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Linux/crypto/ecc.c

  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 
969 int crypto_ecdh_shared_secret(unsigned int curve_id, unsigned int ndigits,
970                        const u8 *private_key, unsigned int private_key_len,
971                        const u8 *public_key, unsigned int public_key_len,
972                        u8 *secret, unsigned int secret_len)
973 {
974         int ret = 0;
975         struct ecc_point *product, *pk;
976         u64 priv[ndigits];
977         u64 rand_z[ndigits];
978         unsigned int nbytes;
979         const struct ecc_curve *curve = ecc_get_curve(curve_id);
980 
981         if (!private_key || !public_key || !curve) {
982                 ret = -EINVAL;
983                 goto out;
984         }
985 
986         nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT;
987 
988         get_random_bytes(rand_z, nbytes);
989 
990         pk = ecc_alloc_point(ndigits);
991         if (!pk) {
992                 ret = -ENOMEM;
993                 goto out;
994         }
995 
996         product = ecc_alloc_point(ndigits);
997         if (!product) {
998                 ret = -ENOMEM;
999                 goto err_alloc_product;
1000         }
1001 
1002         ecc_swap_digits((const u64 *)public_key, pk->x, ndigits);
1003         ecc_swap_digits((const u64 *)&public_key[nbytes], pk->y, ndigits);
1004         ecc_swap_digits((const u64 *)private_key, priv, ndigits);
1005 
1006         ecc_point_mult(product, pk, priv, rand_z, curve->p, ndigits);
1007 
1008         ecc_swap_digits(product->x, (u64 *)secret, ndigits);
1009 
1010         if (ecc_point_is_zero(product))
1011                 ret = -EFAULT;
1012 
1013         ecc_free_point(product);
1014 err_alloc_product:
1015         ecc_free_point(pk);
1016 out:
1017         return ret;
1018 }
1019 

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