Commit | Line | Data |
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3c4b2390 | 1 | /* |
0d7a7864 VC |
2 | * Copyright (c) 2013, 2014 Kenneth MacKay. All rights reserved. |
3 | * Copyright (c) 2019 Vitaly Chikunov <vt@altlinux.org> | |
3c4b2390 SB |
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 | ||
14bb7676 | 27 | #include <crypto/ecc_curve.h> |
4a2289da | 28 | #include <linux/module.h> |
3c4b2390 SB |
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> | |
6755fd26 | 34 | #include <crypto/rng.h> |
a745d3ac | 35 | #include <crypto/internal/ecc.h> |
0d7a7864 VC |
36 | #include <asm/unaligned.h> |
37 | #include <linux/ratelimit.h> | |
3c4b2390 | 38 | |
3c4b2390 SB |
39 | #include "ecc_curve_defs.h" |
40 | ||
41 | typedef struct { | |
42 | u64 m_low; | |
43 | u64 m_high; | |
44 | } uint128_t; | |
45 | ||
8fb9340e MY |
46 | /* Returns curv25519 curve param */ |
47 | const struct ecc_curve *ecc_get_curve25519(void) | |
48 | { | |
49 | return &ecc_25519; | |
50 | } | |
51 | EXPORT_SYMBOL(ecc_get_curve25519); | |
14bb7676 MY |
52 | |
53 | const struct ecc_curve *ecc_get_curve(unsigned int curve_id) | |
3c4b2390 SB |
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; | |
703c748d SA |
61 | case ECC_CURVE_NIST_P384: |
62 | return &nist_p384; | |
288b46c5 SB |
63 | case ECC_CURVE_NIST_P521: |
64 | return &nist_p521; | |
3c4b2390 SB |
65 | default: |
66 | return NULL; | |
67 | } | |
68 | } | |
14bb7676 | 69 | EXPORT_SYMBOL(ecc_get_curve); |
3c4b2390 | 70 | |
c6ab5c91 SB |
71 | void ecc_digits_from_bytes(const u8 *in, unsigned int nbytes, |
72 | u64 *out, unsigned int ndigits) | |
73 | { | |
74 | int diff = ndigits - DIV_ROUND_UP(nbytes, sizeof(u64)); | |
75 | unsigned int o = nbytes & 7; | |
76 | __be64 msd = 0; | |
77 | ||
78 | /* diff > 0: not enough input bytes: set most significant digits to 0 */ | |
79 | if (diff > 0) { | |
80 | ndigits -= diff; | |
81 | memset(&out[ndigits - 1], 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 | } | |
91 | EXPORT_SYMBOL(ecc_digits_from_bytes); | |
92 | ||
3c4b2390 SB |
93 | static u64 *ecc_alloc_digits_space(unsigned int ndigits) |
94 | { | |
95 | size_t len = ndigits * sizeof(u64); | |
96 | ||
97 | if (!len) | |
98 | return NULL; | |
99 | ||
100 | return kmalloc(len, GFP_KERNEL); | |
101 | } | |
102 | ||
103 | static void ecc_free_digits_space(u64 *space) | |
104 | { | |
453431a5 | 105 | kfree_sensitive(space); |
3c4b2390 SB |
106 | } |
107 | ||
eaffe377 | 108 | struct ecc_point *ecc_alloc_point(unsigned int ndigits) |
3c4b2390 SB |
109 | { |
110 | struct ecc_point *p = kmalloc(sizeof(*p), GFP_KERNEL); | |
111 | ||
112 | if (!p) | |
113 | return NULL; | |
114 | ||
115 | p->x = ecc_alloc_digits_space(ndigits); | |
116 | if (!p->x) | |
117 | goto err_alloc_x; | |
118 | ||
119 | p->y = ecc_alloc_digits_space(ndigits); | |
120 | if (!p->y) | |
121 | goto err_alloc_y; | |
122 | ||
123 | p->ndigits = ndigits; | |
124 | ||
125 | return p; | |
126 | ||
127 | err_alloc_y: | |
128 | ecc_free_digits_space(p->x); | |
129 | err_alloc_x: | |
130 | kfree(p); | |
131 | return NULL; | |
132 | } | |
eaffe377 | 133 | EXPORT_SYMBOL(ecc_alloc_point); |
3c4b2390 | 134 | |
eaffe377 | 135 | void ecc_free_point(struct ecc_point *p) |
3c4b2390 SB |
136 | { |
137 | if (!p) | |
138 | return; | |
139 | ||
453431a5 WL |
140 | kfree_sensitive(p->x); |
141 | kfree_sensitive(p->y); | |
142 | kfree_sensitive(p); | |
3c4b2390 | 143 | } |
eaffe377 | 144 | EXPORT_SYMBOL(ecc_free_point); |
3c4b2390 SB |
145 | |
146 | static void vli_clear(u64 *vli, unsigned int ndigits) | |
147 | { | |
148 | int i; | |
149 | ||
150 | for (i = 0; i < ndigits; i++) | |
151 | vli[i] = 0; | |
152 | } | |
153 | ||
154 | /* Returns true if vli == 0, false otherwise. */ | |
4a2289da | 155 | bool vli_is_zero(const u64 *vli, unsigned int ndigits) |
3c4b2390 SB |
156 | { |
157 | int i; | |
158 | ||
159 | for (i = 0; i < ndigits; i++) { | |
160 | if (vli[i]) | |
161 | return false; | |
162 | } | |
163 | ||
164 | return true; | |
165 | } | |
4a2289da | 166 | EXPORT_SYMBOL(vli_is_zero); |
3c4b2390 | 167 | |
0193b32f | 168 | /* Returns nonzero if bit of vli is set. */ |
3c4b2390 SB |
169 | static u64 vli_test_bit(const u64 *vli, unsigned int bit) |
170 | { | |
171 | return (vli[bit / 64] & ((u64)1 << (bit % 64))); | |
172 | } | |
173 | ||
0d7a7864 VC |
174 | static bool vli_is_negative(const u64 *vli, unsigned int ndigits) |
175 | { | |
176 | return vli_test_bit(vli, ndigits * 64 - 1); | |
177 | } | |
178 | ||
3c4b2390 SB |
179 | /* Counts the number of 64-bit "digits" in vli. */ |
180 | static unsigned int vli_num_digits(const u64 *vli, unsigned int ndigits) | |
181 | { | |
182 | int i; | |
183 | ||
184 | /* Search from the end until we find a non-zero digit. | |
185 | * We do it in reverse because we expect that most digits will | |
186 | * be nonzero. | |
187 | */ | |
188 | for (i = ndigits - 1; i >= 0 && vli[i] == 0; i--); | |
189 | ||
190 | return (i + 1); | |
191 | } | |
192 | ||
193 | /* Counts the number of bits required for vli. */ | |
eaffe377 | 194 | unsigned int vli_num_bits(const u64 *vli, unsigned int ndigits) |
3c4b2390 SB |
195 | { |
196 | unsigned int i, num_digits; | |
197 | u64 digit; | |
198 | ||
199 | num_digits = vli_num_digits(vli, ndigits); | |
200 | if (num_digits == 0) | |
201 | return 0; | |
202 | ||
203 | digit = vli[num_digits - 1]; | |
204 | for (i = 0; digit; i++) | |
205 | digit >>= 1; | |
206 | ||
207 | return ((num_digits - 1) * 64 + i); | |
208 | } | |
eaffe377 | 209 | EXPORT_SYMBOL(vli_num_bits); |
3c4b2390 | 210 | |
0d7a7864 VC |
211 | /* Set dest from unaligned bit string src. */ |
212 | void vli_from_be64(u64 *dest, const void *src, unsigned int ndigits) | |
213 | { | |
214 | int i; | |
215 | const u64 *from = src; | |
216 | ||
217 | for (i = 0; i < ndigits; i++) | |
218 | dest[i] = get_unaligned_be64(&from[ndigits - 1 - i]); | |
219 | } | |
220 | EXPORT_SYMBOL(vli_from_be64); | |
221 | ||
222 | void vli_from_le64(u64 *dest, const void *src, unsigned int ndigits) | |
223 | { | |
224 | int i; | |
225 | const u64 *from = src; | |
226 | ||
227 | for (i = 0; i < ndigits; i++) | |
228 | dest[i] = get_unaligned_le64(&from[i]); | |
229 | } | |
230 | EXPORT_SYMBOL(vli_from_le64); | |
231 | ||
3c4b2390 SB |
232 | /* Sets dest = src. */ |
233 | static void vli_set(u64 *dest, const u64 *src, unsigned int ndigits) | |
234 | { | |
235 | int i; | |
236 | ||
237 | for (i = 0; i < ndigits; i++) | |
238 | dest[i] = src[i]; | |
239 | } | |
240 | ||
241 | /* Returns sign of left - right. */ | |
4a2289da | 242 | int vli_cmp(const u64 *left, const u64 *right, unsigned int ndigits) |
3c4b2390 SB |
243 | { |
244 | int i; | |
245 | ||
246 | for (i = ndigits - 1; i >= 0; i--) { | |
247 | if (left[i] > right[i]) | |
248 | return 1; | |
249 | else if (left[i] < right[i]) | |
250 | return -1; | |
251 | } | |
252 | ||
253 | return 0; | |
254 | } | |
4a2289da | 255 | EXPORT_SYMBOL(vli_cmp); |
3c4b2390 SB |
256 | |
257 | /* Computes result = in << c, returning carry. Can modify in place | |
258 | * (if result == in). 0 < shift < 64. | |
259 | */ | |
260 | static u64 vli_lshift(u64 *result, const u64 *in, unsigned int shift, | |
261 | unsigned int ndigits) | |
262 | { | |
263 | u64 carry = 0; | |
264 | int i; | |
265 | ||
266 | for (i = 0; i < ndigits; i++) { | |
267 | u64 temp = in[i]; | |
268 | ||
269 | result[i] = (temp << shift) | carry; | |
270 | carry = temp >> (64 - shift); | |
271 | } | |
272 | ||
273 | return carry; | |
274 | } | |
275 | ||
276 | /* Computes vli = vli >> 1. */ | |
277 | static void vli_rshift1(u64 *vli, unsigned int ndigits) | |
278 | { | |
279 | u64 *end = vli; | |
280 | u64 carry = 0; | |
281 | ||
282 | vli += ndigits; | |
283 | ||
