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TOMOYO Linux Cross Reference
Linux/crypto/ecc.c

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  1 /*
  2  * Copyright (c) 2013, 2014 Kenneth MacKay. All rights reserved.
  3  * Copyright (c) 2019 Vitaly Chikunov <vt@altlinux.org>
  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 <crypto/ecc_curve.h>
 28 #include <linux/module.h>
 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>
 34 #include <crypto/rng.h>
 35 #include <crypto/internal/ecc.h>
 36 #include <asm/unaligned.h>
 37 #include <linux/ratelimit.h>
 38 
 39 #include "ecc_curve_defs.h"
 40 
 41 typedef struct {
 42         u64 m_low;
 43         u64 m_high;
 44 } uint128_t;
 45 
 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);
 52 
 53 const struct ecc_curve *ecc_get_curve(unsigned int curve_id)
 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;
 61         case ECC_CURVE_NIST_P384:
 62                 return &nist_p384;
 63         default:
 64                 return NULL;
 65         }
 66 }
 67 EXPORT_SYMBOL(ecc_get_curve);
 68 
 69 static u64 *ecc_alloc_digits_space(unsigned int ndigits)
 70 {
 71         size_t len = ndigits * sizeof(u64);
 72 
 73         if (!len)
 74                 return NULL;
 75 
 76         return kmalloc(len, GFP_KERNEL);
 77 }
 78 
 79 static void ecc_free_digits_space(u64 *space)
 80 {
 81         kfree_sensitive(space);
 82 }
 83 
 84 struct ecc_point *ecc_alloc_point(unsigned int ndigits)
 85 {
 86         struct ecc_point *p = kmalloc(sizeof(*p), GFP_KERNEL);
 87 
 88         if (!p)
 89                 return NULL;
 90 
 91         p->x = ecc_alloc_digits_space(ndigits);
 92         if (!p->x)
 93                 goto err_alloc_x;
 94 
 95         p->y = ecc_alloc_digits_space(ndigits);
 96         if (!p->y)
 97                 goto err_alloc_y;
 98 
 99         p->ndigits = ndigits;
100 
101         return p;
102 
103 err_alloc_y:
104         ecc_free_digits_space(p->x);
105 err_alloc_x:
106         kfree(p);
107         return NULL;
108 }
109 EXPORT_SYMBOL(ecc_alloc_point);
110 
111 void ecc_free_point(struct ecc_point *p)
112 {
113         if (!p)
114                 return;
115 
116         kfree_sensitive(p->x);
117         kfree_sensitive(p->y);
118         kfree_sensitive(p);
119 }
120 EXPORT_SYMBOL(ecc_free_point);
121 
122 static void vli_clear(u64 *vli, unsigned int ndigits)
123 {
124         int i;
125 
126         for (i = 0; i < ndigits; i++)
127                 vli[i] = 0;
128 }
129 
130 /* Returns true if vli == 0, false otherwise. */
131 bool vli_is_zero(const u64 *vli, unsigned int ndigits)
132 {
133         int i;
134 
135         for (i = 0; i < ndigits; i++) {
136                 if (vli[i])
137                         return false;
138         }
139 
140         return true;
141 }
142 EXPORT_SYMBOL(vli_is_zero);
143 
144 /* Returns nonzero if bit of vli is set. */
145 static u64 vli_test_bit(const u64 *vli, unsigned int bit)
146 {
147         return (vli[bit / 64] & ((u64)1 << (bit % 64)));
148 }
149 
150 static bool vli_is_negative(const u64 *vli, unsigned int ndigits)
151 {
152         return vli_test_bit(vli, ndigits * 64 - 1);
153 }
154 
155 /* Counts the number of 64-bit "digits" in vli. */
156 static unsigned int vli_num_digits(const u64 *vli, unsigned int ndigits)
157 {
158         int i;
159 
160         /* Search from the end until we find a non-zero digit.
161          * We do it in reverse because we expect that most digits will
162          * be nonzero.
163          */
164         for (i = ndigits - 1; i >= 0 && vli[i] == 0; i--);
165 
166         return (i + 1);
167 }
168 
169 /* Counts the number of bits required for vli. */
170 unsigned int vli_num_bits(const u64 *vli, unsigned int ndigits)
171 {
172         unsigned int i, num_digits;
173         u64 digit;
174 
175         num_digits = vli_num_digits(vli, ndigits);
176         if (num_digits == 0)
177                 return 0;
178 
179         digit = vli[num_digits - 1];
180         for (i = 0; digit; i++)
181                 digit >>= 1;
182 
183         return ((num_digits - 1) * 64 + i);
184 }
185 EXPORT_SYMBOL(vli_num_bits);
186 
187 /* Set dest from unaligned bit string src. */
188 void vli_from_be64(u64 *dest, const void *src, unsigned int ndigits)
189 {
190         int i;
191         const u64 *from = src;
192 
193         for (i = 0; i < ndigits; i++)
194                 dest[i] = get_unaligned_be64(&from[ndigits - 1 - i]);
195 }
196 EXPORT_SYMBOL(vli_from_be64);
197 
198 void vli_from_le64(u64 *dest, const void *src, unsigned int ndigits)
199 {
200         int i;
201         const u64 *from = src;
202 
203         for (i = 0; i < ndigits; i++)
204                 dest[i] = get_unaligned_le64(&from[i]);
205 }
206 EXPORT_SYMBOL(vli_from_le64);
207 
208 /* Sets dest = src. */
209 static void vli_set(u64 *dest, const u64 *src, unsigned int ndigits)
210 {
211         int i;
212 
213         for (i = 0; i < ndigits; i++)
214                 dest[i] = src[i];
215 }
216 
217 /* Returns sign of left - right. */
218 int vli_cmp(const u64 *left, const u64 *right, unsigned int ndigits)
219 {
220         int i;
221 
222         for (i = ndigits - 1; i >= 0; i--) {
223                 if (left[i] > right[i])
224                         return 1;
225                 else if (left[i] < right[i])
226                         return -1;
227         }
228 
229         return 0;
230 }
231 EXPORT_SYMBOL(vli_cmp);
232 
233 /* Computes result = in << c, returning carry. Can modify in place
234  * (if result == in). 0 < shift < 64.
