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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#include <crypto/rng.h>
33
34#include "ecc.h"
35#include "ecc_curve_defs.h"
36
37typedef struct {
38 u64 m_low;
39 u64 m_high;
40} uint128_t;
41
42static inline const struct ecc_curve *ecc_get_curve(unsigned int curve_id)
43{
44 switch (curve_id) {
45 /* In FIPS mode only allow P256 and higher */
46 case ECC_CURVE_NIST_P192:
47 return fips_enabled ? NULL : &nist_p192;
48 case ECC_CURVE_NIST_P256:
49 return &nist_p256;
50 default:
51 return NULL;
52 }
53}
54
55static u64 *ecc_alloc_digits_space(unsigned int ndigits)
56{
57 size_t len = ndigits * sizeof(u64);
58
59 if (!len)
60 return NULL;
61
62 return kmalloc(len, GFP_KERNEL);
63}
64
65static void ecc_free_digits_space(u64 *space)
66{
67 kzfree(space);
68}
69
70static struct ecc_point *ecc_alloc_point(unsigned int ndigits)
71{
72 struct ecc_point *p = kmalloc(sizeof(*p), GFP_KERNEL);
73
74 if (!p)
75 return NULL;
76
77 p->x = ecc_alloc_digits_space(ndigits);
78 if (!p->x)
79 goto err_alloc_x;
80
81 p->y = ecc_alloc_digits_space(ndigits);
82 if (!p->y)
83 goto err_alloc_y;
84
85 p->ndigits = ndigits;
86
87 return p;
88
89err_alloc_y:
90 ecc_free_digits_space(p->x);
91err_alloc_x:
92 kfree(p);
93 return NULL;
94}
95
96static void ecc_free_point(struct ecc_point *p)
97{
98 if (!p)
99 return;
100
101 kzfree(p->x);
102 kzfree(p->y);
103 kzfree(p);
104}
105
106static void vli_clear(u64 *vli, unsigned int ndigits)
107{
108 int i;
109
110 for (i = 0; i < ndigits; i++)
111 vli[i] = 0;
112}
113
114/* Returns true if vli == 0, false otherwise. */
115static bool vli_is_zero(const u64 *vli, unsigned int ndigits)
116{
117 int i;
118
119 for (i = 0; i < ndigits; i++) {
120 if (vli[i])
121 return false;
122 }
123
124 return true;
125}
126
127/* Returns nonzero if bit bit of vli is set. */
128static u64 vli_test_bit(const u64 *vli, unsigned int bit)
129{
130 return (vli[bit / 64] & ((u64)1 << (bit % 64)));
131}
132
133/* Counts the number of 64-bit "digits" in vli. */
134static unsigned int vli_num_digits(const u64 *vli, unsigned int ndigits)
135{
136 int i;
137
138 /* Search from the end until we find a non-zero digit.
139 * We do it in reverse because we expect that most digits will
140 * be nonzero.
141 */
142 for (i = ndigits - 1; i >= 0 && vli[i] == 0; i--);
143
144 return (i + 1);
145}
146
147/* Counts the number of bits required for vli. */
148static unsigned int vli_num_bits(const u64 *vli, unsigned int ndigits)
149{
150 unsigned int i, num_digits;
151 u64 digit;
152
153 num_digits = vli_num_digits(vli, ndigits);
154 if (num_digits == 0)
155 return 0;
156
157 digit = vli[num_digits - 1];
158 for (i = 0; digit; i++)
159 digit >>= 1;
160
161 return ((num_digits - 1) * 64 + i);
162}
163
164/* Sets dest = src. */
165static void vli_set(u64 *dest, const u64 *src, unsigned int ndigits)
166{
167 int i;
168
169 for (i = 0; i < ndigits; i++)
170 dest[i] = src[i];
171}
172
173/* Returns sign of left - right. */
174static int vli_cmp(const u64 *left, const u64 *right, unsigned int ndigits)
175{
176 int i;
177
178 for (i = ndigits - 1; i >= 0; i--) {
179 if (left[i] > right[i])
180 return 1;
181 else if (left[i] < right[i])
182 return -1;
183 }
184
185 return 0;
186}
187
188/* Computes result = in << c, returning carry. Can modify in place
189 * (if result == in). 0 < shift < 64.