284 | while (vli-- > end) { | |
285 | u64 temp = *vli; | |
286 | *vli = (temp >> 1) | carry; | |
287 | carry = temp << 63; | |
288 | } | |
289 | } | |
290 | ||
291 | /* Computes result = left + right, returning carry. Can modify in place. */ | |
292 | static u64 vli_add(u64 *result, const u64 *left, const u64 *right, | |
293 | unsigned int ndigits) | |
294 | { | |
295 | u64 carry = 0; | |
296 | int i; | |
297 | ||
298 | for (i = 0; i < ndigits; i++) { | |
299 | u64 sum; | |
300 | ||
301 | sum = left[i] + right[i] + carry; | |
302 | if (sum != left[i]) | |
303 | carry = (sum < left[i]); | |
304 | ||
305 | result[i] = sum; | |
306 | } | |
307 | ||
308 | return carry; | |
309 | } | |
310 | ||
0d7a7864 VC |
311 | /* Computes result = left + right, returning carry. Can modify in place. */ |
312 | static u64 vli_uadd(u64 *result, const u64 *left, u64 right, | |
313 | unsigned int ndigits) | |
314 | { | |
315 | u64 carry = right; | |
316 | int i; | |
317 | ||
318 | for (i = 0; i < ndigits; i++) { | |
319 | u64 sum; | |
320 | ||
321 | sum = left[i] + carry; | |
322 | if (sum != left[i]) | |
323 | carry = (sum < left[i]); | |
324 | else | |
325 | carry = !!carry; | |
326 | ||
327 | result[i] = sum; | |
328 | } | |
329 | ||
330 | return carry; | |
331 | } | |
332 | ||
3c4b2390 | 333 | /* Computes result = left - right, returning borrow. Can modify in place. */ |
4a2289da | 334 | u64 vli_sub(u64 *result, const u64 *left, const u64 *right, |
3c4b2390 SB |
335 | unsigned int ndigits) |
336 | { | |
337 | u64 borrow = 0; | |
338 | int i; | |
339 | ||
340 | for (i = 0; i < ndigits; i++) { | |
341 | u64 diff; | |
342 | ||
343 | diff = left[i] - right[i] - borrow; | |
344 | if (diff != left[i]) | |
345 | borrow = (diff > left[i]); | |
346 | ||
347 | result[i] = diff; | |
348 | } | |
349 | ||
350 | return borrow; | |
351 | } | |
4a2289da | 352 | EXPORT_SYMBOL(vli_sub); |
3c4b2390 | 353 | |
0d7a7864 VC |
354 | /* Computes result = left - right, returning borrow. Can modify in place. */ |
355 | static u64 vli_usub(u64 *result, const u64 *left, u64 right, | |
356 | unsigned int ndigits) | |
357 | { | |
358 | u64 borrow = right; | |
359 | int i; | |
360 | ||
361 | for (i = 0; i < ndigits; i++) { | |
362 | u64 diff; | |
363 | ||
364 | diff = left[i] - borrow; | |
365 | if (diff != left[i]) | |
366 | borrow = (diff > left[i]); | |
367 | ||
368 | result[i] = diff; | |
369 | } | |
370 | ||
371 | return borrow; | |
372 | } | |
373 | ||
3c4b2390 SB |
374 | static uint128_t mul_64_64(u64 left, u64 right) |
375 | { | |
0d7a7864 | 376 | uint128_t result; |
c12d3362 | 377 | #if defined(CONFIG_ARCH_SUPPORTS_INT128) |
0d7a7864 VC |
378 | unsigned __int128 m = (unsigned __int128)left * right; |
379 | ||
380 | result.m_low = m; | |
381 | result.m_high = m >> 64; | |
382 | #else | |
3c4b2390 SB |
383 | u64 a0 = left & 0xffffffffull; |
384 | u64 a1 = left >> 32; | |
385 | u64 b0 = right & 0xffffffffull; | |
386 | u64 b1 = right >> 32; | |
387 | u64 m0 = a0 * b0; | |
388 | u64 m1 = a0 * b1; | |
389 | u64 m2 = a1 * b0; | |
390 | u64 m3 = a1 * b1; | |
3c4b2390 SB |
391 | |
392 | m2 += (m0 >> 32); | |
393 | m2 += m1; | |
394 | ||
395 | /* Overflow */ | |
396 | if (m2 < m1) | |
397 | m3 += 0x100000000ull; | |
398 | ||
399 | result.m_low = (m0 & 0xffffffffull) | (m2 << 32); | |
400 | result.m_high = m3 + (m2 >> 32); | |
0d7a7864 | 401 | #endif |
3c4b2390 SB |
402 | return result; |
403 | } | |
404 | ||
405 | static uint128_t add_128_128(uint128_t a, uint128_t b) | |
406 | { | |
407 | uint128_t result; | |
408 | ||
409 | result.m_low = a.m_low + b.m_low; | |
410 | result.m_high = a.m_high + b.m_high + (result.m_low < a.m_low); | |
411 | ||
412 | return result; | |
413 | } | |
414 | ||
415 | static void vli_mult(u64 *result, const u64 *left, const u64 *right, | |
416 | unsigned int ndigits) | |
417 | { | |
418 | uint128_t r01 = { 0, 0 }; | |
419 | u64 r2 = 0; | |
420 | unsigned int i, k; | |
421 | ||
422 | /* Compute each digit of result in sequence, maintaining the | |
423 | * carries. | |
424 | */ | |
425 | for (k = 0; k < ndigits * 2 - 1; k++) { | |
426 | unsigned int min; | |
427 | ||
428 | if (k < ndigits) | |
429 | min = 0; | |
430 | else | |
431 | min = (k + 1) - ndigits; | |
432 | ||
433 | for (i = min; i <= k && i < ndigits; i++) { | |
434 | uint128_t product; | |
435 | ||
436 | product = mul_64_64(left[i], right[k - i]); | |
437 | ||
438 | r01 = add_128_128(r01, product); | |
439 | r2 += (r01.m_high < product.m_high); | |
440 | } | |
441 | ||
442 | result[k] = r01.m_low; | |
443 | r01.m_low = r01.m_high; | |
444 | r01.m_high = r2; | |
445 | r2 = 0; | |
446 | } | |
447 | ||
448 | result[ndigits * 2 - 1] = r01.m_low; | |
449 | } | |
450 | ||
0d7a7864 VC |
451 | /* Compute product = left * right, for a small right value. */ |
452 | static void vli_umult(u64 *result, const u64 *left, u32 right, | |
453 | unsigned int ndigits) | |
454 | { | |
455 | uint128_t r01 = { 0 }; | |
456 | unsigned int k; | |
457 | ||
458 | for (k = 0; k < ndigits; k++) { | |
459 | uint128_t product; | |
460 | ||
461 | product = mul_64_64(left[k], right); | |
462 | r01 = add_128_128(r01, product); | |
463 | /* no carry */ | |
464 | result[k] = r01.m_low; | |
465 | r01.m_low = r01.m_high; | |
466 | r01.m_high = 0; | |
467 | } | |
468 | result[k] = r01.m_low; | |
469 | for (++k; k < ndigits * 2; k++) | |
470 | result[k] = 0; | |
471 | } | |
472 | ||
3c4b2390 SB |
473 | static void vli_square(u64 *result, const u64 *left, unsigned int ndigits) |
474 | { | |
475 | uint128_t r01 = { 0, 0 }; | |
476 | u64 r2 = 0; | |
477 | int i, k; | |
478 | ||
479 | for (k = 0; k < ndigits * 2 - 1; k++) { | |
480 | unsigned int min; | |
481 | ||
482 | if (k < ndigits) | |
483 | min = 0; | |
484 | else | |
485 | min = (k + 1) - ndigits; | |
486 | ||
487 | for (i = min; i <= k && i <= k - i; i++) { | |
488 | uint128_t product; | |
489 | ||
490 | product = mul_64_64(left[i], left[k - i]); | |
491 | ||
492 | if (i < k - i) { | |
493 | r2 += product.m_high >> 63; | |
494 | product.m_high = (product.m_high << 1) | | |
495 | (product.m_low >> 63); | |
496 | product.m_low <<= 1; | |
497 | } | |
498 | ||
499 | r01 = add_128_128(r01, product); | |
500 | r2 += (r01.m_high < product.m_high); | |
501 | } | |
502 | ||
503 | result[k] = r01.m_low; | |
504 | r01.m_low = r01.m_high; | |
505 | r01.m_high = r2; | |
506 | r2 = 0; | |
507 | } | |
508 | ||
509 | result[ndigits * 2 - 1] = r01.m_low; | |
510 | } | |
511 | ||
512 | /* Computes result = (left + right) % mod. | |
513 | * Assumes that left < mod and right < mod, result != mod. | |
514 | */ | |
515 | static void vli_mod_add(u64 *result, const u64 *left, const u64 *right, | |
516 | const u64 *mod, unsigned int ndigits) | |
517 | { | |
518 | u64 carry; | |
519 | ||
520 | carry = vli_add(result, left, right, ndigits); | |
521 | ||
522 | /* result > mod (result = mod + remainder), so subtract mod to | |
523 | * get remainder. | |
524 | */ | |
525 | if (carry || vli_cmp(result, mod, ndigits) >= 0) | |
526 | vli_sub(result, result, mod, ndigits); | |
527 | } | |
528 | ||
529 | /* Computes result = (left - right) % mod. | |
530 | * Assumes that left < mod and right < mod, result != mod. | |
531 | */ | |
532 | static void vli_mod_sub(u64 *result, const u64 *left, const u64 *right, | |
533 | const u64 *mod, unsigned int ndigits) | |
534 | { | |
535 | u64 borrow = vli_sub(result, left, right, ndigits); | |
536 | ||
537 | /* In this case, p_result == -diff == (max int) - diff. | |
538 | * Since -x % d == d - x, we can get the correct result from | |
539 | * result + mod (with overflow). | |
540 | */ | |
541 | if (borrow) | |
542 | vli_add(result, result, mod, ndigits); | |
543 | } | |
544 | ||
0d7a7864 VC |
545 | /* |
546 | * Computes result = product % mod | |