235  */
236 static u64 vli_lshift(u64 *result, const u64 *in, unsigned int shift,
237                       unsigned int ndigits)
238 {
239         u64 carry = 0;
240         int i;
241 
242         for (i = 0; i < ndigits; i++) {
243                 u64 temp = in[i];
244 
245                 result[i] = (temp << shift) | carry;
246                 carry = temp >> (64 - shift);
247         }
248 
249         return carry;
250 }
251 
252 /* Computes vli = vli >> 1. */
253 static void vli_rshift1(u64 *vli, unsigned int ndigits)
254 {
255         u64 *end = vli;
256         u64 carry = 0;
257 
258         vli += ndigits;
259 
260         while (vli-- > end) {
261                 u64 temp = *vli;
262                 *vli = (temp >> 1) | carry;
263                 carry = temp << 63;
264         }
265 }
266 
267 /* Computes result = left + right, returning carry. Can modify in place. */
268 static u64 vli_add(u64 *result, const u64 *left, const u64 *right,
269                    unsigned int ndigits)
270 {
271         u64 carry = 0;
272         int i;
273 
274         for (i = 0; i < ndigits; i++) {
275                 u64 sum;
276 
277                 sum = left[i] + right[i] + carry;
278                 if (sum != left[i])
279                         carry = (sum < left[i]);
280 
281                 result[i] = sum;
282         }
283 
284         return carry;
285 }
286 
287 /* Computes result = left + right, returning carry. Can modify in place. */
288 static u64 vli_uadd(u64 *result, const u64 *left, u64 right,
289                     unsigned int ndigits)
290 {
291         u64 carry = right;
292         int i;
293 
294         for (i = 0; i < ndigits; i++) {
295                 u64 sum;
296 
297                 sum = left[i] + carry;
298                 if (sum != left[i])
299                         carry = (sum < left[i]);
300                 else
301                         carry = !!carry;
302 
303                 result[i] = sum;
304         }
305 
306         return carry;
307 }
308 
309 /* Computes result = left - right, returning borrow. Can modify in place. */
310 u64 vli_sub(u64 *result, const u64 *left, const u64 *right,
311                    unsigned int ndigits)
312 {
313         u64 borrow = 0;
314         int i;
315 
316         for (i = 0; i < ndigits; i++) {
317                 u64 diff;
318 
319                 diff = left[i] - right[i] - borrow;
320                 if (diff != left[i])
321                         borrow = (diff > left[i]);
322 
323                 result[i] = diff;
324         }
325 
326         return borrow;
327 }
328 EXPORT_SYMBOL(vli_sub);
329 
330 /* Computes result = left - right, returning borrow. Can modify in place. */
331 static u64 vli_usub(u64 *result, const u64 *left, u64 right,
332              unsigned int ndigits)
333 {
334         u64 borrow = right;
335         int i;
336 
337         for (i = 0; i < ndigits; i++) {
338                 u64 diff;
339 
340                 diff = left[i] - borrow;
341                 if (diff != left[i])
342                         borrow = (diff > left[i]);
343 
344                 result[i] = diff;
345         }
346 
347         return borrow;
348 }
349 
350 static uint128_t mul_64_64(u64 left, u64 right)
351 {
352         uint128_t result;
353 #if defined(CONFIG_ARCH_SUPPORTS_INT128)
354         unsigned __int128 m = (unsigned __int128)left * right;
355 
356         result.m_low  = m;
357         result.m_high = m >> 64;
358 #else
359         u64 a0 = left & 0xffffffffull;
360         u64 a1 = left >> 32;
361         u64 b0 = right & 0xffffffffull;
362         u64 b1 = right >> 32;
363         u64 m0 = a0 * b0;
364         u64 m1 = a0 * b1;
365         u64 m2 = a1 * b0;
366         u64 m3 = a1 * b1;
367 
368         m2 += (m0 >> 32);
369         m2 += m1;
370 
371         /* Overflow */
372         if (m2 < m1)
373                 m3 += 0x100000000ull;
374 
375         result.m_low = (m0 & 0xffffffffull) | (m2 << 32);
376         result.m_high = m3 + (m2 >> 32);
377 #endif
378         return result;
379 }
380 
381 static uint128_t add_128_128(uint128_t a, uint128_t b)
382 {
383         uint128_t result;
384 
385         result.m_low = a.m_low + b.m_low;
386         result.m_high = a.m_high + b.m_high + (result.m_low < a.m_low);
387 
388         return result;
389 }
390 
391 static void vli_mult(u64 *result, const u64 *left, const u64 *right,
392                      unsigned int ndigits)
393 {
394         uint128_t r01 = { 0, 0 };
395         u64 r2 = 0;
396         unsigned int i, k;
397 
398         /* Compute each digit of result in sequence, maintaining the
399          * carries.