190 */
191static u64 vli_lshift(u64 *result, const u64 *in, unsigned int shift,
192 unsigned int ndigits)
193{
194 u64 carry = 0;
195 int i;
196
197 for (i = 0; i < ndigits; i++) {
198 u64 temp = in[i];
199
200 result[i] = (temp << shift) | carry;
201 carry = temp >> (64 - shift);
202 }
203
204 return carry;
205}
206
207/* Computes vli = vli >> 1. */
208static void vli_rshift1(u64 *vli, unsigned int ndigits)
209{
210 u64 *end = vli;
211 u64 carry = 0;
212
213 vli += ndigits;
214
215 while (vli-- > end) {
216 u64 temp = *vli;
217 *vli = (temp >> 1) | carry;
218 carry = temp << 63;
219 }
220}
221
222/* Computes result = left + right, returning carry. Can modify in place. */
223static u64 vli_add(u64 *result, const u64 *left, const u64 *right,
224 unsigned int ndigits)
225{
226 u64 carry = 0;
227 int i;
228
229 for (i = 0; i < ndigits; i++) {
230 u64 sum;
231
232 sum = left[i] + right[i] + carry;
233 if (sum != left[i])
234 carry = (sum < left[i]);
235
236 result[i] = sum;
237 }
238
239 return carry;
240}
241
242/* Computes result = left - right, returning borrow. Can modify in place. */
243static u64 vli_sub(u64 *result, const u64 *left, const u64 *right,
244 unsigned int ndigits)
245{
246 u64 borrow = 0;
247 int i;
248
249 for (i = 0; i < ndigits; i++) {
250 u64 diff;
251
252 diff = left[i] - right[i] - borrow;
253 if (diff != left[i])
254 borrow = (diff > left[i]);
255
256 result[i] = diff;
257 }
258
259 return borrow;
260}
261
262static uint128_t mul_64_64(u64 left, u64 right)
263{
264 u64 a0 = left & 0xffffffffull;
265 u64 a1 = left >> 32;
266 u64 b0 = right & 0xffffffffull;
267 u64 b1 = right >> 32;
268 u64 m0 = a0 * b0;
269 u64 m1 = a0 * b1;
270 u64 m2 = a1 * b0;
271 u64 m3 = a1 * b1;
272 uint128_t result;
273
274 m2 += (m0 >> 32);
275 m2 += m1;
276
277 /* Overflow */
278 if (m2 < m1)
279 m3 += 0x100000000ull;
280
281 result.m_low = (m0 & 0xffffffffull) | (m2 << 32);
282 result.m_high = m3 + (m2 >> 32);
283
284 return result;
285}
286
287static uint128_t add_128_128(uint128_t a, uint128_t b)
288{
289 uint128_t result;
290
291 result.m_low = a.m_low + b.m_low;
292 result.m_high = a.m_high + b.m_high + (result.m_low < a.m_low);
293
294 return result;
295}
296
297static void vli_mult(u64 *result, const u64 *left, const u64 *right,
298 unsigned int ndigits)
299{
300 uint128_t r01 = { 0, 0 };
301 u64 r2 = 0;
302 unsigned int i, k;
303
304 /* Compute each digit of result in sequence, maintaining the
305 * carries.
306 */
307 for (k = 0; k < ndigits * 2 - 1; k++) {
308 unsigned int min;
309
310 if (k < ndigits)
311 min = 0;
312 else
313 min = (k + 1) - ndigits;
314
315 for (i = min; i <= k && i < ndigits; i++) {
316 uint128_t product;
317
318 product = mul_64_64(left[i], right[k - i]);
319
320 r01 = add_128_128(r01, product);
321 r2 += (r01.m_high < product.m_high);
322 }
323
324 result[k] = r01.m_low;
325 r01.m_low = r01.m_high;
326 r01.m_high = r2;
327 r2 = 0;
328 }
329
330 result[ndigits * 2 - 1] = r01.m_low;
331}
332
333static void vli_square(u64 *result, const u64 *left, unsigned int ndigits)
334{
335 uint128_t r01 = { 0, 0 };
336 u64 r2 = 0;
337 int i, k;
338
339 for (k = 0; k < ndigits * 2 - 1; k++) {
340 unsigned int min;
341
342 if (k < ndigits)
343 min = 0;
344 else
345 min = (k + 1) - ndigits;
346
347 for (i = min; i <= k && i <= k - i; i++) {
348 uint128_t product;
349
350 product = mul_64_64(left[i], left[k - i]);
351
352 if (i < k - i) {
353 r2 += product.m_high >> 63;
354 product.m_high = (product.m_high << 1) |
355 (product.m_low >> 63);
356 product.m_low <<= 1;
357 }
358
359 r01 = add_128_128(r01, product);
360 r2 += (r01.m_high < product.m_high);
361 }
362
363 result[k] = r01.m_low;
364 r01.m_low = r01.m_high;
365 r01.m_high = r2;
366 r2 = 0;
367 }
368
369 result[ndigits * 2 - 1] = r01.m_low;
370}
371
372/* Computes result = (left + right) % mod.
373 * Assumes that left < mod and right < mod, result != mod.