547 | * for special form moduli: p = 2^k-c, for small c (note the minus sign) | |
548 | * | |
549 | * References: | |
550 | * R. Crandall, C. Pomerance. Prime Numbers: A Computational Perspective. | |
551 | * 9 Fast Algorithms for Large-Integer Arithmetic. 9.2.3 Moduli of special form | |
552 | * Algorithm 9.2.13 (Fast mod operation for special-form moduli). | |
553 | */ | |
554 | static void vli_mmod_special(u64 *result, const u64 *product, | |
555 | const u64 *mod, unsigned int ndigits) | |
556 | { | |
557 | u64 c = -mod[0]; | |
558 | u64 t[ECC_MAX_DIGITS * 2]; | |
559 | u64 r[ECC_MAX_DIGITS * 2]; | |
560 | ||
561 | vli_set(r, product, ndigits * 2); | |
562 | while (!vli_is_zero(r + ndigits, ndigits)) { | |
563 | vli_umult(t, r + ndigits, c, ndigits); | |
564 | vli_clear(r + ndigits, ndigits); | |
565 | vli_add(r, r, t, ndigits * 2); | |
566 | } | |
567 | vli_set(t, mod, ndigits); | |
568 | vli_clear(t + ndigits, ndigits); | |
569 | while (vli_cmp(r, t, ndigits * 2) >= 0) | |
570 | vli_sub(r, r, t, ndigits * 2); | |
571 | vli_set(result, r, ndigits); | |
572 | } | |
573 | ||
574 | /* | |
575 | * Computes result = product % mod | |
576 | * for special form moduli: p = 2^{k-1}+c, for small c (note the plus sign) | |
577 | * where k-1 does not fit into qword boundary by -1 bit (such as 255). | |
578 | ||
579 | * References (loosely based on): | |
580 | * A. Menezes, P. van Oorschot, S. Vanstone. Handbook of Applied Cryptography. | |
581 | * 14.3.4 Reduction methods for moduli of special form. Algorithm 14.47. | |
582 | * URL: http://cacr.uwaterloo.ca/hac/about/chap14.pdf | |
583 | * | |
584 | * H. Cohen, G. Frey, R. Avanzi, C. Doche, T. Lange, K. Nguyen, F. Vercauteren. | |
585 | * Handbook of Elliptic and Hyperelliptic Curve Cryptography. | |
586 | * Algorithm 10.25 Fast reduction for special form moduli | |
587 | */ | |
588 | static void vli_mmod_special2(u64 *result, const u64 *product, | |
589 | const u64 *mod, unsigned int ndigits) | |
590 | { | |
591 | u64 c2 = mod[0] * 2; | |
592 | u64 q[ECC_MAX_DIGITS]; | |
593 | u64 r[ECC_MAX_DIGITS * 2]; | |
594 | u64 m[ECC_MAX_DIGITS * 2]; /* expanded mod */ | |
595 | int carry; /* last bit that doesn't fit into q */ | |
596 | int i; | |
597 | ||
598 | vli_set(m, mod, ndigits); | |
599 | vli_clear(m + ndigits, ndigits); | |
600 | ||
601 | vli_set(r, product, ndigits); | |
602 | /* q and carry are top bits */ | |
603 | vli_set(q, product + ndigits, ndigits); | |
604 | vli_clear(r + ndigits, ndigits); | |
605 | carry = vli_is_negative(r, ndigits); | |
606 | if (carry) | |
607 | r[ndigits - 1] &= (1ull << 63) - 1; | |
608 | for (i = 1; carry || !vli_is_zero(q, ndigits); i++) { | |
609 | u64 qc[ECC_MAX_DIGITS * 2]; | |
610 | ||
611 | vli_umult(qc, q, c2, ndigits); | |
612 | if (carry) | |
613 | vli_uadd(qc, qc, mod[0], ndigits * 2); | |
614 | vli_set(q, qc + ndigits, ndigits); | |
615 | vli_clear(qc + ndigits, ndigits); | |
616 | carry = vli_is_negative(qc, ndigits); | |
617 | if (carry) | |
618 | qc[ndigits - 1] &= (1ull << 63) - 1; | |
619 | if (i & 1) | |
620 | vli_sub(r, r, qc, ndigits * 2); | |
621 | else | |
622 | vli_add(r, r, qc, ndigits * 2); | |
623 | } | |
624 | while (vli_is_negative(r, ndigits * 2)) | |
625 | vli_add(r, r, m, ndigits * 2); | |
626 | while (vli_cmp(r, m, ndigits * 2) >= 0) | |
627 | vli_sub(r, r, m, ndigits * 2); | |
628 | ||
629 | vli_set(result, r, ndigits); | |
630 | } | |
631 | ||
632 | /* | |
633 | * Computes result = product % mod, where product is 2N words long. | |
634 | * Reference: Ken MacKay's micro-ecc. | |
635 | * Currently only designed to work for curve_p or curve_n. | |
636 | */ | |
637 | static void vli_mmod_slow(u64 *result, u64 *product, const u64 *mod, | |
638 | unsigned int ndigits) | |
639 | { | |
640 | u64 mod_m[2 * ECC_MAX_DIGITS]; | |
641 | u64 tmp[2 * ECC_MAX_DIGITS]; | |
642 | u64 *v[2] = { tmp, product }; | |
643 | u64 carry = 0; | |
644 | unsigned int i; | |
645 | /* Shift mod so its highest set bit is at the maximum position. */ | |
646 | int shift = (ndigits * 2 * 64) - vli_num_bits(mod, ndigits); | |
647 | int word_shift = shift / 64; | |
648 | int bit_shift = shift % 64; | |
649 | ||
650 | vli_clear(mod_m, word_shift); | |
651 | if (bit_shift > 0) { | |
652 | for (i = 0; i < ndigits; ++i) { | |
653 | mod_m[word_shift + i] = (mod[i] << bit_shift) | carry; | |
654 | carry = mod[i] >> (64 - bit_shift); | |
655 | } | |
656 | } else | |
657 | vli_set(mod_m + word_shift, mod, ndigits); | |
658 | ||
659 | for (i = 1; shift >= 0; --shift) { | |
660 | u64 borrow = 0; | |
661 | unsigned int j; | |
662 | ||
663 | for (j = 0; j < ndigits * 2; ++j) { | |
664 | u64 diff = v[i][j] - mod_m[j] - borrow; | |
665 | ||
666 | if (diff != v[i][j]) | |
667 | borrow = (diff > v[i][j]); | |
668 | v[1 - i][j] = diff; | |
669 | } | |
670 | i = !(i ^ borrow); /* Swap the index if there was no borrow */ | |
671 | vli_rshift1(mod_m, ndigits); | |
672 | mod_m[ndigits - 1] |= mod_m[ndigits] << (64 - 1); | |
673 | vli_rshift1(mod_m + ndigits, ndigits); | |
674 | } | |
675 | vli_set(result, v[i], ndigits); | |
676 | } | |
677 | ||
678 | /* Computes result = product % mod using Barrett's reduction with precomputed | |
679 | * value mu appended to the mod after ndigits, mu = (2^{2w} / mod) and have | |
680 | * length ndigits + 1, where mu * (2^w - 1) should not overflow ndigits | |
681 | * boundary. | |
682 | * | |
683 | * Reference: | |
684 | * R. Brent, P. Zimmermann. Modern Computer Arithmetic. 2010. | |
685 | * 2.4.1 Barrett's algorithm. Algorithm 2.5. | |
686 | */ | |
687 | static void vli_mmod_barrett(u64 *result, u64 *product, const u64 *mod, | |
688 | unsigned int ndigits) | |
689 | { | |
690 | u64 q[ECC_MAX_DIGITS * 2]; | |
691 | u64 r[ECC_MAX_DIGITS * 2]; | |
692 | const u64 *mu = mod + ndigits; | |
693 | ||
694 | vli_mult(q, product + ndigits, mu, ndigits); | |
695 | if (mu[ndigits]) | |
696 | vli_add(q + ndigits, q + ndigits, product + ndigits, ndigits); | |
697 | vli_mult(r, mod, q + ndigits, ndigits); | |
698 | vli_sub(r, product, r, ndigits * 2); | |
699 | while (!vli_is_zero(r + ndigits, ndigits) || | |
700 | vli_cmp(r, mod, ndigits) != -1) { | |
701 | u64 carry; | |
702 | ||
703 | carry = vli_sub(r, r, mod, ndigits); | |
704 | vli_usub(r + ndigits, r + ndigits, carry, ndigits); | |
705 | } | |
706 | vli_set(result, r, ndigits); | |
707 | } | |
708 | ||
3c4b2390 SB |
709 | /* Computes p_result = p_product % curve_p. |
710 | * See algorithm 5 and 6 from | |
711 | * http://www.isys.uni-klu.ac.at/PDF/2001-0126-MT.pdf | |
712 | */ | |
713 | static void vli_mmod_fast_192(u64 *result, const u64 *product, | |
714 | const u64 *curve_prime, u64 *tmp) | |
715 | { | |
526d23fc | 716 | const unsigned int ndigits = ECC_CURVE_NIST_P192_DIGITS; |
3c4b2390 SB |
717 | int carry; |
718 | ||
719 | vli_set(result, product, ndigits); | |
720 | ||
721 | vli_set(tmp, &product[3], ndigits); | |
722 | carry = vli_add(result, result, tmp, ndigits); | |
723 | ||
724 | tmp[0] = 0; | |
725 | tmp[1] = product[3]; | |
726 | tmp[2] = product[4]; | |
727 | carry += vli_add(result, result, tmp, ndigits); | |
728 | ||
729 | tmp[0] = tmp[1] = product[5]; | |
730 | tmp[2] = 0; | |
731 | carry += vli_add(result, result, tmp, ndigits); | |
732 | ||
733 | while (carry || vli_cmp(curve_prime, result, ndigits) != 1) | |
734 | carry -= vli_sub(result, result, curve_prime, ndigits); | |
735 | } | |
736 | ||
737 | /* Computes result = product % curve_prime | |
738 | * from http://www.nsa.gov/ia/_files/nist-routines.pdf | |
739 | */ | |
740 | static void vli_mmod_fast_256(u64 *result, const u64 *product, | |
741 | const u64 *curve_prime, u64 *tmp) | |
742 | { | |
743 | int carry; | |