400          */
401         for (k = 0; k < ndigits * 2 - 1; k++) {
402                 unsigned int min;
403 
404                 if (k < ndigits)
405                         min = 0;
406                 else
407                         min = (k + 1) - ndigits;
408 
409                 for (i = min; i <= k && i < ndigits; i++) {
410                         uint128_t product;
411 
412                         product = mul_64_64(left[i], right[k - i]);
413 
414                         r01 = add_128_128(r01, product);
415                         r2 += (r01.m_high < product.m_high);
416                 }
417 
418                 result[k] = r01.m_low;
419                 r01.m_low = r01.m_high;
420                 r01.m_high = r2;
421                 r2 = 0;
422         }
423 
424         result[ndigits * 2 - 1] = r01.m_low;
425 }
426 
427 /* Compute product = left * right, for a small right value. */
428 static void vli_umult(u64 *result, const u64 *left, u32 right,
429                       unsigned int ndigits)
430 {
431         uint128_t r01 = { 0 };
432         unsigned int k;
433 
434         for (k = 0; k < ndigits; k++) {
435                 uint128_t product;
436 
437                 product = mul_64_64(left[k], right);
438                 r01 = add_128_128(r01, product);
439                 /* no carry */
440                 result[k] = r01.m_low;
441                 r01.m_low = r01.m_high;
442                 r01.m_high = 0;
443         }
444         result[k] = r01.m_low;
445         for (++k; k < ndigits * 2; k++)
446                 result[k] = 0;
447 }
448 
449 static void vli_square(u64 *result, const u64 *left, unsigned int ndigits)
450 {
451         uint128_t r01 = { 0, 0 };
452         u64 r2 = 0;
453         int i, k;
454 
455         for (k = 0; k < ndigits * 2 - 1; k++) {
456                 unsigned int min;
457 
458                 if (k < ndigits)
459                         min = 0;
460                 else
461                         min = (k + 1) - ndigits;
462 
463                 for (i = min; i <= k && i <= k - i; i++) {
464                         uint128_t product;
465 
466                         product = mul_64_64(left[i], left[k - i]);
467 
468                         if (i < k - i) {
469                                 r2 += product.m_high >> 63;
470                                 product.m_high = (product.m_high << 1) |
471                                                  (product.m_low >> 63);
472                                 product.m_low <<= 1;
473                         }
474 
475                         r01 = add_128_128(r01, product);
476                         r2 += (r01.m_high < product.m_high);
477                 }
478 
479                 result[k] = r01.m_low;
480                 r01.m_low = r01.m_high;
481                 r01.m_high = r2;
482                 r2 = 0;
483         }
484 
485         result[ndigits * 2 - 1] = r01.m_low;
486 }
487 
488 /* Computes result = (left + right) % mod.
489  * Assumes that left < mod and right < mod, result != mod.
490  */
491 static void vli_mod_add(u64 *result, const u64 *left, const u64 *right,
492                         const u64 *mod, unsigned int ndigits)
493 {
494         u64 carry;
495 
496         carry = vli_add(result, left, right, ndigits);
497 
498         /* result > mod (result = mod + remainder), so subtract mod to
499          * get remainder.
500          */
501         if (carry || vli_cmp(result, mod, ndigits) >= 0)
502                 vli_sub(result, result, mod, ndigits);
503 }
504 
505 /* Computes result = (left - right) % mod.
506  * Assumes that left < mod and right < mod, result != mod.
507  */
508 static void vli_mod_sub(u64 *result, const u64 *left, const u64 *right,
509                         const u64 *mod, unsigned int ndigits)
510 {
511         u64 borrow = vli_sub(result, left, right, ndigits);
512 
513         /* In this case, p_result == -diff == (max int) - diff.
514          * Since -x % d == d - x, we can get the correct result from
515          * result + mod (with overflow).
516          */
517         if (borrow)
518                 vli_add(result, result, mod, ndigits);
519 }
520 
521 /*
522  * Computes result = product % mod
523  * for special form moduli: p = 2^k-c, for small c (note the minus sign)
524  *
525  * References:
526  * R. Crandall, C. Pomerance. Prime Numbers: A Computational Perspective.
527  * 9 Fast Algorithms for Large-Integer Arithmetic. 9.2.3 Moduli of special form
528  * Algorithm 9.2.13 (Fast mod operation for special-form moduli).