374 */
375static void vli_mod_add(u64 *result, const u64 *left, const u64 *right,
376 const u64 *mod, unsigned int ndigits)
377{
378 u64 carry;
379
380 carry = vli_add(result, left, right, ndigits);
381
382 /* result > mod (result = mod + remainder), so subtract mod to
383 * get remainder.
384 */
385 if (carry || vli_cmp(result, mod, ndigits) >= 0)
386 vli_sub(result, result, mod, ndigits);
387}
388
389/* Computes result = (left - right) % mod.
390 * Assumes that left < mod and right < mod, result != mod.
391 */
392static void vli_mod_sub(u64 *result, const u64 *left, const u64 *right,
393 const u64 *mod, unsigned int ndigits)
394{
395 u64 borrow = vli_sub(result, left, right, ndigits);
396
397 /* In this case, p_result == -diff == (max int) - diff.
398 * Since -x % d == d - x, we can get the correct result from
399 * result + mod (with overflow).
400 */
401 if (borrow)
402 vli_add(result, result, mod, ndigits);
403}
404
405/* Computes p_result = p_product % curve_p.
406 * See algorithm 5 and 6 from
407 * http://www.isys.uni-klu.ac.at/PDF/2001-0126-MT.pdf
408 */
409static void vli_mmod_fast_192(u64 *result, const u64 *product,
410 const u64 *curve_prime, u64 *tmp)
411{
412 const unsigned int ndigits = 3;
413 int carry;
414
415 vli_set(result, product, ndigits);
416
417 vli_set(tmp, &product[3], ndigits);
418 carry = vli_add(result, result, tmp, ndigits);
419
420 tmp[0] = 0;
421 tmp[1] = product[3];
422 tmp[2] = product[4];
423 carry += vli_add(result, result, tmp, ndigits);
424
425 tmp[0] = tmp[1] = product[5];
426 tmp[2] = 0;
427 carry += vli_add(result, result, tmp, ndigits);
428
429 while (carry || vli_cmp(curve_prime, result, ndigits) != 1)
430 carry -= vli_sub(result, result, curve_prime, ndigits);
431}
432
433/* Computes result = product % curve_prime
434 * from http://www.nsa.gov/ia/_files/nist-routines.pdf
435 */
436static void vli_mmod_fast_256(u64 *result, const u64 *product,
437 const u64 *curve_prime, u64 *tmp)
438{
439 int carry;
440 const unsigned int ndigits = 4;
441
442 /* t */
443 vli_set(result, product, ndigits);
444
445 /* s1 */
446 tmp[0] = 0;
447 tmp[1] = product[5] & 0xffffffff00000000ull;
448 tmp[2] = product[6];
449 tmp[3] = product[7];
450 carry = vli_lshift(tmp, tmp, 1, ndigits);
451 carry += vli_add(result, result, tmp, ndigits);
452
453 /* s2 */
454 tmp[1] = product[6] << 32;
455 tmp[2] = (product[6] >> 32) | (product[7] << 32);
456 tmp[3] = product[7] >> 32;
457 carry += vli_lshift(tmp, tmp, 1, ndigits);
458 carry += vli_add(result, result, tmp, ndigits);
459
460 /* s3 */
461 tmp[0] = product[4];
462 tmp[1] = product[5] & 0xffffffff;
463 tmp[2] = 0;
464 tmp[3] = product[7];
465 carry += vli_add(result, result, tmp, ndigits);
466
467 /* s4 */
468 tmp[0] = (product[4] >> 32) | (product[5] << 32);
469 tmp[1] = (product[5] >> 32) | (product[6] & 0xffffffff00000000ull);
470 tmp[2] = product[7];
471 tmp[3] = (product[6] >> 32) | (product[4] << 32);
472 carry += vli_add(result, result, tmp, ndigits);
473
474 /* d1 */
475 tmp[0] = (product[5] >> 32) | (product[6] << 32);
476 tmp[1] = (product[6] >> 32);
477 tmp[2] = 0;
478 tmp[3] = (product[4] & 0xffffffff) | (product[5] << 32);
479 carry -= vli_sub(result, result, tmp, ndigits);
480
481 /* d2 */
482 tmp[0] = product[6];
483 tmp[1] = product[7];
484 tmp[2] = 0;
485 tmp[3] = (product[4] >> 32) | (product[5] & 0xffffffff00000000ull);
486 carry -= vli_sub(result, result, tmp, ndigits);