526d23fc | 744 | const unsigned int ndigits = ECC_CURVE_NIST_P256_DIGITS; |
3c4b2390 SB |
745 | |
746 | /* t */ | |
747 | vli_set(result, product, ndigits); | |
748 | ||
749 | /* s1 */ | |
750 | tmp[0] = 0; | |
751 | tmp[1] = product[5] & 0xffffffff00000000ull; | |
752 | tmp[2] = product[6]; | |
753 | tmp[3] = product[7]; | |
754 | carry = vli_lshift(tmp, tmp, 1, ndigits); | |
755 | carry += vli_add(result, result, tmp, ndigits); | |
756 | ||
757 | /* s2 */ | |
758 | tmp[1] = product[6] << 32; | |
759 | tmp[2] = (product[6] >> 32) | (product[7] << 32); | |
760 | tmp[3] = product[7] >> 32; | |
761 | carry += vli_lshift(tmp, tmp, 1, ndigits); | |
762 | carry += vli_add(result, result, tmp, ndigits); | |
763 | ||
764 | /* s3 */ | |
765 | tmp[0] = product[4]; | |
766 | tmp[1] = product[5] & 0xffffffff; | |
767 | tmp[2] = 0; | |
768 | tmp[3] = product[7]; | |
769 | carry += vli_add(result, result, tmp, ndigits); | |
770 | ||
771 | /* s4 */ | |
772 | tmp[0] = (product[4] >> 32) | (product[5] << 32); | |
773 | tmp[1] = (product[5] >> 32) | (product[6] & 0xffffffff00000000ull); | |
774 | tmp[2] = product[7]; | |
775 | tmp[3] = (product[6] >> 32) | (product[4] << 32); | |
776 | carry += vli_add(result, result, tmp, ndigits); | |
777 | ||
778 | /* d1 */ | |
779 | tmp[0] = (product[5] >> 32) | (product[6] << 32); | |
780 | tmp[1] = (product[6] >> 32); | |
781 | tmp[2] = 0; | |
782 | tmp[3] = (product[4] & 0xffffffff) | (product[5] << 32); | |
783 | carry -= vli_sub(result, result, tmp, ndigits); | |
784 | ||
785 | /* d2 */ | |
786 | tmp[0] = product[6]; | |
787 | tmp[1] = product[7]; | |
788 | tmp[2] = 0; | |
789 | tmp[3] = (product[4] >> 32) | (product[5] & 0xffffffff00000000ull); | |
790 | carry -= vli_sub(result, result, tmp, ndigits); | |
791 | ||
792 | /* d3 */ | |
793 | tmp[0] = (product[6] >> 32) | (product[7] << 32); | |
794 | tmp[1] = (product[7] >> 32) | (product[4] << 32); | |
795 | tmp[2] = (product[4] >> 32) | (product[5] << 32); | |
796 | tmp[3] = (product[6] << 32); | |
797 | carry -= vli_sub(result, result, tmp, ndigits); | |
798 | ||
799 | /* d4 */ | |
800 | tmp[0] = product[7]; | |
801 | tmp[1] = product[4] & 0xffffffff00000000ull; | |
802 | tmp[2] = product[5]; | |
803 | tmp[3] = product[6] & 0xffffffff00000000ull; | |
804 | carry -= vli_sub(result, result, tmp, ndigits); | |
805 | ||
806 | if (carry < 0) { | |
807 | do { | |
808 | carry += vli_add(result, result, curve_prime, ndigits); | |
809 | } while (carry < 0); | |
810 | } else { | |
811 | while (carry || vli_cmp(curve_prime, result, ndigits) != 1) | |
812 | carry -= vli_sub(result, result, curve_prime, ndigits); | |
813 | } | |
814 | } | |
815 | ||
149ca161 SA |
816 | #define SL32OR32(x32, y32) (((u64)x32 << 32) | y32) |
817 | #define AND64H(x64) (x64 & 0xffFFffFF00000000ull) | |
818 | #define AND64L(x64) (x64 & 0x00000000ffFFffFFull) | |
819 | ||
820 | /* Computes result = product % curve_prime | |
821 | * from "Mathematical routines for the NIST prime elliptic curves" | |
822 | */ | |
823 | static void vli_mmod_fast_384(u64 *result, const u64 *product, | |
824 | const u64 *curve_prime, u64 *tmp) | |
825 | { | |
826 | int carry; | |
526d23fc | 827 | const unsigned int ndigits = ECC_CURVE_NIST_P384_DIGITS; |
149ca161 SA |
828 | |
829 | /* t */ | |
830 | vli_set(result, product, ndigits); | |
831 | ||
832 | /* s1 */ | |
833 | tmp[0] = 0; // 0 || 0 | |
834 | tmp[1] = 0; // 0 || 0 | |
835 | tmp[2] = SL32OR32(product[11], (product[10]>>32)); //a22||a21 | |
836 | tmp[3] = product[11]>>32; // 0 ||a23 | |
837 | tmp[4] = 0; // 0 || 0 | |
838 | tmp[5] = 0; // 0 || 0 | |
839 | carry = vli_lshift(tmp, tmp, 1, ndigits); | |
840 | carry += vli_add(result, result, tmp, ndigits); | |
841 | ||
842 | /* s2 */ | |
843 | tmp[0] = product[6]; //a13||a12 | |
844 | tmp[1] = product[7]; //a15||a14 | |
845 | tmp[2] = product[8]; //a17||a16 | |
846 | tmp[3] = product[9]; //a19||a18 | |
847 | tmp[4] = product[10]; //a21||a20 | |
848 | tmp[5] = product[11]; //a23||a22 | |
849 | carry += vli_add(result, result, tmp, ndigits); | |
850 | ||
851 | /* s3 */ | |
852 | tmp[0] = SL32OR32(product[11], (product[10]>>32)); //a22||a21 | |
853 | tmp[1] = SL32OR32(product[6], (product[11]>>32)); //a12||a23 | |
854 | tmp[2] = SL32OR32(product[7], (product[6])>>32); //a14||a13 | |
855 | tmp[3] = SL32OR32(product[8], (product[7]>>32)); //a16||a15 | |
856 | tmp[4] = SL32OR32(product[9], (product[8]>>32)); //a18||a17 | |
857 | tmp[5] = SL32OR32(product[10], (product[9]>>32)); //a20||a19 | |
858 | carry += vli_add(result, result, tmp, ndigits); | |
859 | ||
860 | /* s4 */ | |
861 | tmp[0] = AND64H(product[11]); //a23|| 0 | |
862 | tmp[1] = (product[10]<<32); //a20|| 0 | |
863 | tmp[2] = product[6]; //a13||a12 | |
864 | tmp[3] = product[7]; //a15||a14 | |
865 | tmp[4] = product[8]; //a17||a16 | |
866 | tmp[5] = product[9]; //a19||a18 | |
867 | carry += vli_add(result, result, tmp, ndigits); | |
868 | ||
869 | /* s5 */ | |
870 | tmp[0] = 0; // 0|| 0 | |
871 | tmp[1] = 0; // 0|| 0 | |
872 | tmp[2] = product[10]; //a21||a20 | |
873 | tmp[3] = product[11]; //a23||a22 | |
874 | tmp[4] = 0; // 0|| 0 | |
875 | tmp[5] = 0; // 0|| 0 | |
876 | carry += vli_add(result, result, tmp, ndigits); | |
877 | ||
878 | /* s6 */ | |
879 | tmp[0] = AND64L(product[10]); // 0 ||a20 | |
880 | tmp[1] = AND64H(product[10]); //a21|| 0 | |
881 | tmp[2] = product[11]; //a23||a22 | |
882 | tmp[3] = 0; // 0 || 0 | |
883 | tmp[4] = 0; // 0 || 0 | |
884 | tmp[5] = 0; // 0 || 0 | |
885 | carry += vli_add(result, result, tmp, ndigits); | |
886 | ||
887 | /* d1 */ | |
888 | tmp[0] = SL32OR32(product[6], (product[11]>>32)); //a12||a23 | |
889 | tmp[1] = SL32OR32(product[7], (product[6]>>32)); //a14||a13 | |
890 | tmp[2] = SL32OR32(product[8], (product[7]>>32)); //a16||a15 | |
891 | tmp[3] = SL32OR32(product[9], (product[8]>>32)); //a18||a17 | |
892 | tmp[4] = SL32OR32(product[10], (product[9]>>32)); //a20||a19 | |
893 | tmp[5] = SL32OR32(product[11], (product[10]>>32)); //a22||a21 | |
894 | carry -= vli_sub(result, result, tmp, ndigits); | |
895 | ||
896 | /* d2 */ | |
897 | tmp[0] = (product[10]<<32); //a20|| 0 | |
898 | tmp[1] = SL32OR32(product[11], (product[10]>>32)); //a22||a21 | |
899 | tmp[2] = (product[11]>>32); // 0 ||a23 | |
900 | tmp[3] = 0; // 0 || 0 | |
901 | tmp[4] = 0; // 0 || 0 | |
902 | tmp[5] = 0; // 0 || 0 | |
903 | carry -= vli_sub(result, result, tmp, ndigits); | |
904 | ||
905 | /* d3 */ | |
906 | tmp[0] = 0; // 0 || 0 | |
907 | tmp[1] = AND64H(product[11]); //a23|| 0 | |
908 | tmp[2] = product[11]>>32; // 0 ||a23 | |
909 | tmp[3] = 0; // 0 || 0 | |
910 | tmp[4] = 0; // 0 || 0 | |
911 | tmp[5] = 0; // 0 || 0 | |
912 | carry -= vli_sub(result, result, tmp, ndigits); | |
913 | ||
914 | if (carry < 0) { | |
915 | do { | |
916 | carry += vli_add(result, result, curve_prime, ndigits); | |
917 | } while (carry < 0); | |
918 | } else { | |
919 | while (carry || vli_cmp(curve_prime, result, ndigits) != 1) | |
920 | carry -= vli_sub(result, result, curve_prime, ndigits); | |
921 | } | |
922 | ||
923 | } | |
924 | ||
925 | #undef SL32OR32 | |
926 | #undef AND64H | |
927 | #undef AND64L | |
928 | ||
e7fb0627 SB |
929 | /* |
930 | * Computes result = product % curve_prime | |
931 | * from "Recommendations for Discrete Logarithm-Based Cryptography: | |
932 | * Elliptic Curve Domain Parameters" section G.1.4 | |
933 | */ | |
934 | static void vli_mmod_fast_521(u64 *result, const u64 *product, | |
935 | const u64 *curve_prime, u64 *tmp) | |
936 | { | |
937 | const unsigned int ndigits = ECC_CURVE_NIST_P521_DIGITS; | |
938 | size_t i; | |
939 | ||
940 | /* Initialize result with lowest 521 bits from product */ | |
941 | vli_set(result, product, ndigits); | |
942 | result[8] &= 0x1ff; | |
943 | ||