529  */
530 static void vli_mmod_special(u64 *result, const u64 *product,
531                               const u64 *mod, unsigned int ndigits)
532 {
533         u64 c = -mod[0];
534         u64 t[ECC_MAX_DIGITS * 2];
535         u64 r[ECC_MAX_DIGITS * 2];
536 
537         vli_set(r, product, ndigits * 2);
538         while (!vli_is_zero(r + ndigits, ndigits)) {
539                 vli_umult(t, r + ndigits, c, ndigits);
540                 vli_clear(r + ndigits, ndigits);
541                 vli_add(r, r, t, ndigits * 2);
542         }
543         vli_set(t, mod, ndigits);
544         vli_clear(t + ndigits, ndigits);
545         while (vli_cmp(r, t, ndigits * 2) >= 0)
546                 vli_sub(r, r, t, ndigits * 2);
547         vli_set(result, r, ndigits);
548 }
549 
550 /*
551  * Computes result = product % mod
552  * for special form moduli: p = 2^{k-1}+c, for small c (note the plus sign)
553  * where k-1 does not fit into qword boundary by -1 bit (such as 255).
554 
555  * References (loosely based on):
556  * A. Menezes, P. van Oorschot, S. Vanstone. Handbook of Applied Cryptography.
557  * 14.3.4 Reduction methods for moduli of special form. Algorithm 14.47.
558  * URL: http://cacr.uwaterloo.ca/hac/about/chap14.pdf
559  *
560  * H. Cohen, G. Frey, R. Avanzi, C. Doche, T. Lange, K. Nguyen, F. Vercauteren.
561  * Handbook of Elliptic and Hyperelliptic Curve Cryptography.
562  * Algorithm 10.25 Fast reduction for special form moduli
563  */
564 static void vli_mmod_special2(u64 *result, const u64 *product,
565                                const u64 *mod, unsigned int ndigits)
566 {
567         u64 c2 = mod[0] * 2;
568         u64 q[ECC_MAX_DIGITS];
569         u64 r[ECC_MAX_DIGITS * 2];
570         u64 m[ECC_MAX_DIGITS * 2]; /* expanded mod */
571         int carry; /* last bit that doesn't fit into q */
572         int i;
573 
574         vli_set(m, mod, ndigits);
575         vli_clear(m + ndigits, ndigits);
576 
577         vli_set(r, product, ndigits);
578         /* q and carry are top bits */
579         vli_set(q, product + ndigits, ndigits);
580         vli_clear(r + ndigits, ndigits);
581         carry = vli_is_negative(r, ndigits);
582         if (carry)
583                 r[ndigits - 1] &= (1ull << 63) - 1;
584         for (i = 1; carry || !vli_is_zero(q, ndigits); i++) {
585                 u64 qc[ECC_MAX_DIGITS * 2];
586 
587                 vli_umult(qc, q, c2, ndigits);
588                 if (carry)
589                         vli_uadd(qc, qc, mod[0], ndigits * 2);
590                 vli_set(q, qc + ndigits, ndigits);
591                 vli_clear(qc + ndigits, ndigits);
592                 carry = vli_is_negative(qc, ndigits);
593                 if (carry)
594                         qc[ndigits - 1] &= (1ull << 63) - 1;
595                 if (i & 1)
596                         vli_sub(r, r, qc, ndigits * 2);
597                 else
598                         vli_add(r, r, qc, ndigits * 2);
599         }
600         while (vli_is_negative(r, ndigits * 2))
601                 vli_add(r, r, m, ndigits * 2);
602         while (vli_cmp(r, m, ndigits * 2) >= 0)
603                 vli_sub(r, r, m, ndigits * 2);
604 
605         vli_set(result, r, ndigits);
606 }
607 
608 /*
609  * Computes result = product % mod, where product is 2N words long.
610  * Reference: Ken MacKay's micro-ecc.
611  * Currently only designed to work for curve_p or curve_n.
612  */
613 static void vli_mmod_slow(u64 *result, u64 *product, const u64 *mod,
614                           unsigned int ndigits)
615 {
616         u64 mod_m[2 * ECC_MAX_DIGITS];
617         u64 tmp[2 * ECC_MAX_DIGITS];
618         u64 *v[2] = { tmp, product };
619         u64 carry = 0;
620         unsigned int i;
621         /* Shift mod so its highest set bit is at the maximum position. */
622         int shift = (ndigits * 2 * 64) - vli_num_bits(mod, ndigits);
623         int word_shift = shift / 64;
624         int bit_shift = shift % 64;
625 
626         vli_clear(mod_m, word_shift);
627         if (bit_shift > 0) {
628                 for (i = 0; i < ndigits; ++i) {
629                         mod_m[word_shift + i] = (mod[i] << bit_shift) | carry;
630                         carry = mod[i] >> (64 - bit_shift);
631                 }
632         } else
633                 vli_set(mod_m + word_shift, mod, ndigits);
634 
635         for (i = 1; shift >= 0; --shift) {
636                 u64 borrow = 0;
637                 unsigned int j;
638 
639                 for (j = 0; j < ndigits * 2; ++j) {
640                         u64 diff = v[i][j] - mod_m[j] - borrow;
641 
642                         if (diff != v[i][j])
643                                 borrow = (diff > v[i][j]);
644                         v[1 - i][j] = diff;
645                 }
646                 i = !(i ^ borrow); /* Swap the index if there was no borrow */
647                 vli_rshift1(mod_m, ndigits);
648                 mod_m[ndigits - 1] |= mod_m[ndigits] << (64 - 1);
649                 vli_rshift1(mod_m + ndigits, ndigits);
650         }
651         vli_set(result, v[i], ndigits);
652 }
653 
654 /* Computes result = product % mod using Barrett's reduction with precomputed
655  * value mu appended to the mod after ndigits, mu = (2^{2w} / mod) and have
656  * length ndigits + 1, where mu * (2^w - 1) should not overflow ndigits
657  * boundary.
