xffffffff00000000ull;
824 tmp[2] = product[5];
825 tmp[3] = product[6] & 0xffffffff00000000ull;
826 carry -= vli_sub(result, result, tmp, ndigits);
827
828 if (carry < 0) {
829 do {
830 carry += vli_add(result, result, curve_prime, ndigits);
831 } while (carry < 0);
832 } else {
833 while (carry || vli_cmp(curve_prime, result, ndigits) != 1)
834 carry -= vli_sub(result, result, curve_prime, ndigits);
835 }
836}
837
838#define SL32OR32(x32, y32) (((u64)x32 << 32) | y32)
839#define AND64H(x64) (x64 & 0xffFFffFF00000000ull)
840#define AND64L(x64) (x64 & 0x00000000ffFFffFFull)
841
842/* Computes result = product % curve_prime
843 * from "Mathematical routines for the NIST prime elliptic curves"
844 */
845static void vli_mmod_fast_384(u64 *result, const u64 *product,
846 const u64 *curve_prime, u64 *tmp)
847{
848 int carry;
849 const unsigned int ndigits = ECC_CURVE_NIST_P384_DIGITS;
850
851 /* t */
852 vli_set(result, product, ndigits);
853
854 /* s1 */
855 tmp[0] = 0; // 0 || 0
856 tmp[1] = 0; // 0 || 0
857 tmp[2] = SL32OR32(product[11], (product[10]>>32)); //a22||a21
858 tmp[3] = product[11]>>32; // 0 ||a23
859 tmp[4] = 0; // 0 || 0
860 tmp[5] = 0; // 0 || 0
861 carry = vli_lshift(tmp, tmp, 1, ndigits);
862 carry += vli_add(result, result, tmp, ndigits);
863
864 /* s2 */
865 tmp[0] = product[6]; //a13||a12
866 tmp[1] = product[7]; //a15||a14
867 tmp[2] = product[8]; //a17||a16
868 tmp[3] = product[9]; //a19||a18
869 tmp[4] = product[10]; //a21||a20
870 tmp[5] = product[11]; //a23||a22
871 carry += vli_add(result, result, tmp, ndigits);
872
873 /* s3 */
874 tmp[0] = SL32OR32(product[11], (product[10]>>32)); //a22||a21
875 tmp[1] = SL32OR32(product[6], (product[11]>>32)); //a12||a23
876 tmp[2] = SL32OR32(product[7], (product[6])>>32); //a14||a13
877 tmp[3] = SL32OR32(product[8], (product[7]>>32)); //a16||a15
878 tmp[4] = SL32OR32(product[9], (product[8]>>32)); //a18||a17
879 tmp[5] = SL32OR32(product[10], (product[9]>>32)); //a20||a19
880 carry += vli_add(result, result, tmp, ndigits);
881
882 /* s4 */
883 tmp[0] = AND64H(product[11]); //a23|| 0
884 tmp[1] = (product[10]<<32); //a20|| 0
885 tmp[2] = product[6]; //a13||a12
886 tmp[3] = product[7]; //a15||a14
887 tmp[4] = product[8]; //a17||a16
888 tmp[5] = product[9]; //a19||a18
889 carry += vli_add(result, result, tmp, ndigits);
890
891 /* s5 */
892 tmp[0] = 0; // 0|| 0
893 tmp[1] = 0; // 0|| 0
894 tmp[2] = product[10]; //a21||a20
895 tmp[3] = product[11]; //a23||a22
896 tmp[4] = 0; // 0|| 0
897 tmp[5] = 0; // 0|| 0
898 carry += vli_add(result, result, tmp, ndigits);
899
900 /* s6 */
901 tmp[0] = AND64L(product[10]); // 0 ||a20
902 tmp[1] = AND64H(product[10]); //a21|| 0
903 tmp[2] = product[11]; //a23||a22
904 tmp[3] = 0; // 0 || 0
905 tmp[4] = 0; // 0 || 0
906 tmp[5] = 0; // 0 || 0
907 carry += vli_add(result, result, tmp, ndigits);
908
909 /* d1 */
910 tmp[0] = SL32OR32(product[6], (product[11]>>32)); //a12||a23
911 tmp[1] = SL32OR32(product[7], (product[6]>>32)); //a14||a13
912 tmp[2] = SL32OR32(product[8], (product[7]>>32)); //a16||a15
913 tmp[3] = SL32OR32(product[9], (product[8]>>32)); //a18||a17
914 tmp[4] = SL32OR32(product[10], (product[9]>>32)); //a20||a19
915 tmp[5] = SL32OR32(product[11], (product[10]>>32)); //a22||a21
916 carry -= vli_sub(result, result, tmp, ndigits);
917
918 /* d2 */
919 tmp[0] = (product[10]<<32); //a20|| 0
920 tmp[1] = SL32OR32(product[11], (product[10]>>32)); //a22||a21
921 tmp[2] = (product[11]>>32); // 0 ||a23
922 tmp[3] = 0; // 0 || 0
923 tmp[4] = 0; // 0 || 0
924 tmp[5] = 0; // 0 || 0
925 carry -= vli_sub(result, result, tmp, ndigits);
926
927 /* d3 */
928 tmp[0] = 0; // 0 || 0
929 tmp[1] = AND64H(product[11]); //a23|| 0
930 tmp[2] = product[11]>>32; // 0 ||a23
931 tmp[3] = 0; // 0 || 0
932 tmp[4] = 0; // 0 || 0
933 tmp[5] = 0; // 0 || 0