944 | for (i = 0; i < ndigits; i++) | |
945 | tmp[i] = (product[8 + i] >> 9) | (product[9 + i] << 55); | |
946 | tmp[8] &= 0x1ff; | |
947 | ||
948 | vli_mod_add(result, result, tmp, curve_prime, ndigits); | |
949 | } | |
950 | ||
0d7a7864 VC |
951 | /* Computes result = product % curve_prime for different curve_primes. |
952 | * | |
953 | * Note that curve_primes are distinguished just by heuristic check and | |
954 | * not by complete conformance check. | |
955 | */ | |
3c4b2390 | 956 | static bool vli_mmod_fast(u64 *result, u64 *product, |
149ca161 | 957 | const struct ecc_curve *curve) |
3c4b2390 | 958 | { |
d5c3b178 | 959 | u64 tmp[2 * ECC_MAX_DIGITS]; |
149ca161 SA |
960 | const u64 *curve_prime = curve->p; |
961 | const unsigned int ndigits = curve->g.ndigits; | |
3c4b2390 | 962 | |
149ca161 SA |
963 | /* All NIST curves have name prefix 'nist_' */ |
964 | if (strncmp(curve->name, "nist_", 5) != 0) { | |
0d7a7864 VC |
965 | /* Try to handle Pseudo-Marsenne primes. */ |
966 | if (curve_prime[ndigits - 1] == -1ull) { | |
967 | vli_mmod_special(result, product, curve_prime, | |
968 | ndigits); | |
969 | return true; | |
970 | } else if (curve_prime[ndigits - 1] == 1ull << 63 && | |
971 | curve_prime[ndigits - 2] == 0) { | |
972 | vli_mmod_special2(result, product, curve_prime, | |
973 | ndigits); | |
974 | return true; | |
975 | } | |
976 | vli_mmod_barrett(result, product, curve_prime, ndigits); | |
977 | return true; | |
978 | } | |
979 | ||
3c4b2390 | 980 | switch (ndigits) { |
526d23fc | 981 | case ECC_CURVE_NIST_P192_DIGITS: |
3c4b2390 SB |
982 | vli_mmod_fast_192(result, product, curve_prime, tmp); |
983 | break; | |
526d23fc | 984 | case ECC_CURVE_NIST_P256_DIGITS: |
3c4b2390 SB |
985 | vli_mmod_fast_256(result, product, curve_prime, tmp); |
986 | break; | |
526d23fc | 987 | case ECC_CURVE_NIST_P384_DIGITS: |
149ca161 SA |
988 | vli_mmod_fast_384(result, product, curve_prime, tmp); |
989 | break; | |
e7fb0627 SB |
990 | case ECC_CURVE_NIST_P521_DIGITS: |
991 | vli_mmod_fast_521(result, product, curve_prime, tmp); | |
992 | break; | |
3c4b2390 | 993 | default: |
0d7a7864 | 994 | pr_err_ratelimited("ecc: unsupported digits size!\n"); |
3c4b2390 SB |
995 | return false; |
996 | } | |
997 | ||
998 | return true; | |
999 | } | |
1000 | ||
0d7a7864 VC |
1001 | /* Computes result = (left * right) % mod. |
1002 | * Assumes that mod is big enough curve order. | |
1003 | */ | |
1004 | void vli_mod_mult_slow(u64 *result, const u64 *left, const u64 *right, | |
1005 | const u64 *mod, unsigned int ndigits) | |
1006 | { | |
1007 | u64 product[ECC_MAX_DIGITS * 2]; | |
1008 | ||
1009 | vli_mult(product, left, right, ndigits); | |
1010 | vli_mmod_slow(result, product, mod, ndigits); | |
1011 | } | |
1012 | EXPORT_SYMBOL(vli_mod_mult_slow); | |
1013 | ||
3c4b2390 SB |
1014 | /* Computes result = (left * right) % curve_prime. */ |
1015 | static void vli_mod_mult_fast(u64 *result, const u64 *left, const u64 *right, | |
149ca161 | 1016 | const struct ecc_curve *curve) |
3c4b2390 | 1017 | { |
d5c3b178 | 1018 | u64 product[2 * ECC_MAX_DIGITS]; |
3c4b2390 | 1019 | |
149ca161 SA |
1020 | vli_mult(product, left, right, curve->g.ndigits); |
1021 | vli_mmod_fast(result, product, curve); | |
3c4b2390 SB |
1022 | } |
1023 | ||
1024 | /* Computes result = left^2 % curve_prime. */ | |
1025 | static void vli_mod_square_fast(u64 *result, const u64 *left, | |
149ca161 | 1026 | const struct ecc_curve *curve) |
3c4b2390 | 1027 | { |
d5c3b178 | 1028 | u64 product[2 * ECC_MAX_DIGITS]; |
3c4b2390 | 1029 | |
149ca161 SA |
1030 | vli_square(product, left, curve->g.ndigits); |
1031 | vli_mmod_fast(result, product, curve); | |
3c4b2390 SB |
1032 | } |
1033 | ||
1034 | #define EVEN(vli) (!(vli[0] & 1)) | |
1035 | /* Computes result = (1 / p_input) % mod. All VLIs are the same size. | |
1036 | * See "From Euclid's GCD to Montgomery Multiplication to the Great Divide" | |
1037 | * https://labs.oracle.com/techrep/2001/smli_tr-2001-95.pdf | |
1038 | */ | |
4a2289da | 1039 | void vli_mod_inv(u64 *result, const u64 *input, const u64 *mod, |
3c4b2390 SB |
1040 | unsigned int ndigits) |
1041 | { | |
d5c3b178 KC |
1042 | u64 a[ECC_MAX_DIGITS], b[ECC_MAX_DIGITS]; |
1043 | u64 u[ECC_MAX_DIGITS], v[ECC_MAX_DIGITS]; | |
3c4b2390 SB |
1044 | u64 carry; |
1045 | int cmp_result; | |
1046 | ||
1047 | if (vli_is_zero(input, ndigits)) { | |
1048 | vli_clear(result, ndigits); | |
1049 | return; | |
1050 | } | |
1051 | ||
1052 | vli_set(a, input, ndigits); | |
1053 | vli_set(b, mod, ndigits); | |
1054 | vli_clear(u, ndigits); | |
1055 | u[0] = 1; | |
1056 | vli_clear(v, ndigits); | |
1057 | ||
1058 | while ((cmp_result = vli_cmp(a, b, ndigits)) != 0) { | |
1059 | carry = 0; | |
1060 | ||
1061 | if (EVEN(a)) { | |
1062 | vli_rshift1(a, ndigits); | |
1063 | ||
1064 | if (!EVEN(u)) | |
1065 | carry = vli_add(u, u, mod, ndigits); | |
1066 | ||
1067 | vli_rshift1(u, ndigits); | |
1068 | if (carry) | |
1069 | u[ndigits - 1] |= 0x8000000000000000ull; | |
1070 | } else if (EVEN(b)) { | |
1071 | vli_rshift1(b, ndigits); | |
1072 | ||
1073 | if (!EVEN(v)) | |
1074 | carry = vli_add(v, v, mod, ndigits); | |
1075 | ||
1076 | vli_rshift1(v, ndigits); | |
1077 | if (carry) | |
1078 | v[ndigits - 1] |= 0x8000000000000000ull; | |
1079 | } else if (cmp_result > 0) { | |
1080 | vli_sub(a, a, b, ndigits); | |
1081 | vli_rshift1(a, ndigits); | |
1082 | ||
1083 | if (vli_cmp(u, v, ndigits) < 0) | |
1084 | vli_add(u, u, mod, ndigits); | |
1085 | ||
1086 | vli_sub(u, u, v, ndigits); | |
1087 | if (!EVEN(u)) | |
1088 | carry = vli_add(u, u, mod, ndigits); | |
1089 | ||
1090 | vli_rshift1(u, ndigits); | |
1091 | if (carry) | |
1092 | u[ndigits - 1] |= 0x8000000000000000ull; | |
1093 | } else { | |
1094 | vli_sub(b, b, a, ndigits); | |
1095 | vli_rshift1(b, ndigits); | |
1096 | ||
1097 | if (vli_cmp(v, u, ndigits) < 0) | |
1098 | vli_add(v, v, mod, ndigits); | |
1099 | ||
1100 | vli_sub(v, v, u, ndigits); | |
1101 | if (!EVEN(v)) | |
1102 | carry = vli_add(v, v, mod, ndigits); | |
1103 | ||
1104 | vli_rshift1(v, ndigits); | |
1105 | if (carry) | |
1106 | v[ndigits - 1] |= 0x8000000000000000ull; | |
1107 | } | |
1108 | } | |
1109 | ||
1110 | vli_set(result, u, ndigits); | |
1111 | } | |
4a2289da | 1112 | EXPORT_SYMBOL(vli_mod_inv); |
3c4b2390 SB |
1113 | |
1114 | /* ------ Point operations ------ */ | |
1115 | ||
1116 | /* Returns true if p_point is the point at infinity, false otherwise. */ | |
eaffe377 | 1117 | bool ecc_point_is_zero(const struct ecc_point *point) |
3c4b2390 SB |
1118 | { |
1119 | return (vli_is_zero(point->x, point->ndigits) && | |
1120 | vli_is_zero(point->y, point->ndigits)); | |
1121 | } | |
eaffe377 | 1122 | EXPORT_SYMBOL(ecc_point_is_zero); |
3c4b2390 SB |
1123 | |
1124 | /* Point multiplication algorithm using Montgomery's ladder with co-Z | |
9332a9e7 | 1125 | * coordinates. From https://eprint.iacr.org/2011/338.pdf |
3c4b2390 SB |
1126 | */ |
1127 | ||
1128 | /* Double in place */ | |
1129 | static void ecc_point_double_jacobian(u64 *x1, u64 *y1, u64 *z1, | |
149ca161 | 1130 | const struct ecc_curve *curve) |
3c4b2390 SB |
1131 | { |
1132 | /* t1 = x, t2 = y, t3 = z */ | |
d5c3b178 KC |
1133 | u64 t4[ECC_MAX_DIGITS]; |
1134 | u64 t5[ECC_MAX_DIGITS]; | |
149ca161 SA |
1135 | const u64 *curve_prime = curve->p; |
1136 | const unsigned int ndigits = curve->g.ndigits; | |
3c4b2390 SB |
1137 | |
1138 | if (vli_is_zero(z1, ndigits)) | |
1139 | return; | |
1140 | ||
1141 | /* t4 = y1^2 */ | |
149ca161 | 1142 | vli_mod_square_fast(t4, y1, curve); |
3c4b2390 | 1143 | /* t5 = x1*y1^2 = A */ |
149ca161 | 1144 | vli_mod_mult_fast(t5, x1, t4, curve); |
3c4b2390 | 1145 | /* t4 = y1^4 */ |
149ca161 | 1146 | vli_mod_square_fast(t4, t4, curve); |