658  *
659  * Reference:
660  * R. Brent, P. Zimmermann. Modern Computer Arithmetic. 2010.
661  * 2.4.1 Barrett's algorithm. Algorithm 2.5.
662  */
663 static void vli_mmod_barrett(u64 *result, u64 *product, const u64 *mod,
664                              unsigned int ndigits)
665 {
666         u64 q[ECC_MAX_DIGITS * 2];
667         u64 r[ECC_MAX_DIGITS * 2];
668         const u64 *mu = mod + ndigits;
669 
670         vli_mult(q, product + ndigits, mu, ndigits);
671         if (mu[ndigits])
672                 vli_add(q + ndigits, q + ndigits, product + ndigits, ndigits);
673         vli_mult(r, mod, q + ndigits, ndigits);
674         vli_sub(r, product, r, ndigits * 2);
675         while (!vli_is_zero(r + ndigits, ndigits) ||
676                vli_cmp(r, mod, ndigits) != -1) {
677                 u64 carry;
678 
679                 carry = vli_sub(r, r, mod, ndigits);
680                 vli_usub(r + ndigits, r + ndigits, carry, ndigits);
681         }
682         vli_set(result, r, ndigits);
683 }
684 
685 /* Computes p_result = p_product % curve_p.
686  * See algorithm 5 and 6 from
687  * http://www.isys.uni-klu.ac.at/PDF/2001-0126-MT.pdf
688  */
689 static void vli_mmod_fast_192(u64 *result, const u64 *product,
690                               const u64 *curve_prime, u64 *tmp)
691 {
692         const unsigned int ndigits = 3;
693         int carry;
694 
695         vli_set(result, product, ndigits);
696 
697         vli_set(tmp, &product[3], ndigits);
698         carry = vli_add(result, result, tmp, ndigits);
699 
700         tmp[0] = 0;
701         tmp[1] = product[3];
702         tmp[2] = product[4];
703         carry += vli_add(result, result, tmp, ndigits);
704 
705         tmp[0] = tmp[1] = product[5];
706         tmp[2] = 0;
707         carry += vli_add(result, result, tmp, ndigits);
708 
709         while (carry || vli_cmp(curve_prime, result, ndigits) != 1)
710                 carry -= vli_sub(result, result, curve_prime, ndigits);
711 }
712 
713 /* Computes result = product % curve_prime
714  * from http://www.nsa.gov/ia/_files/nist-routines.pdf
715  */
716 static void vli_mmod_fast_256(u64 *result, const u64 *product,
717                               const u64 *curve_prime, u64 *tmp)
718 {
719         int carry;
720         const unsigned int ndigits = 4;
721 
722         /* t */
723         vli_set(result, product, ndigits);
724 
725         /* s1 */
726         tmp[0] = 0;
727         tmp[1] = product[5] & 0xffffffff00000000ull;
728         tmp[2] = product[6];
729         tmp[3] = product[7];
730         carry = vli_lshift(tmp, tmp, 1, ndigits);
731         carry += vli_add(result, result, tmp, ndigits);
732 
733         /* s2 */
734         tmp[1] = product[6] << 32;
735         tmp[2] = (product[6] >> 32) | (product[7] << 32);
736         tmp[3] = product[7] >> 32;
737         carry += vli_lshift(tmp, tmp, 1, ndigits);
738         carry += vli_add(result, result, tmp, ndigits);
739 
740         /* s3 */
741         tmp[0] = product[4];
742         tmp[1] = product[5] & 0xffffffff;
743         tmp[2] = 0;
744         tmp[3] = product[7];
745         carry += vli_add(result, result, tmp, ndigits);
746 
747         /* s4 */
748         tmp[0] = (product[4] >> 32) | (product[5] << 32);
749         tmp[1] = (product[5] >> 32) | (product[6] & 0xffffffff00000000ull);
750         tmp[2] = product[7];
751         tmp[3] = (product[6] >> 32) | (product[4] << 32);
752         carry += vli_add(result, result, tmp, ndigits);
753 
754         /* d1 */
755         tmp[0] = (product[5] >> 32) | (product[6] << 32);
756         tmp[1] = (product[6] >> 32);
757         tmp[2] = 0;
758         tmp[3] = (product[4] & 0xffffffff) | (product[5] << 32);
759         carry -= vli_sub(result, result, tmp, ndigits);
760 
761         /* d2 */
762         tmp[0] = product[6];
763         tmp[1] = product[7];
764         tmp[2] = 0;
765         tmp[3] = (product[4] >> 32) | (product[5] & 0xffffffff00000000ull);
766         carry -= vli_sub(result, result, tmp, ndigits);
767 
768         /* d3 */
769         tmp[0] = (product[6] >> 32) | (product[7] << 32);
770         tmp[1] = (product[7] >> 32) | (product[4] << 32);
771         tmp[2] = (product[4] >> 32) | (product[5] << 32);
772         tmp[3] = (product[6] << 32);
773         carry -= vli_sub(result, result, tmp, ndigits);
774 
775         /* d4 */
776         tmp[0] = product[7];
777         tmp[1] = product[4] & 0xffffffff00000000ull;
778         tmp[2] = product[5];
779         tmp[3] = product[6] & 0xffffffff00000000ull;
780         carry -= vli_sub(result, result, tmp, ndigits);
781 
782         if (carry < 0) {
783                 do {
784                         carry += vli_add(result, result, curve_prime, ndigits);
785                 } while (carry < 0);
786         } else {
787                 while (carry || vli_cmp(curve_prime, result, ndigits) != 1)
788                         carry -= vli_sub(result, result, curve_prime, ndigits);
789         }
