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3c4b2390 SB |
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 | ||
36 | typedef struct { | |
37 | u64 m_low; | |
38 | u64 m_high; | |
39 | } uint128_t; | |
40 | ||
41 | static 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 | ||
54 | static 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 | ||
64 | static void ecc_free_digits_space(u64 *space) | |
65 | { | |
66 | kzfree(space); | |
67 | } | |
68 | ||
69 | static 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 | ||
88 | err_alloc_y: | |
89 | ecc_free_digits_space(p->x); | |
90 | err_alloc_x: | |
91 | kfree(p); | |
92 | return NULL; | |
93 | } | |
94 | ||
95 | static 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 | ||
105 | static 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. */ | |
114 | static 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. */ | |
127 | static 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. */ | |
133 | static 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. */ | |
147 | static 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. */ | |
164 | static 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. */ | |
173 | static 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 | */ | |
190 | static 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. */ | |
207 | static 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. */ | |
222 | static 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. */ | |
242 | static 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 | ||
261 | static 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 | ||
286 | static 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 | ||
296 | static 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 | ||
332 | static 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 | */ | |
374 | static 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 | */ | |
391 | static 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 | */ | |
408 | static 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 | */ | |
435 | static 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 | */ | |
514 | static 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. */ | |
535 | static 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. */ | |
545 | static 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 | */ | |
559 | static 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. */ | |
636 | static 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 */ | |
647 | static 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) */ | |
710 | static 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' */ | |
722 | static 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 | */ | |
748 | static 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 | */ | |
789 | static 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 | ||
842 | static 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 | ||
897 | static 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 | ||
906 | int 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 | ||
930 | int 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 | ||
963 | err_free_point: | |
964 | ecc_free_point(pk); | |
965 | out: | |
966 | return ret; | |
967 | } | |
968 | ||
8f44df15 | 969 | int crypto_ecdh_shared_secret(unsigned int curve_id, unsigned int ndigits, |
3c4b2390 SB |
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); | |
1014 | err_alloc_product: | |
1015 | ecc_free_point(pk); | |
1016 | out: | |
1017 | return ret; | |
1018 | } |