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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
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}