790 }
791 
792 #define SL32OR32(x32, y32) (((u64)x32 << 32) | y32)
793 #define AND64H(x64)  (x64 & 0xffFFffFF00000000ull)
794 #define AND64L(x64)  (x64 & 0x00000000ffFFffFFull)
795 
796 /* Computes result = product % curve_prime
797  * from "Mathematical routines for the NIST prime elliptic curves"
798  */
799 static void vli_mmod_fast_384(u64 *result, const u64 *product,
800                                 const u64 *curve_prime, u64 *tmp)
801 {
802         int carry;
803         const unsigned int ndigits = 6;
804 
805         /* t */
806         vli_set(result, product, ndigits);
807 
808         /* s1 */
809         tmp[0] = 0;             // 0 || 0
810         tmp[1] = 0;             // 0 || 0
811         tmp[2] = SL32OR32(product[11], (product[10]>>32));      //a22||a21
812         tmp[3] = product[11]>>32;       // 0 ||a23
813         tmp[4] = 0;             // 0 || 0
814         tmp[5] = 0;             // 0 || 0
815         carry = vli_lshift(tmp, tmp, 1, ndigits);
816         carry += vli_add(result, result, tmp, ndigits);
817 
818         /* s2 */
819         tmp[0] = product[6];    //a13||a12
820         tmp[1] = product[7];    //a15||a14
821         tmp[2] = product[8];    //a17||a16
822         tmp[3] = product[9];    //a19||a18
823         tmp[4] = product[10];   //a21||a20
824         tmp[5] = product[11];   //a23||a22
825         carry += vli_add(result, result, tmp, ndigits);
826 
827         /* s3 */
828         tmp[0] = SL32OR32(product[11], (product[10]>>32));      //a22||a21
829         tmp[1] = SL32OR32(product[6], (product[11]>>32));       //a12||a23
830         tmp[2] = SL32OR32(product[7], (product[6])>>32);        //a14||a13
831         tmp[3] = SL32OR32(product[8], (product[7]>>32));        //a16||a15
832         tmp[4] = SL32OR32(product[9], (product[8]>>32));        //a18||a17
833         tmp[5] = SL32OR32(product[10], (product[9]>>32));       //a20||a19
834         carry += vli_add(result, result, tmp, ndigits);
835 
836         /* s4 */
837         tmp[0] = AND64H(product[11]);   //a23|| 0
838         tmp[1] = (product[10]<<32);     //a20|| 0
839         tmp[2] = product[6];    //a13||a12
840         tmp[3] = product[7];    //a15||a14
841         tmp[4] = product[8];    //a17||a16
842         tmp[5] = product[9];    //a19||a18
843         carry += vli_add(result, result, tmp, ndigits);
844 
845         /* s5 */
846         tmp[0] = 0;             //  0|| 0
847         tmp[1] = 0;             //  0|| 0
848         tmp[2] = product[10];   //a21||a20
849         tmp[3] = product[11];   //a23||a22
850         tmp[4] = 0;             //  0|| 0
851         tmp[5] = 0;             //  0|| 0
852         carry += vli_add(result, result, tmp, ndigits);
853 
854         /* s6 */
855         tmp[0] = AND64L(product[10]);   // 0 ||a20
856         tmp[1] = AND64H(product[10]);   //a21|| 0
857         tmp[2] = product[11];   //a23||a22
858         tmp[3] = 0;             // 0 || 0
859         tmp[4] = 0;             // 0 || 0
860         tmp[5] = 0;             // 0 || 0
861         carry += vli_add(result, result, tmp, ndigits);
862 
863         /* d1 */
864         tmp[0] = SL32OR32(product[6], (product[11]>>32));       //a12||a23
865         tmp[1] = SL32OR32(product[7], (product[6]>>32));        //a14||a13
866         tmp[2] = SL32OR32(product[8], (product[7]>>32));        //a16||a15
867         tmp[3] = SL32OR32(product[9], (product[8]>>32));        //a18||a17
868         tmp[4] = SL32OR32(product[10], (product[9]>>32));       //a20||a19
869         tmp[5] = SL32OR32(product[11], (product[10]>>32));      //a22||a21
870         carry -= vli_sub(result, result, tmp, ndigits);
871 
872         /* d2 */
873         tmp[0] = (product[10]<<32);     //a20|| 0
874         tmp[1] = SL32OR32(product[11], (product[10]>>32));      //a22||a21
875         tmp[2] = (product[11]>>32);     // 0 ||a23
876         tmp[3] = 0;             // 0 || 0
877         tmp[4] = 0;             // 0 || 0
878         tmp[5] = 0;             // 0 || 0
879         carry -= vli_sub(result, result, tmp, ndigits);
880 
881         /* d3 */
882         tmp[0] = 0;             // 0 || 0
883         tmp[1] = AND64H(product[11]);   //a23|| 0
884         tmp[2] = product[11]>>32;       // 0 ||a23
885         tmp[3] = 0;             // 0 || 0
886         tmp[4] = 0;             // 0 || 0
887         tmp[5] = 0;             // 0 || 0
888         carry -= vli_sub(result, result, tmp, ndigits);
889 
890         if (carry < 0) {
891                 do {
892                         carry += vli_add(result, result, curve_prime, ndigits);
893                 } while (carry < 0);
894         } else {
895                 while (carry || vli_cmp(curve_prime, result, ndigits) != 1)
896                         carry -= vli_sub(result, result, curve_prime, ndigits);
897         }
898 
899 }
900 
901 #undef SL32OR32
902 #undef AND64H
903 #undef AND64L
904 
905 /* Computes result = product % curve_prime for different curve_primes.