934 carry -= vli_sub(result, result, tmp, ndigits);
935
936 if (carry < 0) {
937 do {
938 carry += vli_add(result, result, curve_prime, ndigits);
939 } while (carry < 0);
940 } else {
941 while (carry || vli_cmp(curve_prime, result, ndigits) != 1)
942 carry -= vli_sub(result, result, curve_prime, ndigits);
943 }
944
945}
946
947#undef SL32OR32
948#undef AND64H
949#undef AND64L
950
951/*
952 * Computes result = product % curve_prime
953 * from "Recommendations for Discrete Logarithm-Based Cryptography:
954 * Elliptic Curve Domain Parameters" section G.1.4
955 */
956static void vli_mmod_fast_521(u64 *result, const u64 *product,
957 const u64 *curve_prime, u64 *tmp)
958{
959 const unsigned int ndigits = ECC_CURVE_NIST_P521_DIGITS;
960 size_t i;
961
962 /* Initialize result with lowest 521 bits from product */
963 vli_set(result, product, ndigits);
964 result[8] &= 0x1ff;
965
966 for (i = 0; i < ndigits; i++)
967 tmp[i] = (product[8 + i] >> 9) | (product[9 + i] << 55);
968 tmp[8] &= 0x1ff;
969
970 vli_mod_add(result, result, tmp, curve_prime, ndigits);
971}
972
973/* Computes result = product % curve_prime for different curve_primes.
974 *
975 * Note that curve_primes are distinguished just by heuristic check and
976 * not by complete conformance check.
977 */
978static bool vli_mmod_fast(u64 *result, u64 *product,
979 const struct ecc_curve *curve)
980{
981 u64 tmp[2 * ECC_MAX_DIGITS];
982 const u64 *curve_prime = curve->p;
983 const unsigned int ndigits = curve->g.ndigits;
984
985 /* All NIST curves have name prefix 'nist_' */
986 if (strncmp(curve->name, "nist_", 5) != 0) {
987 /* Try to handle Pseudo-Marsenne primes. */
988 if (curve_prime[ndigits - 1] == -1ull) {
989 vli_mmod_special(result, product, curve_prime,
990 ndigits);
991 return true;
992 } else if (curve_prime[ndigits - 1] == 1ull << 63 &&
993 curve_prime[ndigits - 2] == 0) {
994 vli_mmod_special2(result, product, curve_prime,
995 ndigits);
996 return true;
997 }
998 vli_mmod_barrett(result, product, curve_prime, ndigits);
999 return true;
1000 }
1001
1002 switch (ndigits) {
1003 case ECC_CURVE_NIST_P192_DIGITS:
1004 vli_mmod_fast_192(result, product, curve_prime, tmp);
1005 break;
1006 case ECC_CURVE_NIST_P256_DIGITS:
1007 vli_mmod_fast_256(result, product, curve_prime, tmp);
1008 break;
1009 case ECC_CURVE_NIST_P384_DIGITS:
1010 vli_mmod_fast_384(result, product, curve_prime, tmp);
1011 break;
1012 case ECC_CURVE_NIST_P521_DIGITS:
1013 vli_mmod_fast_521(result, product, curve_prime, tmp);
1014 break;
1015 default:
1016 pr_err_ratelimited("ecc: unsupported digits size!\n");
1017 return false;
1018 }
1019
1020 return true;
1021}
1022
1023/* Computes result = (left * right) % mod.
1024 * Assumes that mod is big enough curve order.
1025 */
1026void vli_mod_mult_slow(u64 *result, const u64 *left, const u64 *right,
1027 const u64 *mod, unsigned int ndigits)
1028{
1029 u64 product[ECC_MAX_DIGITS * 2];
1030
1031 vli_mult(product, left, right, ndigits);
1032 vli_mmod_slow(result, product, mod, ndigits);
1033}
1034EXPORT_SYMBOL(vli_mod_mult_slow);
1035
1036/* Computes result = (left * right) % curve_prime. */
1037static void vli_mod_mult_fast(u64 *result, const u64 *left, const u64 *right,
1038 const struct ecc_curve *curve)
1039{
1040 u64 product[2 * ECC_MAX_DIGITS];
1041
1042 vli_mult(product, left, right, curve->g.ndigits);
1043 vli_mmod_fast(result, product, curve);
1044}
1045
1046/* Computes result = left^2 % curve_prime. */
1047static void vli_mod_square_fast(u64 *result, const u64 *left,
1048 const struct ecc_curve *curve)
1049{
1050 u64 product[2 * ECC_MAX_DIGITS];
1051
1052 vli_square(product, left, curve->g.ndigits);
1053 vli_mmod_fast(result, product, curve);
1054}
1055
1056#define EVEN(vli) (!(vli[0] & 1))
1057/* Computes result = (1 / p_input) % mod. All VLIs are the same size.