3c4b2390 | 1147 | /* t2 = y1*z1 = z3 */ |
149ca161 | 1148 | vli_mod_mult_fast(y1, y1, z1, curve); |
3c4b2390 | 1149 | /* t3 = z1^2 */ |
149ca161 | 1150 | vli_mod_square_fast(z1, z1, curve); |
3c4b2390 SB |
1151 | |
1152 | /* t1 = x1 + z1^2 */ | |
1153 | vli_mod_add(x1, x1, z1, curve_prime, ndigits); | |
1154 | /* t3 = 2*z1^2 */ | |
1155 | vli_mod_add(z1, z1, z1, curve_prime, ndigits); | |
1156 | /* t3 = x1 - z1^2 */ | |
1157 | vli_mod_sub(z1, x1, z1, curve_prime, ndigits); | |
1158 | /* t1 = x1^2 - z1^4 */ | |
149ca161 | 1159 | vli_mod_mult_fast(x1, x1, z1, curve); |
3c4b2390 SB |
1160 | |
1161 | /* t3 = 2*(x1^2 - z1^4) */ | |
1162 | vli_mod_add(z1, x1, x1, curve_prime, ndigits); | |
1163 | /* t1 = 3*(x1^2 - z1^4) */ | |
1164 | vli_mod_add(x1, x1, z1, curve_prime, ndigits); | |
1165 | if (vli_test_bit(x1, 0)) { | |
1166 | u64 carry = vli_add(x1, x1, curve_prime, ndigits); | |
1167 | ||
1168 | vli_rshift1(x1, ndigits); | |
1169 | x1[ndigits - 1] |= carry << 63; | |
1170 | } else { | |
1171 | vli_rshift1(x1, ndigits); | |
1172 | } | |
1173 | /* t1 = 3/2*(x1^2 - z1^4) = B */ | |
1174 | ||
1175 | /* t3 = B^2 */ | |
149ca161 | 1176 | vli_mod_square_fast(z1, x1, curve); |
3c4b2390 SB |
1177 | /* t3 = B^2 - A */ |
1178 | vli_mod_sub(z1, z1, t5, curve_prime, ndigits); | |
1179 | /* t3 = B^2 - 2A = x3 */ | |
1180 | vli_mod_sub(z1, z1, t5, curve_prime, ndigits); | |
1181 | /* t5 = A - x3 */ | |
1182 | vli_mod_sub(t5, t5, z1, curve_prime, ndigits); | |
1183 | /* t1 = B * (A - x3) */ | |
149ca161 | 1184 | vli_mod_mult_fast(x1, x1, t5, curve); |
3c4b2390 SB |
1185 | /* t4 = B * (A - x3) - y1^4 = y3 */ |
1186 | vli_mod_sub(t4, x1, t4, curve_prime, ndigits); | |
1187 | ||
1188 | vli_set(x1, z1, ndigits); | |
1189 | vli_set(z1, y1, ndigits); | |
1190 | vli_set(y1, t4, ndigits); | |
1191 | } | |
1192 | ||
1193 | /* Modify (x1, y1) => (x1 * z^2, y1 * z^3) */ | |
149ca161 | 1194 | static void apply_z(u64 *x1, u64 *y1, u64 *z, const struct ecc_curve *curve) |
3c4b2390 | 1195 | { |
d5c3b178 | 1196 | u64 t1[ECC_MAX_DIGITS]; |
3c4b2390 | 1197 | |
149ca161 SA |
1198 | vli_mod_square_fast(t1, z, curve); /* z^2 */ |
1199 | vli_mod_mult_fast(x1, x1, t1, curve); /* x1 * z^2 */ | |
1200 | vli_mod_mult_fast(t1, t1, z, curve); /* z^3 */ | |
1201 | vli_mod_mult_fast(y1, y1, t1, curve); /* y1 * z^3 */ | |
3c4b2390 SB |
1202 | } |
1203 | ||
1204 | /* P = (x1, y1) => 2P, (x2, y2) => P' */ | |
1205 | static void xycz_initial_double(u64 *x1, u64 *y1, u64 *x2, u64 *y2, | |
149ca161 | 1206 | u64 *p_initial_z, const struct ecc_curve *curve) |
3c4b2390 | 1207 | { |
d5c3b178 | 1208 | u64 z[ECC_MAX_DIGITS]; |
149ca161 | 1209 | const unsigned int ndigits = curve->g.ndigits; |
3c4b2390 SB |
1210 | |
1211 | vli_set(x2, x1, ndigits); | |
1212 | vli_set(y2, y1, ndigits); | |
1213 | ||
1214 | vli_clear(z, ndigits); | |
1215 | z[0] = 1; | |
1216 | ||
1217 | if (p_initial_z) | |
1218 | vli_set(z, p_initial_z, ndigits); | |
1219 | ||
149ca161 | 1220 | apply_z(x1, y1, z, curve); |
3c4b2390 | 1221 | |
149ca161 | 1222 | ecc_point_double_jacobian(x1, y1, z, curve); |
3c4b2390 | 1223 | |
149ca161 | 1224 | apply_z(x2, y2, z, curve); |
3c4b2390 SB |
1225 | } |
1226 | ||
1227 | /* Input P = (x1, y1, Z), Q = (x2, y2, Z) | |
1228 | * Output P' = (x1', y1', Z3), P + Q = (x3, y3, Z3) | |
1229 | * or P => P', Q => P + Q | |
1230 | */ | |
149ca161 SA |
1231 | static void xycz_add(u64 *x1, u64 *y1, u64 *x2, u64 *y2, |
1232 | const struct ecc_curve *curve) | |
3c4b2390 SB |
1233 | { |
1234 | /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */ | |
d5c3b178 | 1235 | u64 t5[ECC_MAX_DIGITS]; |
149ca161 SA |
1236 | const u64 *curve_prime = curve->p; |
1237 | const unsigned int ndigits = curve->g.ndigits; | |
3c4b2390 SB |
1238 | |
1239 | /* t5 = x2 - x1 */ | |
1240 | vli_mod_sub(t5, x2, x1, curve_prime, ndigits); | |
1241 | /* t5 = (x2 - x1)^2 = A */ | |
149ca161 | 1242 | vli_mod_square_fast(t5, t5, curve); |
3c4b2390 | 1243 | /* t1 = x1*A = B */ |
149ca161 | 1244 | vli_mod_mult_fast(x1, x1, t5, curve); |
3c4b2390 | 1245 | /* t3 = x2*A = C */ |
149ca161 | 1246 | vli_mod_mult_fast(x2, x2, t5, curve); |
3c4b2390 SB |
1247 | /* t4 = y2 - y1 */ |
1248 | vli_mod_sub(y2, y2, y1, curve_prime, ndigits); | |
1249 | /* t5 = (y2 - y1)^2 = D */ | |
149ca161 | 1250 | vli_mod_square_fast(t5, y2, curve); |
3c4b2390 SB |
1251 | |
1252 | /* t5 = D - B */ | |
1253 | vli_mod_sub(t5, t5, x1, curve_prime, ndigits); | |
1254 | /* t5 = D - B - C = x3 */ | |
1255 | vli_mod_sub(t5, t5, x2, curve_prime, ndigits); | |
1256 | /* t3 = C - B */ | |
1257 | vli_mod_sub(x2, x2, x1, curve_prime, ndigits); | |
1258 | /* t2 = y1*(C - B) */ | |
149ca161 | 1259 | vli_mod_mult_fast(y1, y1, x2, curve); |
3c4b2390 SB |
1260 | /* t3 = B - x3 */ |
1261 | vli_mod_sub(x2, x1, t5, curve_prime, ndigits); | |
1262 | /* t4 = (y2 - y1)*(B - x3) */ | |
149ca161 | 1263 | vli_mod_mult_fast(y2, y2, x2, curve); |
3c4b2390 SB |
1264 | /* t4 = y3 */ |
1265 | vli_mod_sub(y2, y2, y1, curve_prime, ndigits); | |
1266 | ||
1267 | vli_set(x2, t5, ndigits); | |
1268 | } | |
1269 | ||
1270 | /* Input P = (x1, y1, Z), Q = (x2, y2, Z) | |
1271 | * Output P + Q = (x3, y3, Z3), P - Q = (x3', y3', Z3) | |
1272 | * or P => P - Q, Q => P + Q | |
1273 | */ | |
149ca161 SA |
1274 | static void xycz_add_c(u64 *x1, u64 *y1, u64 *x2, u64 *y2, |
1275 | const struct ecc_curve *curve) | |
3c4b2390 SB |
1276 | { |
1277 | /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */ | |
d5c3b178 KC |
1278 | u64 t5[ECC_MAX_DIGITS]; |
1279 | u64 t6[ECC_MAX_DIGITS]; | |
1280 | u64 t7[ECC_MAX_DIGITS]; | |
149ca161 SA |
1281 | const u64 *curve_prime = curve->p; |
1282 | const unsigned int ndigits = curve->g.ndigits; | |
3c4b2390 SB |
1283 | |
1284 | /* t5 = x2 - x1 */ | |
1285 | vli_mod_sub(t5, x2, x1, curve_prime, ndigits); | |
1286 | /* t5 = (x2 - x1)^2 = A */ | |
149ca161 | 1287 | vli_mod_square_fast(t5, t5, curve); |
3c4b2390 | 1288 | /* t1 = x1*A = B */ |
149ca161 | 1289 | vli_mod_mult_fast(x1, x1, t5, curve); |
3c4b2390 | 1290 | /* t3 = x2*A = C */ |
149ca161 | 1291 | vli_mod_mult_fast(x2, x2, t5, curve); |
3c4b2390 SB |
1292 | /* t4 = y2 + y1 */ |
1293 | vli_mod_add(t5, y2, y1, curve_prime, ndigits); | |
1294 | /* t4 = y2 - y1 */ | |
1295 | vli_mod_sub(y2, y2, y1, curve_prime, ndigits); | |
1296 | ||
1297 | /* t6 = C - B */ | |
1298 | vli_mod_sub(t6, x2, x1, curve_prime, ndigits); | |
1299 | /* t2 = y1 * (C - B) */ | |
149ca161 | 1300 | vli_mod_mult_fast(y1, y1, t6, curve); |
3c4b2390 SB |
1301 | /* t6 = B + C */ |
1302 | vli_mod_add(t6, x1, x2, curve_prime, ndigits); | |
1303 | /* t3 = (y2 - y1)^2 */ | |
149ca161 | 1304 | vli_mod_square_fast(x2, y2, curve); |
3c4b2390 SB |
1305 | /* t3 = x3 */ |
1306 | vli_mod_sub(x2, x2, t6, curve_prime, ndigits); | |
1307 | ||
1308 | /* t7 = B - x3 */ | |
1309 | vli_mod_sub(t7, x1, x2, curve_prime, ndigits); | |
1310 | /* t4 = (y2 - y1)*(B - x3) */ | |
149ca161 | 1311 | vli_mod_mult_fast(y2, y2, t7, curve); |
3c4b2390 SB |
1312 | /* t4 = y3 */ |
1313 | vli_mod_sub(y2, y2, y1, curve_prime, ndigits); | |
1314 | ||
1315 | /* t7 = (y2 + y1)^2 = F */ | |
149ca161 | 1316 | vli_mod_square_fast(t7, t5, curve); |
3c4b2390 SB |
1317 | /* t7 = x3' */ |
1318 | vli_mod_sub(t7, t7, t6, curve_prime, ndigits); | |
1319 | /* t6 = x3' - B */ | |
1320 | vli_mod_sub(t6, t7, x1, curve_prime, ndigits); | |
1321 | /* t6 = (y2 + y1)*(x3' - B) */ | |
149ca161 | 1322 | vli_mod_mult_fast(t6, t6, t5, curve); |
3c4b2390 SB |
1323 | /* t2 = y3' */ |
1324 | vli_mod_sub(y1, t6, y1, curve_prime, ndigits); | |
1325 | ||
1326 | vli_set(x1, t7, ndigits); | |
1327 | } | |
1328 | ||
1329 | static void ecc_point_mult(struct ecc_point *result, | |
1330 | const struct ecc_point *point, const u64 *scalar, | |