906  *
907  * Note that curve_primes are distinguished just by heuristic check and
908  * not by complete conformance check.
909  */
910 static bool vli_mmod_fast(u64 *result, u64 *product,
911                           const struct ecc_curve *curve)
912 {
913         u64 tmp[2 * ECC_MAX_DIGITS];
914         const u64 *curve_prime = curve->p;
915         const unsigned int ndigits = curve->g.ndigits;
916 
917         /* All NIST curves have name prefix 'nist_' */
918         if (strncmp(curve->name, "nist_", 5) != 0) {
919                 /* Try to handle Pseudo-Marsenne primes. */
920                 if (curve_prime[ndigits - 1] == -1ull) {
921                         vli_mmod_special(result, product, curve_prime,
922                                          ndigits);
923                         return true;
924                 } else if (curve_prime[ndigits - 1] == 1ull << 63 &&
925                            curve_prime[ndigits - 2] == 0) {
926                         vli_mmod_special2(result, product, curve_prime,
927                                           ndigits);
928                         return true;
929                 }
930                 vli_mmod_barrett(result, product, curve_prime, ndigits);
931                 return true;
932         }
933 
934         switch (ndigits) {
935         case 3:
936                 vli_mmod_fast_192(result, product, curve_prime, tmp);
937                 break;
938         case 4:
939                 vli_mmod_fast_256(result, product, curve_prime, tmp);
940                 break;
941         case 6:
942                 vli_mmod_fast_384(result, product, curve_prime, tmp);
943                 break;
944         default:
945                 pr_err_ratelimited("ecc: unsupported digits size!\n");
946                 return false;
947         }
948 
949         return true;
950 }
951 
952 /* Computes result = (left * right) % mod.
953  * Assumes that mod is big enough curve order.
954  */
955 void vli_mod_mult_slow(u64 *result, const u64 *left, const u64 *right,
956                        const u64 *mod, unsigned int ndigits)
957 {
958         u64 product[ECC_MAX_DIGITS * 2];
959 
960         vli_mult(product, left, right, ndigits);
961         vli_mmod_slow(result, product, mod, ndigits);
962 }
963 EXPORT_SYMBOL(vli_mod_mult_slow);
964 
965 /* Computes result = (left * right) % curve_prime. */
966 static void vli_mod_mult_fast(u64 *result, const u64 *left, const u64 *right,
967                               const struct ecc_curve *curve)
968 {
969         u64 product[2 * ECC_MAX_DIGITS];
970 
971         vli_mult(product, left, right, curve->g.ndigits);
972         vli_mmod_fast(result, product, curve);
973 }
974 
975 /* Computes result = left^2 % curve_prime. */
976 static void vli_mod_square_fast(u64 *result, const u64 *left,
977                                 const struct ecc_curve *curve)
978 {
979         u64 product[2 * ECC_MAX_DIGITS];
980 
981         vli_square(product, left, curve->g.ndigits);
982         vli_mmod_fast(result, product, curve);
983 }
984 
985 #define EVEN(vli) (!(vli[0] & 1))
986 /* Computes result = (1 / p_input) % mod. All VLIs are the same size.