1058 * See "From Euclid's GCD to Montgomery Multiplication to the Great Divide"
1059 * https://labs.oracle.com/techrep/2001/smli_tr-2001-95.pdf
1060 */
1061void vli_mod_inv(u64 *result, const u64 *input, const u64 *mod,
1062 unsigned int ndigits)
1063{
1064 u64 a[ECC_MAX_DIGITS], b[ECC_MAX_DIGITS];
1065 u64 u[ECC_MAX_DIGITS], v[ECC_MAX_DIGITS];
1066 u64 carry;
1067 int cmp_result;
1068
1069 if (vli_is_zero(input, ndigits)) {
1070 vli_clear(result, ndigits);
1071 return;
1072 }
1073
1074 vli_set(a, input, ndigits);
1075 vli_set(b, mod, ndigits);
1076 vli_clear(u, ndigits);
1077 u[0] = 1;
1078 vli_clear(v, ndigits);
1079
1080 while ((cmp_result = vli_cmp(a, b, ndigits)) != 0) {
1081 carry = 0;
1082
1083 if (EVEN(a)) {
1084 vli_rshift1(a, ndigits);
1085
1086 if (!EVEN(u))
1087 carry = vli_add(u, u, mod, ndigits);
1088
1089 vli_rshift1(u, ndigits);
1090 if (carry)
1091 u[ndigits - 1] |= 0x8000000000000000ull;
1092 } else if (EVEN(b)) {
1093 vli_rshift1(b, ndigits);
1094
1095 if (!EVEN(v))
1096 carry = vli_add(v, v, mod, ndigits);
1097
1098 vli_rshift1(v, ndigits);
1099 if (carry)
1100 v[ndigits - 1] |= 0x8000000000000000ull;
1101 } else if (cmp_result > 0) {
1102 vli_sub(a, a, b, ndigits);
1103 vli_rshift1(a, ndigits);
1104
1105 if (vli_cmp(u, v, ndigits) < 0)
1106 vli_add(u, u, mod, ndigits);
1107
1108 vli_sub(u, u, v, ndigits);
1109 if (!EVEN(u))
1110 carry = vli_add(u, u, mod, ndigits);
1111
1112 vli_rshift1(u, ndigits);
1113 if (carry)
1114 u[ndigits - 1] |= 0x8000000000000000ull;
1115 } else {
1116 vli_sub(b, b, a, ndigits);
1117 vli_rshift1(b, ndigits);
1118
1119 if (vli_cmp(v, u, ndigits) < 0)
1120 vli_add(v, v, mod, ndigits);
1121
1122 vli_sub(v, v, u, ndigits);
1123 if (!EVEN(v))
1124 carry = vli_add(v, v, mod, ndigits);
1125
1126 vli_rshift1(v, ndigits);
1127 if (carry)
1128 v[ndigits - 1] |= 0x8000000000000000ull;
1129 }
1130 }
1131
1132 vli_set(result, u, ndigits);
1133}
1134EXPORT_SYMBOL(vli_mod_inv);
1135
1136/* ------ Point operations ------ */
1137
1138/* Returns true if p_point is the point at infinity, false otherwise. */
1139bool ecc_point_is_zero(const struct ecc_point *point)
1140{
1141 return (vli_is_zero(point->x, point->ndigits) &&
1142 vli_is_zero(point->y, point->ndigits));
1143}
1144EXPORT_SYMBOL(ecc_point_is_zero);
1145
1146/* Point multiplication algorithm using Montgomery's ladder with co-Z
1147 * coordinates. From https://eprint.iacr.org/2011/338.pdf
1148 */
1149
1150/* Double in place */
1151static void ecc_point_double_jacobian(u64 *x1, u64 *y1, u64 *z1,
1152 const struct ecc_curve *curve)
1153{
1154 /* t1 = x, t2 = y, t3 = z */
1155 u64 t4[ECC_MAX_DIGITS];
1156 u64 t5[ECC_MAX_DIGITS];
1157 const u64 *curve_prime = curve->p;
1158 const unsigned int ndigits = curve->g.ndigits;
1159
1160 if (vli_is_zero(z1, ndigits))
1161 return;
1162
1163 /* t4 = y1^2 */
1164 vli_mod_square_fast(t4, y1, curve);
1165 /* t5 = x1*y1^2 = A */
1166 vli_mod_mult_fast(t5, x1, t4, curve);
1167 /* t4 = y1^4 */
1168 vli_mod_square_fast(t4, t4, curve);
1169 /* t2 = y1*z1 = z3 */
1170 vli_mod_mult_fast(y1, y1, z1, curve);
1171 /* t3 = z1^2 */
1172 vli_mod_square_fast(z1, z1, curve);
1173
1174 /* t1 = x1 + z1^2 */
1175 vli_mod_add(x1, x1, z1, curve_prime, ndigits);
1176 /* t3 = 2*z1^2 */
1177 vli_mod_add(z1, z1, z1, curve_prime, ndigits);
1178 /* t3 = x1 - z1^2 */
1179 vli_mod_sub(z1, x1, z1, curve_prime, ndigits);