487
488 /* d3 */
489 tmp[0] = (product[6] >> 32) | (product[7] << 32);
490 tmp[1] = (product[7] >> 32) | (product[4] << 32);
491 tmp[2] = (product[4] >> 32) | (product[5] << 32);
492 tmp[3] = (product[6] << 32);
493 carry -= vli_sub(result, result, tmp, ndigits);
494
495 /* d4 */
496 tmp[0] = product[7];
497 tmp[1] = product[4] & 0xffffffff00000000ull;
498 tmp[2] = product[5];
499 tmp[3] = product[6] & 0xffffffff00000000ull;
500 carry -= vli_sub(result, result, tmp, ndigits);
501
502 if (carry < 0) {
503 do {
504 carry += vli_add(result, result, curve_prime, ndigits);
505 } while (carry < 0);
506 } else {
507 while (carry || vli_cmp(curve_prime, result, ndigits) != 1)
508 carry -= vli_sub(result, result, curve_prime, ndigits);
509 }
510}
511
512/* Computes result = product % curve_prime
513 * from http://www.nsa.gov/ia/_files/nist-routines.pdf
514*/
515static bool vli_mmod_fast(u64 *result, u64 *product,
516 const u64 *curve_prime, unsigned int ndigits)
517{
518 u64 tmp[2 * ndigits];
519
520 switch (ndigits) {
521 case 3:
522 vli_mmod_fast_192(result, product, curve_prime, tmp);
523 break;
524 case 4:
525 vli_mmod_fast_256(result, product, curve_prime, tmp);
526 break;
527 default:
528 pr_err("unsupports digits size!\n");
529 return false;
530 }
531
532 return true;
533}
534
535/* Computes result = (left * right) % curve_prime. */
536static void vli_mod_mult_fast(u64 *result, const u64 *left, const u64 *right,
537 const u64 *curve_prime, unsigned int ndigits)
538{
539 u64 product[2 * ndigits];
540
541 vli_mult(product, left, right, ndigits);
542 vli_mmod_fast(result, product, curve_prime, ndigits);
543}
544
545/* Computes result = left^2 % curve_prime. */
546static void vli_mod_square_fast(u64 *result, const u64 *left,
547 const u64 *curve_prime, unsigned int ndigits)
548{
549 u64 product[2 * ndigits];
550
551 vli_square(product, left, ndigits);
552 vli_mmod_fast(result, product, curve_prime, ndigits);
553}
554
555#define EVEN(vli) (!(vli[0] & 1))
556/* Computes result = (1 / p_input) % mod. All VLIs are the same size.
557 * See "From Euclid's GCD to Montgomery Multiplication to the Great Divide"
558 * https://labs.oracle.com/techrep/2001/smli_tr-2001-95.pdf
559 */
560static void vli_mod_inv(u64 *result, const u64 *input, const u64 *mod,
561 unsigned int ndigits)
562{
563 u64 a[ndigits], b[ndigits];
564 u64 u[ndigits], v[ndigits];
565 u64 carry;
566 int cmp_result;
567
568 if (vli_is_zero(input, ndigits)) {
569 vli_clear(result, ndigits);
570 return;
571 }
572
573 vli_set(a, input, ndigits);
574 vli_set(b, mod, ndigits);
575 vli_clear(u, ndigits);
576 u[0] = 1;
577 vli_clear(v, ndigits);
578
579 while ((cmp_result = vli_cmp(a, b, ndigits)) != 0) {
580 carry = 0;
581
582 if (EVEN(a)) {
583 vli_rshift1(a, ndigits);
584
585 if (!EVEN(u))
586 carry = vli_add(u, u, mod, ndigits);
587
588 vli_rshift1(u, ndigits);
589 if (carry)
590 u[ndigits - 1] |= 0x8000000000000000ull;
591 } else if (EVEN(b)) {
592 vli_rshift1(b, ndigits);
593
594 if (!EVEN(v))
595 carry = vli_add(v, v, mod, ndigits);
596
597 vli_rshift1(v, ndigits);
598 if (carry)
599 v[ndigits - 1] |= 0x8000000000000000ull;
600 } else if (cmp_result > 0) {
601 vli_sub(a, a, b, ndigits);
602 vli_rshift1(a, ndigits);
603
604 if (vli_cmp(u, v, ndigits) < 0)
605 vli_add(u, u, mod, ndigits);
606
607 vli_sub(u, u, v, ndigits);
608 if (!EVEN(u))
609 carry = vli_add(u, u, mod, ndigits);