3da2c1df | 1331 | u64 *initial_z, const struct ecc_curve *curve, |
3c4b2390 SB |
1332 | unsigned int ndigits) |
1333 | { | |
1334 | /* R0 and R1 */ | |
d5c3b178 KC |
1335 | u64 rx[2][ECC_MAX_DIGITS]; |
1336 | u64 ry[2][ECC_MAX_DIGITS]; | |
1337 | u64 z[ECC_MAX_DIGITS]; | |
3da2c1df VC |
1338 | u64 sk[2][ECC_MAX_DIGITS]; |
1339 | u64 *curve_prime = curve->p; | |
3c4b2390 | 1340 | int i, nb; |
3da2c1df VC |
1341 | int num_bits; |
1342 | int carry; | |
1343 | ||
1344 | carry = vli_add(sk[0], scalar, curve->n, ndigits); | |
1345 | vli_add(sk[1], sk[0], curve->n, ndigits); | |
1346 | scalar = sk[!carry]; | |
114e8043 SB |
1347 | if (curve->nbits == 521) /* NIST P521 */ |
1348 | num_bits = curve->nbits + 2; | |
1349 | else | |
1350 | num_bits = sizeof(u64) * ndigits * 8 + 1; | |
3c4b2390 SB |
1351 | |
1352 | vli_set(rx[1], point->x, ndigits); | |
1353 | vli_set(ry[1], point->y, ndigits); | |
1354 | ||
149ca161 | 1355 | xycz_initial_double(rx[1], ry[1], rx[0], ry[0], initial_z, curve); |
3c4b2390 SB |
1356 | |
1357 | for (i = num_bits - 2; i > 0; i--) { | |
1358 | nb = !vli_test_bit(scalar, i); | |
149ca161 SA |
1359 | xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb], curve); |
1360 | xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve); | |
3c4b2390 SB |
1361 | } |
1362 | ||
1363 | nb = !vli_test_bit(scalar, 0); | |
149ca161 | 1364 | xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb], curve); |
3c4b2390 SB |
1365 | |
1366 | /* Find final 1/Z value. */ | |
1367 | /* X1 - X0 */ | |
1368 | vli_mod_sub(z, rx[1], rx[0], curve_prime, ndigits); | |
1369 | /* Yb * (X1 - X0) */ | |
149ca161 | 1370 | vli_mod_mult_fast(z, z, ry[1 - nb], curve); |
3c4b2390 | 1371 | /* xP * Yb * (X1 - X0) */ |
149ca161 | 1372 | vli_mod_mult_fast(z, z, point->x, curve); |
3c4b2390 SB |
1373 | |
1374 | /* 1 / (xP * Yb * (X1 - X0)) */ | |
1375 | vli_mod_inv(z, z, curve_prime, point->ndigits); | |
1376 | ||
1377 | /* yP / (xP * Yb * (X1 - X0)) */ | |
149ca161 | 1378 | vli_mod_mult_fast(z, z, point->y, curve); |
3c4b2390 | 1379 | /* Xb * yP / (xP * Yb * (X1 - X0)) */ |
149ca161 | 1380 | vli_mod_mult_fast(z, z, rx[1 - nb], curve); |
3c4b2390 SB |
1381 | /* End 1/Z calculation */ |
1382 | ||
149ca161 | 1383 | xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve); |
3c4b2390 | 1384 | |
149ca161 | 1385 | apply_z(rx[0], ry[0], z, curve); |
3c4b2390 SB |
1386 | |
1387 | vli_set(result->x, rx[0], ndigits); | |
1388 | vli_set(result->y, ry[0], ndigits); | |
1389 | } | |
1390 | ||
0d7a7864 VC |
1391 | /* Computes R = P + Q mod p */ |
1392 | static void ecc_point_add(const struct ecc_point *result, | |
1393 | const struct ecc_point *p, const struct ecc_point *q, | |
1394 | const struct ecc_curve *curve) | |
1395 | { | |
1396 | u64 z[ECC_MAX_DIGITS]; | |
1397 | u64 px[ECC_MAX_DIGITS]; | |
1398 | u64 py[ECC_MAX_DIGITS]; | |
1399 | unsigned int ndigits = curve->g.ndigits; | |
1400 | ||
1401 | vli_set(result->x, q->x, ndigits); | |
1402 | vli_set(result->y, q->y, ndigits); | |
1403 | vli_mod_sub(z, result->x, p->x, curve->p, ndigits); | |
1404 | vli_set(px, p->x, ndigits); | |
1405 | vli_set(py, p->y, ndigits); | |
149ca161 | 1406 | xycz_add(px, py, result->x, result->y, curve); |
0d7a7864 | 1407 | vli_mod_inv(z, z, curve->p, ndigits); |
149ca161 | 1408 | apply_z(result->x, result->y, z, curve); |
0d7a7864 VC |
1409 | } |
1410 | ||
1411 | /* Computes R = u1P + u2Q mod p using Shamir's trick. | |
1412 | * Based on: Kenneth MacKay's micro-ecc (2014). | |
1413 | */ | |
1414 | void ecc_point_mult_shamir(const struct ecc_point *result, | |
1415 | const u64 *u1, const struct ecc_point *p, | |
1416 | const u64 *u2, const struct ecc_point *q, | |
1417 | const struct ecc_curve *curve) | |
1418 | { | |
1419 | u64 z[ECC_MAX_DIGITS]; | |
1420 | u64 sump[2][ECC_MAX_DIGITS]; | |
1421 | u64 *rx = result->x; | |
1422 | u64 *ry = result->y; | |
1423 | unsigned int ndigits = curve->g.ndigits; | |
1424 | unsigned int num_bits; | |
1425 | struct ecc_point sum = ECC_POINT_INIT(sump[0], sump[1], ndigits); | |
1426 | const struct ecc_point *points[4]; | |
1427 | const struct ecc_point *point; | |
1428 | unsigned int idx; | |
1429 | int i; | |
1430 | ||
1431 | ecc_point_add(&sum, p, q, curve); | |
1432 | points[0] = NULL; | |
1433 | points[1] = p; | |
1434 | points[2] = q; | |
1435 | points[3] = ∑ | |
1436 | ||
149ca161 | 1437 | num_bits = max(vli_num_bits(u1, ndigits), vli_num_bits(u2, ndigits)); |
0d7a7864 | 1438 | i = num_bits - 1; |
5072b1c2 HX |
1439 | idx = !!vli_test_bit(u1, i); |
1440 | idx |= (!!vli_test_bit(u2, i)) << 1; | |
0d7a7864 VC |
1441 | point = points[idx]; |
1442 | ||
1443 | vli_set(rx, point->x, ndigits); | |
1444 | vli_set(ry, point->y, ndigits); | |
1445 | vli_clear(z + 1, ndigits - 1); | |
1446 | z[0] = 1; | |
1447 | ||
1448 | for (--i; i >= 0; i--) { | |
149ca161 | 1449 | ecc_point_double_jacobian(rx, ry, z, curve); |
5072b1c2 HX |
1450 | idx = !!vli_test_bit(u1, i); |
1451 | idx |= (!!vli_test_bit(u2, i)) << 1; | |
0d7a7864 VC |
1452 | point = points[idx]; |
1453 | if (point) { | |
1454 | u64 tx[ECC_MAX_DIGITS]; | |
1455 | u64 ty[ECC_MAX_DIGITS]; | |
1456 | u64 tz[ECC_MAX_DIGITS]; | |
1457 | ||
1458 | vli_set(tx, point->x, ndigits); | |
1459 | vli_set(ty, point->y, ndigits); | |
149ca161 | 1460 | apply_z(tx, ty, z, curve); |
0d7a7864 | 1461 | vli_mod_sub(tz, rx, tx, curve->p, ndigits); |
149ca161 SA |
1462 | xycz_add(tx, ty, rx, ry, curve); |
1463 | vli_mod_mult_fast(z, z, tz, curve); | |
0d7a7864 VC |
1464 | } |
1465 | } | |
1466 | vli_mod_inv(z, z, curve->p, ndigits); | |
149ca161 | 1467 | apply_z(rx, ry, z, curve); |
0d7a7864 VC |
1468 | } |
1469 | EXPORT_SYMBOL(ecc_point_mult_shamir); | |
1470 | ||
dbad7b69 JV |
1471 | /* |
1472 | * This function performs checks equivalent to Appendix A.4.2 of FIPS 186-5. | |
1473 | * Whereas A.4.2 results in an integer in the interval [1, n-1], this function | |
1474 | * ensures that the integer is in the range of [2, n-3]. We are slightly | |
1475 | * stricter because of the currently used scalar multiplication algorithm. | |
1476 | */ | |
2eb4942b VC |
1477 | static int __ecc_is_key_valid(const struct ecc_curve *curve, |
1478 | const u64 *private_key, unsigned int ndigits) | |
3c4b2390 | 1479 | { |
2eb4942b VC |
1480 | u64 one[ECC_MAX_DIGITS] = { 1, }; |
1481 | u64 res[ECC_MAX_DIGITS]; | |
3c4b2390 SB |
1482 | |
1483 | if (!private_key) | |
1484 | return -EINVAL; | |
1485 | ||
2eb4942b | 1486 | if (curve->g.ndigits != ndigits) |
3c4b2390 SB |
1487 | return -EINVAL; |
1488 | ||
2eb4942b VC |
1489 | /* Make sure the private key is in the range [2, n-3]. */ |
1490 | if (vli_cmp(one, private_key, ndigits) != -1) | |
3c4b2390 | 1491 | return -EINVAL; |
2eb4942b VC |
1492 | vli_sub(res, curve->n, one, ndigits); |
1493 | vli_sub(res, res, one, ndigits); | |
1494 | if (vli_cmp(res, private_key, ndigits) != 1) | |
3c4b2390 SB |
1495 | return -EINVAL; |
1496 | ||
1497 | return 0; | |
1498 | } | |
1499 | ||
2eb4942b VC |
1500 | int ecc_is_key_valid(unsigned int curve_id, unsigned int ndigits, |
1501 | const u64 *private_key, unsigned int private_key_len) | |
1502 | { | |
1503 | int nbytes; | |
1504 | const struct ecc_curve *curve = ecc_get_curve(curve_id); | |
1505 | ||
1506 | nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT; | |
1507 | ||
1508 | if (private_key_len != nbytes) | |
1509 | return -EINVAL; | |
1510 | ||
1511 | return __ecc_is_key_valid(curve, private_key, ndigits); | |
1512 | } | |
4a2289da | 1513 | EXPORT_SYMBOL(ecc_is_key_valid); |
2eb4942b | 1514 | |
6755fd26 | 1515 | /* |
dbad7b69 JV |
1516 | * ECC private keys are generated using the method of rejection sampling, |
1517 | * equivalent to that described in FIPS 186-5, Appendix A.2.2. | |
6755fd26 TDA |
1518 | * |