1180 /* t1 = x1^2 - z1^4 */
1181 vli_mod_mult_fast(x1, x1, z1, curve);
1182
1183 /* t3 = 2*(x1^2 - z1^4) */
1184 vli_mod_add(z1, x1, x1, curve_prime, ndigits);
1185 /* t1 = 3*(x1^2 - z1^4) */
1186 vli_mod_add(x1, x1, z1, curve_prime, ndigits);
1187 if (vli_test_bit(x1, 0)) {
1188 u64 carry = vli_add(x1, x1, curve_prime, ndigits);
1189
1190 vli_rshift1(x1, ndigits);
1191 x1[ndigits - 1] |= carry << 63;
1192 } else {
1193 vli_rshift1(x1, ndigits);
1194 }
1195 /* t1 = 3/2*(x1^2 - z1^4) = B */
1196
1197 /* t3 = B^2 */
1198 vli_mod_square_fast(z1, x1, curve);
1199 /* t3 = B^2 - A */
1200 vli_mod_sub(z1, z1, t5, curve_prime, ndigits);
1201 /* t3 = B^2 - 2A = x3 */
1202 vli_mod_sub(z1, z1, t5, curve_prime, ndigits);
1203 /* t5 = A - x3 */
1204 vli_mod_sub(t5, t5, z1, curve_prime, ndigits);
1205 /* t1 = B * (A - x3) */
1206 vli_mod_mult_fast(x1, x1, t5, curve);
1207 /* t4 = B * (A - x3) - y1^4 = y3 */
1208 vli_mod_sub(t4, x1, t4, curve_prime, ndigits);
1209
1210 vli_set(x1, z1, ndigits);
1211 vli_set(z1, y1, ndigits);
1212 vli_set(y1, t4, ndigits);
1213}
1214
1215/* Modify (x1, y1) => (x1 * z^2, y1 * z^3) */
1216static void apply_z(u64 *x1, u64 *y1, u64 *z, const struct ecc_curve *curve)
1217{
1218 u64 t1[ECC_MAX_DIGITS];
1219
1220 vli_mod_square_fast(t1, z, curve); /* z^2 */
1221 vli_mod_mult_fast(x1, x1, t1, curve); /* x1 * z^2 */
1222 vli_mod_mult_fast(t1, t1, z, curve); /* z^3 */
1223 vli_mod_mult_fast(y1, y1, t1, curve); /* y1 * z^3 */
1224}
1225
1226/* P = (x1, y1) => 2P, (x2, y2) => P' */
1227static void xycz_initial_double(u64 *x1, u64 *y1, u64 *x2, u64 *y2,
1228 u64 *p_initial_z, const struct ecc_curve *curve)
1229{
1230 u64 z[ECC_MAX_DIGITS];
1231 const unsigned int ndigits = curve->g.ndigits;
1232
1233 vli_set(x2, x1, ndigits);
1234 vli_set(y2, y1, ndigits);
1235
1236 vli_clear(z, ndigits);
1237 z[0] = 1;
1238
1239 if (p_initial_z)
1240 vli_set(z, p_initial_z, ndigits);
1241
1242 apply_z(x1, y1, z, curve);
1243
1244 ecc_point_double_jacobian(x1, y1, z, curve);
1245
1246 apply_z(x2, y2, z, curve);
1247}
1248
1249/* Input P = (x1, y1, Z), Q = (x2, y2, Z)
1250 * Output P' = (x1', y1', Z3), P + Q = (x3, y3, Z3)
1251 * or P => P', Q => P + Q
1252 */
1253static void xycz_add(u64 *x1, u64 *y1, u64 *x2, u64 *y2,
1254 const struct ecc_curve *curve)
1255{
1256 /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
1257 u64 t5[ECC_MAX_DIGITS];
1258 const u64 *curve_prime = curve->p;
1259 const unsigned int ndigits = curve->g.ndigits;
1260
1261 /* t5 = x2 - x1 */
1262 vli_mod_sub(t5, x2, x1, curve_prime, ndigits);
1263 /* t5 = (x2 - x1)^2 = A */
1264 vli_mod_square_fast(t5, t5, curve);
1265 /* t1 = x1*A = B */
1266 vli_mod_mult_fast(x1, x1, t5, curve);
1267 /* t3 = x2*A = C */
1268 vli_mod_mult_fast(x2, x2, t5, curve);
1269 /* t4 = y2 - y1 */
1270 vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
1271 /* t5 = (y2 - y1)^2 = D */
1272 vli_mod_square_fast(t5, y2, curve);
1273
1274 /* t5 = D - B */
1275 vli_mod_sub(t5, t5, x1, curve_prime, ndigits);
1276 /* t5 = D - B - C = x3 */
1277 vli_mod_sub(t5, t5, x2, curve_prime, ndigits);
1278 /* t3 = C - B */
1279 vli_mod_sub(x2, x2, x1, curve_prime, ndigits);
1280 /* t2 = y1*(C - B) */
1281 vli_mod_mult_fast(y1, y1, x2, curve);
1282 /* t3 = B - x3 */
1283 vli_mod_sub(x2, x1, t5, curve_prime, ndigits);
1284 /* t4 = (y2 - y1)*(B - x3) */