610
611 vli_rshift1(u, ndigits);
612 if (carry)
613 u[ndigits - 1] |= 0x8000000000000000ull;
614 } else {
615 vli_sub(b, b, a, ndigits);
616 vli_rshift1(b, ndigits);
617
618 if (vli_cmp(v, u, ndigits) < 0)
619 vli_add(v, v, mod, ndigits);
620
621 vli_sub(v, v, u, ndigits);
622 if (!EVEN(v))
623 carry = vli_add(v, v, mod, ndigits);
624
625 vli_rshift1(v, ndigits);
626 if (carry)
627 v[ndigits - 1] |= 0x8000000000000000ull;
628 }
629 }
630
631 vli_set(result, u, ndigits);
632}
633
634/* ------ Point operations ------ */
635
636/* Returns true if p_point is the point at infinity, false otherwise. */
637static bool ecc_point_is_zero(const struct ecc_point *point)
638{
639 return (vli_is_zero(point->x, point->ndigits) &&
640 vli_is_zero(point->y, point->ndigits));
641}
642
643/* Point multiplication algorithm using Montgomery's ladder with co-Z
644 * coordinates. From http://eprint.iacr.org/2011/338.pdf
645 */
646
647/* Double in place */
648static void ecc_point_double_jacobian(u64 *x1, u64 *y1, u64 *z1,
649 u64 *curve_prime, unsigned int ndigits)
650{
651 /* t1 = x, t2 = y, t3 = z */
652 u64 t4[ndigits];
653 u64 t5[ndigits];
654
655 if (vli_is_zero(z1, ndigits))
656 return;
657
658 /* t4 = y1^2 */
659 vli_mod_square_fast(t4, y1, curve_prime, ndigits);
660 /* t5 = x1*y1^2 = A */
661 vli_mod_mult_fast(t5, x1, t4, curve_prime, ndigits);
662 /* t4 = y1^4 */
663 vli_mod_square_fast(t4, t4, curve_prime, ndigits);
664 /* t2 = y1*z1 = z3 */
665 vli_mod_mult_fast(y1, y1, z1, curve_prime, ndigits);
666 /* t3 = z1^2 */
667 vli_mod_square_fast(z1, z1, curve_prime, ndigits);
668
669 /* t1 = x1 + z1^2 */
670 vli_mod_add(x1, x1, z1, curve_prime, ndigits);
671 /* t3 = 2*z1^2 */
672 vli_mod_add(z1, z1, z1, curve_prime, ndigits);
673 /* t3 = x1 - z1^2 */
674 vli_mod_sub(z1, x1, z1, curve_prime, ndigits);
675 /* t1 = x1^2 - z1^4 */
676 vli_mod_mult_fast(x1, x1, z1, curve_prime, ndigits);
677
678 /* t3 = 2*(x1^2 - z1^4) */
679 vli_mod_add(z1, x1, x1, curve_prime, ndigits);
680 /* t1 = 3*(x1^2 - z1^4) */
681 vli_mod_add(x1, x1, z1, curve_prime, ndigits);
682 if (vli_test_bit(x1, 0)) {
683 u64 carry = vli_add(x1, x1, curve_prime, ndigits);
684
685 vli_rshift1(x1, ndigits);
686 x1[ndigits - 1] |= carry << 63;
687 } else {
688 vli_rshift1(x1, ndigits);
689 }
690 /* t1 = 3/2*(x1^2 - z1^4) = B */
691
692 /* t3 = B^2 */
693 vli_mod_square_fast(z1, x1, curve_prime, ndigits);
694 /* t3 = B^2 - A */
695 vli_mod_sub(z1, z1, t5, curve_prime, ndigits);
696 /* t3 = B^2 - 2A = x3 */
697 vli_mod_sub(z1, z1, t5, curve_prime, ndigits);
698 /* t5 = A - x3 */
699 vli_mod_sub(t5, t5, z1, curve_prime, ndigits);
700 /* t1 = B * (A - x3) */
701 vli_mod_mult_fast(x1, x1, t5, curve_prime, ndigits);
702 /* t4 = B * (A - x3) - y1^4 = y3 */
703 vli_mod_sub(t4, x1, t4, curve_prime, ndigits);
704
705 vli_set(x1, z1, ndigits);
706 vli_set(z1, y1, ndigits);
707 vli_set(y1, t4, ndigits);
708}
709
710/* Modify (x1, y1) => (x1 * z^2, y1 * z^3) */
711static void apply_z(u64 *x1, u64 *y1, u64 *z, u64 *curve_prime,
712 unsigned int ndigits)
713{
714 u64 t1[ndigits];
715
716 vli_mod_square_fast(t1, z, curve_prime, ndigits); /* z^2 */
717 vli_mod_mult_fast(x1, x1, t1, curve_prime, ndigits); /* x1 * z^2 */
718 vli_mod_mult_fast(t1, t1, z, curve_prime, ndigits); /* z^3 */
719 vli_mod_mult_fast(y1, y1, t1, curve_prime, ndigits); /* y1 * z^3 */
720}
721
722/* P = (x1, y1) => 2P, (x2, y2) => P' */