1519 | * This method generates a private key uniformly distributed in the range | |
dbad7b69 | 1520 | * [2, n-3]. |
6755fd26 | 1521 | */ |
01474b70 SB |
1522 | int ecc_gen_privkey(unsigned int curve_id, unsigned int ndigits, |
1523 | u64 *private_key) | |
6755fd26 TDA |
1524 | { |
1525 | const struct ecc_curve *curve = ecc_get_curve(curve_id); | |
6755fd26 TDA |
1526 | unsigned int nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT; |
1527 | unsigned int nbits = vli_num_bits(curve->n, ndigits); | |
1528 | int err; | |
1529 | ||
dbad7b69 JV |
1530 | /* |
1531 | * Step 1 & 2: check that N is included in Table 1 of FIPS 186-5, | |
1532 | * section 6.1.1. | |
1533 | */ | |
01474b70 | 1534 | if (nbits < 224) |
6755fd26 TDA |
1535 | return -EINVAL; |
1536 | ||
1537 | /* | |
dbad7b69 | 1538 | * FIPS 186-5 recommends that the private key should be obtained from a |
6755fd26 TDA |
1539 | * RBG with a security strength equal to or greater than the security |
1540 | * strength associated with N. | |
1541 | * | |
1542 | * The maximum security strength identified by NIST SP800-57pt1r4 for | |
1543 | * ECC is 256 (N >= 512). | |
1544 | * | |
1545 | * This condition is met by the default RNG because it selects a favored | |
1546 | * DRBG with a security strength of 256. | |
1547 | */ | |
1548 | if (crypto_get_default_rng()) | |
4c0e22c9 | 1549 | return -EFAULT; |
6755fd26 | 1550 | |
dbad7b69 | 1551 | /* Step 3: obtain N returned_bits from the DRBG. */ |
01474b70 SB |
1552 | err = crypto_rng_get_bytes(crypto_default_rng, |
1553 | (u8 *)private_key, nbytes); | |
6755fd26 TDA |
1554 | crypto_put_default_rng(); |
1555 | if (err) | |
1556 | return err; | |
1557 | ||
dbad7b69 | 1558 | /* Step 4: make sure the private key is in the valid range. */ |
01474b70 | 1559 | if (__ecc_is_key_valid(curve, private_key, ndigits)) |
6755fd26 TDA |
1560 | return -EINVAL; |
1561 | ||
6755fd26 TDA |
1562 | return 0; |
1563 | } | |
4a2289da | 1564 | EXPORT_SYMBOL(ecc_gen_privkey); |
6755fd26 | 1565 | |
7380c56d TDA |
1566 | int ecc_make_pub_key(unsigned int curve_id, unsigned int ndigits, |
1567 | const u64 *private_key, u64 *public_key) | |
3c4b2390 SB |
1568 | { |
1569 | int ret = 0; | |
1570 | struct ecc_point *pk; | |
3c4b2390 SB |
1571 | const struct ecc_curve *curve = ecc_get_curve(curve_id); |
1572 | ||
01474b70 | 1573 | if (!private_key) { |
3c4b2390 SB |
1574 | ret = -EINVAL; |
1575 | goto out; | |
1576 | } | |
1577 | ||
3c4b2390 SB |
1578 | pk = ecc_alloc_point(ndigits); |
1579 | if (!pk) { | |
1580 | ret = -ENOMEM; | |
1581 | goto out; | |
1582 | } | |
1583 | ||
01474b70 | 1584 | ecc_point_mult(pk, &curve->g, private_key, NULL, curve, ndigits); |
6914dd53 SM |
1585 | |
1586 | /* SP800-56A rev 3 5.6.2.1.3 key check */ | |
1587 | if (ecc_is_pubkey_valid_full(curve, pk)) { | |
3c4b2390 SB |
1588 | ret = -EAGAIN; |
1589 | goto err_free_point; | |
1590 | } | |
1591 | ||
ad269597 TDA |
1592 | ecc_swap_digits(pk->x, public_key, ndigits); |
1593 | ecc_swap_digits(pk->y, &public_key[ndigits], ndigits); | |
3c4b2390 SB |
1594 | |
1595 | err_free_point: | |
1596 | ecc_free_point(pk); | |
1597 | out: | |
1598 | return ret; | |
1599 | } | |
4a2289da | 1600 | EXPORT_SYMBOL(ecc_make_pub_key); |
3c4b2390 | 1601 | |
ea169a30 | 1602 | /* SP800-56A section 5.6.2.3.4 partial verification: ephemeral keys only */ |
4a2289da VC |
1603 | int ecc_is_pubkey_valid_partial(const struct ecc_curve *curve, |
1604 | struct ecc_point *pk) | |
ea169a30 SM |
1605 | { |
1606 | u64 yy[ECC_MAX_DIGITS], xxx[ECC_MAX_DIGITS], w[ECC_MAX_DIGITS]; | |
1607 | ||
0d7a7864 VC |
1608 | if (WARN_ON(pk->ndigits != curve->g.ndigits)) |
1609 | return -EINVAL; | |
1610 | ||
ea169a30 SM |
1611 | /* Check 1: Verify key is not the zero point. */ |
1612 | if (ecc_point_is_zero(pk)) | |
1613 | return -EINVAL; | |
1614 | ||
1615 | /* Check 2: Verify key is in the range [1, p-1]. */ | |
1616 | if (vli_cmp(curve->p, pk->x, pk->ndigits) != 1) | |
1617 | return -EINVAL; | |
1618 | if (vli_cmp(curve->p, pk->y, pk->ndigits) != 1) | |
1619 | return -EINVAL; | |
1620 | ||
1621 | /* Check 3: Verify that y^2 == (x^3 + a·x + b) mod p */ | |
149ca161 SA |
1622 | vli_mod_square_fast(yy, pk->y, curve); /* y^2 */ |
1623 | vli_mod_square_fast(xxx, pk->x, curve); /* x^2 */ | |
1624 | vli_mod_mult_fast(xxx, xxx, pk->x, curve); /* x^3 */ | |
1625 | vli_mod_mult_fast(w, curve->a, pk->x, curve); /* a·x */ | |
ea169a30 SM |
1626 | vli_mod_add(w, w, curve->b, curve->p, pk->ndigits); /* a·x + b */ |
1627 | vli_mod_add(w, w, xxx, curve->p, pk->ndigits); /* x^3 + a·x + b */ | |
1628 | if (vli_cmp(yy, w, pk->ndigits) != 0) /* Equation */ | |
1629 | return -EINVAL; | |
1630 | ||
1631 | return 0; | |
ea169a30 | 1632 | } |
4a2289da | 1633 | EXPORT_SYMBOL(ecc_is_pubkey_valid_partial); |
ea169a30 | 1634 | |
6914dd53 SM |
1635 | /* SP800-56A section 5.6.2.3.3 full verification */ |
1636 | int ecc_is_pubkey_valid_full(const struct ecc_curve *curve, | |
1637 | struct ecc_point *pk) | |
1638 | { | |
1639 | struct ecc_point *nQ; | |
1640 | ||
1641 | /* Checks 1 through 3 */ | |
1642 | int ret = ecc_is_pubkey_valid_partial(curve, pk); | |
1643 | ||
1644 | if (ret) | |
1645 | return ret; | |
1646 | ||
1647 | /* Check 4: Verify that nQ is the zero point. */ | |
1648 | nQ = ecc_alloc_point(pk->ndigits); | |
1649 | if (!nQ) | |
1650 | return -ENOMEM; | |
1651 | ||
1652 | ecc_point_mult(nQ, pk, curve->n, NULL, curve, pk->ndigits); | |
1653 | if (!ecc_point_is_zero(nQ)) | |
1654 | ret = -EINVAL; | |
1655 | ||
1656 | ecc_free_point(nQ); | |
1657 | ||
1658 | return ret; | |
1659 | } | |
1660 | EXPORT_SYMBOL(ecc_is_pubkey_valid_full); | |
1661 | ||
8f44df15 | 1662 | int crypto_ecdh_shared_secret(unsigned int curve_id, unsigned int ndigits, |
ad269597 TDA |
1663 | const u64 *private_key, const u64 *public_key, |
1664 | u64 *secret) | |
3c4b2390 SB |
1665 | { |
1666 | int ret = 0; | |
1667 | struct ecc_point *product, *pk; | |
d5c3b178 KC |
1668 | u64 rand_z[ECC_MAX_DIGITS]; |
1669 | unsigned int nbytes; | |
3c4b2390 SB |
1670 | const struct ecc_curve *curve = ecc_get_curve(curve_id); |
1671 | ||
01474b70 | 1672 | if (!private_key || !public_key || ndigits > ARRAY_SIZE(rand_z)) { |
3c4b2390 SB |
1673 | ret = -EINVAL; |
1674 | goto out; | |
1675 | } | |
1676 | ||
d5c3b178 | 1677 | nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT; |
3c4b2390 | 1678 | |
d5c3b178 | 1679 | get_random_bytes(rand_z, nbytes); |
3c4b2390 SB |
1680 | |
1681 | pk = ecc_alloc_point(ndigits); | |
1682 | if (!pk) { | |
1683 | ret = -ENOMEM; | |
d5c3b178 | 1684 | goto out; |
3c4b2390 SB |
1685 | } |
1686 | ||
ea169a30 SM |
1687 | ecc_swap_digits(public_key, pk->x, ndigits); |
1688 | ecc_swap_digits(&public_key[ndigits], pk->y, ndigits); | |
1689 | ret = ecc_is_pubkey_valid_partial(curve, pk); | |
1690 | if (ret) | |
1691 | goto err_alloc_product; | |
1692 | ||
3c4b2390 SB |
1693 | product = ecc_alloc_point(ndigits); |
1694 | if (!product) { | |
1695 | ret = -ENOMEM; | |
1696 | goto err_alloc_product; | |
1697 | } | |
1698 | ||
01474b70 | 1699 | ecc_point_mult(product, pk, private_key, rand_z, curve, ndigits); |
3c4b2390 | 1700 | |
e7d2b41e | 1701 | if (ecc_point_is_zero(product)) { |
3c4b2390 | 1702 | ret = -EFAULT; |
e7d2b41e SM |
1703 | goto err_validity; |
1704 | } | |
1705 | ||
1706 | ecc_swap_digits(product->x, secret, ndigits); | |
3c4b2390 | 1707 | |
e7d2b41e | 1708 | err_validity: |
e7d2b41e | 1709 | memzero_explicit(rand_z, sizeof(rand_z)); |
3c4b2390 SB |
1710 | ecc_free_point(product); |
1711 | err_alloc_product: | |
1712 | ecc_free_point(pk); | |
1713 | out: | |
1714 | return ret; | |
1715 | } | |
4a2289da VC |
1716 | EXPORT_SYMBOL(crypto_ecdh_shared_secret); |
1717 | ||
1718 | MODULE_LICENSE("Dual BSD/GPL"); |