1285 vli_mod_mult_fast(y2, y2, x2, curve);
1286 /* t4 = y3 */
1287 vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
1288
1289 vli_set(x2, t5, ndigits);
1290}
1291
1292/* Input P = (x1, y1, Z), Q = (x2, y2, Z)
1293 * Output P + Q = (x3, y3, Z3), P - Q = (x3', y3', Z3)
1294 * or P => P - Q, Q => P + Q
1295 */
1296static void xycz_add_c(u64 *x1, u64 *y1, u64 *x2, u64 *y2,
1297 const struct ecc_curve *curve)
1298{
1299 /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
1300 u64 t5[ECC_MAX_DIGITS];
1301 u64 t6[ECC_MAX_DIGITS];
1302 u64 t7[ECC_MAX_DIGITS];
1303 const u64 *curve_prime = curve->p;
1304 const unsigned int ndigits = curve->g.ndigits;
1305
1306 /* t5 = x2 - x1 */
1307 vli_mod_sub(t5, x2, x1, curve_prime, ndigits);
1308 /* t5 = (x2 - x1)^2 = A */
1309 vli_mod_square_fast(t5, t5, curve);
1310 /* t1 = x1*A = B */
1311 vli_mod_mult_fast(x1, x1, t5, curve);
1312 /* t3 = x2*A = C */
1313 vli_mod_mult_fast(x2, x2, t5, curve);
1314 /* t4 = y2 + y1 */
1315 vli_mod_add(t5, y2, y1, curve_prime, ndigits);
1316 /* t4 = y2 - y1 */
1317 vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
1318
1319 /* t6 = C - B */
1320 vli_mod_sub(t6, x2, x1, curve_prime, ndigits);
1321 /* t2 = y1 * (C - B) */
1322 vli_mod_mult_fast(y1, y1, t6, curve);
1323 /* t6 = B + C */
1324 vli_mod_add(t6, x1, x2, curve_prime, ndigits);
1325 /* t3 = (y2 - y1)^2 */
1326 vli_mod_square_fast(x2, y2, curve);
1327 /* t3 = x3 */
1328 vli_mod_sub(x2, x2, t6, curve_prime, ndigits);
1329
1330 /* t7 = B - x3 */
1331 vli_mod_sub(t7, x1, x2, curve_prime, ndigits);
1332 /* t4 = (y2 - y1)*(B - x3) */
1333 vli_mod_mult_fast(y2, y2, t7, curve);
1334 /* t4 = y3 */
1335 vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
1336
1337 /* t7 = (y2 + y1)^2 = F */
1338 vli_mod_square_fast(t7, t5, curve);
1339 /* t7 = x3' */
1340 vli_mod_sub(t7, t7, t6, curve_prime, ndigits);
1341 /* t6 = x3' - B */
1342 vli_mod_sub(t6, t7, x1, curve_prime, ndigits);
1343 /* t6 = (y2 + y1)*(x3' - B) */
1344 vli_mod_mult_fast(t6, t6, t5, curve);
1345 /* t2 = y3' */
1346 vli_mod_sub(y1, t6, y1, curve_prime, ndigits);
1347
1348 vli_set(x1, t7, ndigits);
1349}
1350
1351static void ecc_point_mult(struct ecc_point *result,
1352 const struct ecc_point *point, const u64 *scalar,
1353 u64 *initial_z, const struct ecc_curve *curve,
1354 unsigned int ndigits)
1355{
1356 /* R0 and R1 */
1357 u64 rx[2][ECC_MAX_DIGITS];
1358 u64 ry[2][ECC_MAX_DIGITS];
1359 u64 z[ECC_MAX_DIGITS];
1360 u64 sk[2][ECC_MAX_DIGITS];
1361 u64 *curve_prime = curve->p;
1362 int i, nb;
1363 int num_bits;
1364 int carry;
1365
1366 carry = vli_add(sk[0], scalar, curve->n, ndigits);
1367 vli_add(sk[1], sk[0], curve->n, ndigits);
1368 scalar = sk[!carry];
1369 if (curve->nbits == 521) /* NIST P521 */
1370 num_bits = curve->nbits + 2;
1371 else
1372 num_bits = sizeof(u64) * ndigits * 8 + 1;
1373
1374 vli_set(rx[1], point->x, ndigits);
1375 vli_set(ry[1], point->y, ndigits);
1376
1377 xycz_initial_double(rx[1], ry[1], rx[0], ry[0], initial_z, curve);
1378
1379 for (i = num_bits - 2; i > 0; i--) {
1380 nb = !vli_test_bit(scalar, i);
1381 xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb], curve);
1382 xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve);
1383 }
1384
1385 nb = !vli_test_bit(scalar, 0);
1386 xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb], curve);
1387
1388 /* Find final 1/Z value. */