723static void xycz_initial_double(u64 *x1, u64 *y1, u64 *x2, u64 *y2,
724 u64 *p_initial_z, u64 *curve_prime,
725 unsigned int ndigits)
726{
727 u64 z[ndigits];
728
729 vli_set(x2, x1, ndigits);
730 vli_set(y2, y1, ndigits);
731
732 vli_clear(z, ndigits);
733 z[0] = 1;
734
735 if (p_initial_z)
736 vli_set(z, p_initial_z, ndigits);
737
738 apply_z(x1, y1, z, curve_prime, ndigits);
739
740 ecc_point_double_jacobian(x1, y1, z, curve_prime, ndigits);
741
742 apply_z(x2, y2, z, curve_prime, ndigits);
743}
744
745/* Input P = (x1, y1, Z), Q = (x2, y2, Z)
746 * Output P' = (x1', y1', Z3), P + Q = (x3, y3, Z3)
747 * or P => P', Q => P + Q
748 */
749static void xycz_add(u64 *x1, u64 *y1, u64 *x2, u64 *y2, u64 *curve_prime,
750 unsigned int ndigits)
751{
752 /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
753 u64 t5[ndigits];
754
755 /* t5 = x2 - x1 */
756 vli_mod_sub(t5, x2, x1, curve_prime, ndigits);
757 /* t5 = (x2 - x1)^2 = A */
758 vli_mod_square_fast(t5, t5, curve_prime, ndigits);
759 /* t1 = x1*A = B */
760 vli_mod_mult_fast(x1, x1, t5, curve_prime, ndigits);
761 /* t3 = x2*A = C */
762 vli_mod_mult_fast(x2, x2, t5, curve_prime, ndigits);
763 /* t4 = y2 - y1 */
764 vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
765 /* t5 = (y2 - y1)^2 = D */
766 vli_mod_square_fast(t5, y2, curve_prime, ndigits);
767
768 /* t5 = D - B */
769 vli_mod_sub(t5, t5, x1, curve_prime, ndigits);
770 /* t5 = D - B - C = x3 */
771 vli_mod_sub(t5, t5, x2, curve_prime, ndigits);
772 /* t3 = C - B */
773 vli_mod_sub(x2, x2, x1, curve_prime, ndigits);
774 /* t2 = y1*(C - B) */
775 vli_mod_mult_fast(y1, y1, x2, curve_prime, ndigits);
776 /* t3 = B - x3 */
777 vli_mod_sub(x2, x1, t5, curve_prime, ndigits);
778 /* t4 = (y2 - y1)*(B - x3) */
779 vli_mod_mult_fast(y2, y2, x2, curve_prime, ndigits);
780 /* t4 = y3 */
781 vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
782
783 vli_set(x2, t5, ndigits);
784}
785
786/* Input P = (x1, y1, Z), Q = (x2, y2, Z)
787 * Output P + Q = (x3, y3, Z3), P - Q = (x3', y3', Z3)
788 * or P => P - Q, Q => P + Q
789 */
790static void xycz_add_c(u64 *x1, u64 *y1, u64 *x2, u64 *y2, u64 *curve_prime,
791 unsigned int ndigits)
792{
793 /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
794 u64 t5[ndigits];
795 u64 t6[ndigits];
796 u64 t7[ndigits];
797
798 /* t5 = x2 - x1 */
799 vli_mod_sub(t5, x2, x1, curve_prime, ndigits);
800 /* t5 = (x2 - x1)^2 = A */
801 vli_mod_square_fast(t5, t5, curve_prime, ndigits);
802 /* t1 = x1*A = B */
803 vli_mod_mult_fast(x1, x1, t5, curve_prime, ndigits);
804 /* t3 = x2*A = C */
805 vli_mod_mult_fast(x2, x2, t5, curve_prime, ndigits);
806 /* t4 = y2 + y1 */
807 vli_mod_add(t5, y2, y1, curve_prime, ndigits);
808 /* t4 = y2 - y1 */
809 vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
810
811 /* t6 = C - B */
812 vli_mod_sub(t6, x2, x1, curve_prime, ndigits);
813 /* t2 = y1 * (C - B) */
814 vli_mod_mult_fast(y1, y1, t6, curve_prime, ndigits);
815 /* t6 = B + C */
816 vli_mod_add(t6, x1, x2, curve_prime, ndigits);
817 /* t3 = (y2 - y1)^2 */
818 vli_mod_square_fast(x2, y2, curve_prime, ndigits);
819 /* t3 = x3 */
820 vli_mod_sub(x2, x2, t6, curve_prime, ndigits);
821
822 /* t7 = B - x3 */
823 vli_mod_sub(t7, x1, x2, curve_prime, ndigits);
824 /* t4 = (y2 - y1)*(B - x3) */
825 vli_mod_mult_fast(y2, y2, t7, curve_prime, ndigits);
826 /* t4 = y3 */
827 vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
828