1389 /* X1 - X0 */
1390 vli_mod_sub(z, rx[1], rx[0], curve_prime, ndigits);
1391 /* Yb * (X1 - X0) */
1392 vli_mod_mult_fast(z, z, ry[1 - nb], curve);
1393 /* xP * Yb * (X1 - X0) */
1394 vli_mod_mult_fast(z, z, point->x, curve);
1395
1396 /* 1 / (xP * Yb * (X1 - X0)) */
1397 vli_mod_inv(z, z, curve_prime, point->ndigits);
1398
1399 /* yP / (xP * Yb * (X1 - X0)) */
1400 vli_mod_mult_fast(z, z, point->y, curve);
1401 /* Xb * yP / (xP * Yb * (X1 - X0)) */
1402 vli_mod_mult_fast(z, z, rx[1 - nb], curve);
1403 /* End 1/Z calculation */
1404
1405 xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve);
1406
1407 apply_z(rx[0], ry[0], z, curve);
1408
1409 vli_set(result->x, rx[0], ndigits);
1410 vli_set(result->y, ry[0], ndigits);
1411}
1412
1413/* Computes R = P + Q mod p */
1414static void ecc_point_add(const struct ecc_point *result,
1415 const struct ecc_point *p, const struct ecc_point *q,
1416 const struct ecc_curve *curve)
1417{
1418 u64 z[ECC_MAX_DIGITS];
1419 u64 px[ECC_MAX_DIGITS];
1420 u64 py[ECC_MAX_DIGITS];
1421 unsigned int ndigits = curve->g.ndigits;
1422
1423 vli_set(result->x, q->x, ndigits);
1424 vli_set(result->y, q->y, ndigits);
1425 vli_mod_sub(z, result->x, p->x, curve->p, ndigits);
1426 vli_set(px, p->x, ndigits);
1427 vli_set(py, p->y, ndigits);
1428 xycz_add(px, py, result->x, result->y, curve);
1429 vli_mod_inv(z, z, curve->p, ndigits);
1430 apply_z(result->x, result->y, z, curve);
1431}
1432
1433/* Computes R = u1P + u2Q mod p using Shamir's trick.
1434 * Based on: Kenneth MacKay's micro-ecc (2014).
1435 */
1436void ecc_point_mult_shamir(const struct ecc_point *result,
1437 const u64 *u1, const struct ecc_point *p,
1438 const u64 *u2, const struct ecc_point *q,
1439 const struct ecc_curve *curve)
1440{
1441 u64 z[ECC_MAX_DIGITS];
1442 u64 sump[2][ECC_MAX_DIGITS];
1443 u64 *rx = result->x;
1444 u64 *ry = result->y;
1445 unsigned int ndigits = curve->g.ndigits;
1446 unsigned int num_bits;
1447 struct ecc_point sum = ECC_POINT_INIT(sump[0], sump[1], ndigits);
1448 const struct ecc_point *points[4];
1449 const struct ecc_point *point;
1450 unsigned int idx;
1451 int i;
1452
1453 ecc_point_add(&sum, p, q, curve);
1454 points[0] = NULL;
1455 points[1] = p;
1456 points[2] = q;
1457 points[3] = &sum;
1458
1459 num_bits = max(vli_num_bits(u1, ndigits), vli_num_bits(u2, ndigits));
1460 i = num_bits - 1;
1461 idx = !!vli_test_bit(u1, i);
1462 idx |= (!!vli_test_bit(u2, i)) << 1;
1463 point = points[idx];
1464
1465 vli_set(rx, point->x, ndigits);
1466 vli_set(ry, point->y, ndigits);
1467 vli_clear(z + 1, ndigits - 1);
1468 z[0] = 1;
1469
1470 for (--i; i >= 0; i--) {
1471 ecc_point_double_jacobian(rx, ry, z, curve);
1472 idx = !!vli_test_bit(u1, i);
1473 idx |= (!!vli_test_bit(u2, i)) << 1;
1474 point = points[idx];
1475 if (point) {
1476 u64 tx[ECC_MAX_DIGITS];
1477 u64 ty[ECC_MAX_DIGITS];
1478 u64 tz[ECC_MAX_DIGITS];
1479
1480 vli_set(tx, point->x, ndigits);
1481 vli_set(ty, point->y, ndigits);
1482 apply_z(tx, ty, z, curve);
1483 vli_mod_sub(tz, rx, tx, curve->p, ndigits);
1484 xycz_add(tx, ty, rx, ry, curve);
1485 vli_mod_mult_fast(z, z, tz, curve);
1486 }
1487 }
1488 vli_mod_inv(z, z, curve->p, ndigits);
1489 apply_z(rx, ry, z, curve);
1490}
1491EXPORT_SYMBOL(ecc_point_mult_shamir);
1492
1493/*
1494 * This function performs checks equivalent to Appendix A.4.2 of FIPS 186-5.
1495 * Whereas A.4.2 results in an integer in the interval [1, n-1], this function
1496 * ensures that the integer is in the range of [2, n-3]. We are slightly
1497 * stricter because of the currently used scalar multiplication algorithm.
1498 */
1499static int __ecc_is_key_valid(const struct ecc_curve *curve,
1500 const u64 *private_key, unsigned int ndigits)
1501{
1502 u64 one[ECC_MAX_DIGITS] = { 1, };
1503 u64 res[ECC_MAX_DIGITS];
1504
1505 if (!private_key)
1506 return -EINVAL;
1507
1508 if (curve->g.ndigits != ndigits)
1509 return -EINVAL;
1510
1511 /* Make sure the private key is in the range [2, n-3]. */
1512 if (vli_cmp(one, private_key, ndigits) != -1)
1513 return -EINVAL;
1514 vli_sub(res, curve->n, one, ndigits);
1515 vli_sub(res, res, one, ndigits);
1516 if (vli_cmp(res, private_key, ndigits) != 1)
1517 return -EINVAL;
1518
1519 return 0;
1520}
1521
1522int ecc_is_key_valid(unsigned int curve_id, unsigned int ndigits,
1523 const u64 *private_key, unsigned int private_key_len)
1524{
1525 int nbytes;
1526 const struct ecc_curve *curve = ecc_get_curve(curve_id);
1527
1528 nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT;
1529
1530 if (private_key_len != nbytes)
1531 return -EINVAL;
1532
1533 return __ecc_is_key_valid(curve, private_key, ndigits);
1534}
1535EXPORT_SYMBOL(ecc_is_key_valid);
1536
1537/*
1538 * ECC private keys are generated using the method of rejection sampling,
1539 * equivalent to that described in FIPS 186-5, Appendix A.2.2.
1540 *
1541 * This method generates a private key uniformly distributed in the range
1542 * [2, n-3].
1543 */
1544int ecc_gen_privkey(unsigned int curve_id, unsigned int ndigits,
1545 u64 *private_key)
1546{
1547 const struct ecc_curve *curve = ecc_get_curve(curve_id);
1548 unsigned int nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT;
1549 unsigned int nbits = vli_num_bits(curve->n, ndigits);
1550 int err;
1551
1552 /*
1553 * Step 1 & 2: check that N is included in Table 1 of FIPS 186-5,
1554 * section 6.1.1.
1555 */
1556 if (nbits < 224)
1557 return -EINVAL;
1558
1559 /*
1560 * FIPS 186-5 recommends that the private key should be obtained from a
1561 * RBG with a security strength equal to or greater than the security
1562 * strength associated with N.
1563 *
1564 * The maximum security strength identified by NIST SP800-57pt1r4 for
1565 * ECC is 256 (N >= 512).
1566 *
1567 * This condition is met by stdrng because it selects a favored DRBG
1568 * with a security strength of 256.
1569 */
1570 /* Step 3: obtain N returned_bits from the DRBG. */
1571 err = crypto_stdrng_get_bytes(private_key, nbytes);
1572 if (err)
1573 return err;
1574
1575 /* Step 4: make sure the private key is in the valid range. */
1576 if (__ecc_is_key_valid(curve, private_key, ndigits))
1577 return -EINVAL;
1578
1579 return 0;
1580}
1581EXPORT_SYMBOL(ecc_gen_privkey);
1582
1583int ecc_make_pub_key(unsigned int curve_id, unsigned int ndigits,
1584 const u64 *private_key, u64 *public_key)
1585{
1586 int ret = 0;
1587 struct ecc_point *pk;
1588 const struct ecc_curve *curve = ecc_get_curve(curve_id);
1589
1590 if (!private_key) {
1591 ret = -EINVAL;
1592 goto out;
1593 }
1594
1595 pk = ecc_alloc_point(ndigits);
1596 if (!pk) {
1597 ret = -ENOMEM;
1598 goto out;
1599 }
1600
1601 ecc_point_mult(pk, &curve->g, private_key, NULL, curve, ndigits);
1602
1603 /* SP800-56A rev 3 5.6.2.1.3 key check */
1604 if (ecc_is_pubkey_valid_full(curve, pk)) {
1605 ret = -EAGAIN;
1606 goto err_free_point;
1607 }
1608
1609 ecc_swap_digits(pk->x, public_key, ndigits);
1610 ecc_swap_digits(pk->y, &public_key[ndigits], ndigits);