829 /* t7 = (y2 + y1)^2 = F */
830 vli_mod_square_fast(t7, t5, curve_prime, ndigits);
831 /* t7 = x3' */
832 vli_mod_sub(t7, t7, t6, curve_prime, ndigits);
833 /* t6 = x3' - B */
834 vli_mod_sub(t6, t7, x1, curve_prime, ndigits);
835 /* t6 = (y2 + y1)*(x3' - B) */
836 vli_mod_mult_fast(t6, t6, t5, curve_prime, ndigits);
837 /* t2 = y3' */
838 vli_mod_sub(y1, t6, y1, curve_prime, ndigits);
839
840 vli_set(x1, t7, ndigits);
841}
842
843static void ecc_point_mult(struct ecc_point *result,
844 const struct ecc_point *point, const u64 *scalar,
845 u64 *initial_z, u64 *curve_prime,
846 unsigned int ndigits)
847{
848 /* R0 and R1 */
849 u64 rx[2][ndigits];
850 u64 ry[2][ndigits];
851 u64 z[ndigits];
852 int i, nb;
853 int num_bits = vli_num_bits(scalar, ndigits);
854
855 vli_set(rx[1], point->x, ndigits);
856 vli_set(ry[1], point->y, ndigits);
857
858 xycz_initial_double(rx[1], ry[1], rx[0], ry[0], initial_z, curve_prime,
859 ndigits);
860
861 for (i = num_bits - 2; i > 0; i--) {
862 nb = !vli_test_bit(scalar, i);
863 xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb], curve_prime,
864 ndigits);
865 xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve_prime,
866 ndigits);
867 }
868
869 nb = !vli_test_bit(scalar, 0);
870 xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb], curve_prime,
871 ndigits);
872
873 /* Find final 1/Z value. */
874 /* X1 - X0 */
875 vli_mod_sub(z, rx[1], rx[0], curve_prime, ndigits);
876 /* Yb * (X1 - X0) */
877 vli_mod_mult_fast(z, z, ry[1 - nb], curve_prime, ndigits);
878 /* xP * Yb * (X1 - X0) */
879 vli_mod_mult_fast(z, z, point->x, curve_prime, ndigits);
880
881 /* 1 / (xP * Yb * (X1 - X0)) */
882 vli_mod_inv(z, z, curve_prime, point->ndigits);
883
884 /* yP / (xP * Yb * (X1 - X0)) */
885 vli_mod_mult_fast(z, z, point->y, curve_prime, ndigits);
886 /* Xb * yP / (xP * Yb * (X1 - X0)) */
887 vli_mod_mult_fast(z, z, rx[1 - nb], curve_prime, ndigits);
888 /* End 1/Z calculation */
889
890 xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve_prime, ndigits);
891
892 apply_z(rx[0], ry[0], z, curve_prime, ndigits);
893
894 vli_set(result->x, rx[0], ndigits);
895 vli_set(result->y, ry[0], ndigits);
896}
897
898static inline void ecc_swap_digits(const u64 *in, u64 *out,
899 unsigned int ndigits)
900{
901 int i;
902
903 for (i = 0; i < ndigits; i++)
904 out[i] = __swab64(in[ndigits - 1 - i]);
905}
906
907int ecc_is_key_valid(unsigned int curve_id, unsigned int ndigits,
908 const u64 *private_key, unsigned int private_key_len)
909{
910 int nbytes;
911 const struct ecc_curve *curve = ecc_get_curve(curve_id);
912
913 if (!private_key)
914 return -EINVAL;
915
916 nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT;
917
918 if (private_key_len != nbytes)
919 return -EINVAL;
920
921 if (vli_is_zero(private_key, ndigits))
922 return -EINVAL;
923
924 /* Make sure the private key is in the range [1, n-1]. */
925 if (vli_cmp(curve->n, private_key, ndigits) != 1)
926 return -EINVAL;
927
928 return 0;
929}
930
931/*
932 * ECC private keys are generated using the method of extra random bits,
933 * equivalent to that described in FIPS 186-4, Appendix B.4.1.
934 *
935 * d = (c mod(n–1)) + 1 where c is a string of random bits, 64 bits longer
936 * than requested
937 * 0 <= c mod(n-1) <= n-2 and implies that
938 * 1 <= d <= n-1
939 *
940 * This method generates a private key uniformly distributed in the range
941 * [1, n-1].
942 */
943int ecc_gen_privkey(unsigned int curve_id, unsigned int ndigits, u64 *privkey)
944{
945 const struct ecc_curve *curve = ecc_get_curve(curve_id);
946 u64 priv[ndigits];
947 unsigned int nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT;
948 unsigned int nbits = vli_num_bits(curve->n, ndigits);
949 int err;
950
951 /* Check that N is included in Table 1 of FIPS 186-4, section 6.1.1 */
952 if (nbits < 160)
953 return -EINVAL;
954
955 /*
956 * FIPS 186-4 recommends that the private key should be obtained from a
957 * RBG with a security strength equal to or greater than the security
958 * strength associated with N.
959 *
960 * The maximum security strength identified by NIST SP800-57pt1r4 for
961 * ECC is 256 (N >= 512).
962 *
963 * This condition is met by the default RNG because it selects a favored
964 * DRBG with a security strength of 256.
965 */
966 if (crypto_get_default_rng())
967 return -EFAULT;
968
969 err = crypto_rng_get_bytes(crypto_default_rng, (u8 *)priv, nbytes);
970 crypto_put_default_rng();
971 if (err)
972 return err;
973
974 if (vli_is_zero(priv, ndigits))
975 return -EINVAL;
976
977 /* Make sure the private key is in the range [1, n-1]. */
978 if (vli_cmp(curve->n, priv, ndigits) != 1)
979 return -EINVAL;
980
981 ecc_swap_digits(priv, privkey, ndigits);
982
983 return 0;
984}
985
986int ecc_make_pub_key(unsigned int curve_id, unsigned int ndigits,
987 const u64 *private_key, u64 *public_key)
988{
989 int ret = 0;
990 struct ecc_point *pk;
991 u64 priv[ndigits];
992 const struct ecc_curve *curve = ecc_get_curve(curve_id);
993
994 if (!private_key || !curve) {
995 ret = -EINVAL;
996 goto out;
997 }
998
999 ecc_swap_digits(private_key, priv, ndigits);
1000
1001 pk = ecc_alloc_point(ndigits);
1002 if (!pk) {
1003 ret = -ENOMEM;
1004 goto out;
1005 }
1006
1007 ecc_point_mult(pk, &curve->g, priv, NULL, curve->p, ndigits);
1008 if (ecc_point_is_zero(pk)) {
1009 ret = -EAGAIN;
1010 goto err_free_point;
1011 }
1012
1013 ecc_swap_digits(pk->x, public_key, ndigits);
1014 ecc_swap_digits(pk->y, &public_key[ndigits], ndigits);
1015
1016err_free_point:
1017 ecc_free_point(pk);
1018out:
1019 return ret;
1020}
1021
1022int crypto_ecdh_shared_secret(unsigned int curve_id, unsigned int ndigits,
1023 const u64 *private_key, const u64 *public_key,
1024 u64 *secret)
1025{
1026 int ret = 0;
1027 struct ecc_point *product, *pk;
1028 u64 *priv, *rand_z;
1029 const struct ecc_curve *curve = ecc_get_curve(curve_id);
1030
1031 if (!private_key || !public_key || !curve) {
1032 ret = -EINVAL;
1033 goto out;
1034 }
1035
1036 priv = kmalloc_array(ndigits, sizeof(*priv), GFP_KERNEL);
1037 if (!priv) {
1038 ret = -ENOMEM;
1039 goto out;
1040 }
1041
1042 rand_z = kmalloc_array(ndigits, sizeof(*rand_z), GFP_KERNEL);
1043 if (!rand_z) {
1044 ret = -ENOMEM;
1045 goto kfree_out;
1046 }
1047
1048 pk = ecc_alloc_point(ndigits);
1049 if (!pk) {
1050 ret = -ENOMEM;
1051 goto kfree_out;
1052 }
1053
1054 product = ecc_alloc_point(ndigits);
1055 if (!product) {
1056 ret = -ENOMEM;
1057 goto err_alloc_product;
1058 }
1059
1060 get_random_bytes(rand_z, ndigits << ECC_DIGITS_TO_BYTES_SHIFT);
1061
1062 ecc_swap_digits(public_key, pk->x, ndigits);
1063 ecc_swap_digits(&public_key[ndigits], pk->y, ndigits);
1064 ecc_swap_digits(private_key, priv, ndigits);
1065
1066 ecc_point_mult(product, pk, priv, rand_z, curve->p, ndigits);
1067
1068 ecc_swap_digits(product->x, secret, ndigits);
1069
1070 if (ecc_point_is_zero(product))
1071 ret = -EFAULT;
1072
1073 ecc_free_point(product);
1074err_alloc_product:
1075 ecc_free_point(pk);
1076kfree_out:
1077 kzfree(priv);
1078 kzfree(rand_z);
1079out:
1080 return ret;
1081}