1611
1612err_free_point:
1613 ecc_free_point(pk);
1614out:
1615 return ret;
1616}
1617EXPORT_SYMBOL(ecc_make_pub_key);
1618
1619/* SP800-56A section 5.6.2.3.4 partial verification: ephemeral keys only */
1620int ecc_is_pubkey_valid_partial(const struct ecc_curve *curve,
1621 struct ecc_point *pk)
1622{
1623 u64 yy[ECC_MAX_DIGITS], xxx[ECC_MAX_DIGITS], w[ECC_MAX_DIGITS];
1624
1625 if (WARN_ON(pk->ndigits != curve->g.ndigits))
1626 return -EINVAL;
1627
1628 /* Check 1: Verify key is not the zero point. */
1629 if (ecc_point_is_zero(pk))
1630 return -EINVAL;
1631
1632 /* Check 2: Verify key is in the range [1, p-1]. */
1633 if (vli_cmp(curve->p, pk->x, pk->ndigits) != 1)
1634 return -EINVAL;
1635 if (vli_cmp(curve->p, pk->y, pk->ndigits) != 1)
1636 return -EINVAL;
1637
1638 /* Check 3: Verify that y^2 == (x^3 + a·x + b) mod p */
1639 vli_mod_square_fast(yy, pk->y, curve); /* y^2 */
1640 vli_mod_square_fast(xxx, pk->x, curve); /* x^2 */
1641 vli_mod_mult_fast(xxx, xxx, pk->x, curve); /* x^3 */
1642 vli_mod_mult_fast(w, curve->a, pk->x, curve); /* a·x */
1643 vli_mod_add(w, w, curve->b, curve->p, pk->ndigits); /* a·x + b */
1644 vli_mod_add(w, w, xxx, curve->p, pk->ndigits); /* x^3 + a·x + b */
1645 if (vli_cmp(yy, w, pk->ndigits) != 0) /* Equation */
1646 return -EINVAL;
1647
1648 return 0;
1649}
1650EXPORT_SYMBOL(ecc_is_pubkey_valid_partial);
1651
1652/* SP800-56A section 5.6.2.3.3 full verification */
1653int ecc_is_pubkey_valid_full(const struct ecc_curve *curve,
1654 struct ecc_point *pk)
1655{
1656 struct ecc_point *nQ;
1657
1658 /* Checks 1 through 3 */
1659 int ret = ecc_is_pubkey_valid_partial(curve, pk);
1660
1661 if (ret)
1662 return ret;
1663
1664 /* Check 4: Verify that nQ is the zero point. */
1665 nQ = ecc_alloc_point(pk->ndigits);
1666 if (!nQ)
1667 return -ENOMEM;
1668
1669 ecc_point_mult(nQ, pk, curve->n, NULL, curve, pk->ndigits);
1670 if (!ecc_point_is_zero(nQ))
1671 ret = -EINVAL;
1672
1673 ecc_free_point(nQ);
1674
1675 return ret;
1676}
1677EXPORT_SYMBOL(ecc_is_pubkey_valid_full);
1678
1679int crypto_ecdh_shared_secret(unsigned int curve_id, unsigned int ndigits,
1680 const u64 *private_key, const u64 *public_key,
1681 u64 *secret)
1682{
1683 int ret = 0;
1684 struct ecc_point *product, *pk;
1685 u64 rand_z[ECC_MAX_DIGITS];
1686 unsigned int nbytes;
1687 const struct ecc_curve *curve = ecc_get_curve(curve_id);
1688
1689 if (!private_key || !public_key || ndigits > ARRAY_SIZE(rand_z)) {
1690 ret = -EINVAL;
1691 goto out;
1692 }
1693
1694 nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT;
1695
1696 get_random_bytes(rand_z, nbytes);
1697
1698 pk = ecc_alloc_point(ndigits);
1699 if (!pk) {
1700 ret = -ENOMEM;
1701 goto out;
1702 }
1703
1704 ecc_swap_digits(public_key, pk->x, ndigits);
1705 ecc_swap_digits(&public_key[ndigits], pk->y, ndigits);
1706 ret = ecc_is_pubkey_valid_partial(curve, pk);
1707 if (ret)
1708 goto err_alloc_product;
1709
1710 product = ecc_alloc_point(ndigits);
1711 if (!product) {
1712 ret = -ENOMEM;
1713 goto err_alloc_product;
1714 }
1715
1716 ecc_point_mult(product, pk, private_key, rand_z, curve, ndigits);
1717
1718 if (ecc_point_is_zero(product)) {
1719 ret = -EFAULT;
1720 goto err_validity;
1721 }
1722
1723 ecc_swap_digits(product->x, secret, ndigits);
1724
1725err_validity:
1726 memzero_explicit(rand_z, sizeof(rand_z));
1727 ecc_free_point(product);
1728err_alloc_product:
1729 ecc_free_point(pk);
1730out:
1731 return ret;
1732}
1733EXPORT_SYMBOL(crypto_ecdh_shared_secret);
1734
1735MODULE_DESCRIPTION("core elliptic curve module");
1736MODULE_LICENSE("Dual BSD/GPL");