987  * See "From Euclid's GCD to Montgomery Multiplication to the Great Divide"
988  * https://labs.oracle.com/techrep/2001/smli_tr-2001-95.pdf
989  */
990 void vli_mod_inv(u64 *result, const u64 *input, const u64 *mod,
991                         unsigned int ndigits)
992 {
993         u64 a[ECC_MAX_DIGITS], b[ECC_MAX_DIGITS];
994         u64 u[ECC_MAX_DIGITS], v[ECC_MAX_DIGITS];
995         u64 carry;
996         int cmp_result;
997 
998         if (vli_is_zero(input, ndigits)) {
999                 vli_clear(result, ndigits);
1000                 return;
1001         }
1002 
1003         vli_set(a, input, ndigits);
1004         vli_set(b, mod, ndigits);
1005         vli_clear(u, ndigits);
1006         u[0] = 1;
1007         vli_clear(v, ndigits);
1008 
1009         while ((cmp_result = vli_cmp(a, b, ndigits)) != 0) {
1010                 carry = 0;
1011 
1012                 if (EVEN(a)) {
1013                         vli_rshift1(a, ndigits);
1014 
1015                         if (!EVEN(u))
1016                                 carry = vli_add(u, u, mod, ndigits);
1017 
1018                         vli_rshift1(u, ndigits);
1019                         if (carry)
1020                                 u[ndigits - 1] |= 0x8000000000000000ull;
1021                 } else if (EVEN(b)) {
1022                         vli_rshift1(b, ndigits);
1023 
1024                         if (!EVEN(v))
1025                                 carry = vli_add(v, v, mod, ndigits);
1026 
1027                         vli_rshift1(v, ndigits);
1028                         if (carry)
1029                                 v[ndigits - 1] |= 0x8000000000000000ull;
1030                 } else if (cmp_result > 0) {
1031                         vli_sub(a, a, b, ndigits);
1032                         vli_rshift1(a, ndigits);
1033 
1034                         if (vli_cmp(u, v, ndigits) < 0)
1035                                 vli_add(u, u, mod, ndigits);
1036 
1037                         vli_sub(u, u, v, ndigits);
1038                         if (!EVEN(u))
1039                                 carry = vli_add(u, u, mod, ndigits);
1040 
1041                         vli_rshift1(u, ndigits);
1042                         if (carry)
1043                                 u[ndigits - 1] |= 0x8000000000000000ull;
1044                 } else {
1045                         vli_sub(b, b, a, ndigits);
1046                         vli_rshift1(b, ndigits);
1047 
1048                         if (vli_cmp(v, u, ndigits) < 0)
1049                                 vli_add(v, v, mod, ndigits);
1050 
1051                         vli_sub(v, v, u, ndigits);
1052                         if (!EVEN(v))
1053                                 carry = vli_add(v, v, mod, ndigits);
1054 
1055                         vli_rshift1(v, ndigits);
1056                         if (carry)
1057                                 v[ndigits - 1] |= 0x8000000000000000ull;
1058                 }
1059         }
1060 
1061         vli_set(result, u, ndigits);
1062 }
1063 EXPORT_SYMBOL(vli_mod_inv);
1064 
1065 /* ------ Point operations ------ */
1066 
1067 /* Returns true if p_point is the point at infinity, false otherwise. */
1068 bool ecc_point_is_zero(const struct ecc_point *point)
1069 {
1070         return (vli_is_zero(point->x, point->ndigits) &&
1071                 vli_is_zero(point->y, point->ndigits));
1072 }
1073 EXPORT_SYMBOL(ecc_point_is_zero);
1074 
1075 /* Point multiplication algorithm using Montgomery's ladder with co-Z
1076  * coordinates. From https://eprint.iacr.org/2011/338.pdf
1077  */
1078 
1079 /* Double in place */
1080 static void ecc_point_double_jacobian(u64 *x1, u64 *y1, u64 *z1,
1081                                         const struct ecc_curve *curve)
1082 {
1083         /* t1 = x, t2 = y, t3 = z */
1084         u64 t4[ECC_MAX_DIGITS];
1085         u64 t5[ECC_MAX_DIGITS];
1086         const u64 *curve_prime = curve->p;
1087         const unsigned int ndigits = curve->g.ndigits;
1088 
1089         if (vli_is_zero(z1, ndigits))
1090                 return;
1091 
1092         /* t4 = y1^2 */
1093         vli_mod_square_fast(t4, y1, curve);
1094         /* t5 = x1*y1^2 = A */
1095         vli_mod_mult_fast(t5, x1, t4, curve);
1096         /* t4 = y1^4 */
1097         vli_mod_square_fast(t4, t4, curve);
1098         /* t2 = y1*z1 = z3 */
1099         vli_mod_mult_fast(y1, y1, z1, curve);
1100         /* t3 = z1^2 */
1101         vli_mod_square_fast(z1, z1, curve);
1102 
1103         /* t1 = x1 + z1^2 */
1104         vli_mod_add(x1, x1, z1, curve_prime, ndigits);
1105         /* t3 = 2*z1^2 */
1106         vli_mod_add(z1, z1, z1, curve_prime, ndigits);
1107         /* t3 = x1 - z1^2 */
1108         vli_mod_sub(z1, x1, z1, curve_prime, ndigits);
1109         /* t1 = x1^2 - z1^4 */
1110         vli_mod_mult_fast(x1, x1, z1, curve);
1111 
1112         /* t3 = 2*(x1^2 - z1^4) */
1113         vli_mod_add(z1, x1, x1, curve_prime, ndigits);
1114         /* t1 = 3*(x1^2 - z1^4) */
1115         vli_mod_add(x1, x1, z1, curve_prime, ndigits);
1116         if (vli_test_bit(x1, 0)) {
1117                 u64 carry = vli_add(x1, x1, curve_prime, ndigits);
1118 
1119                 vli_rshift1(x1, ndigits);
1120                 x1[ndigits - 1] |= carry << 63;
1121         } else {
1122                 vli_rshift1(x1, ndigits);
1123         }
1124         /* t1 = 3/2*(x1^2 - z1^4) = B */
1125 
1126         /* t3 = B^2 */
1127         vli_mod_square_fast(z1, x1, curve);
1128         /* t3 = B^2 - A */
1129         vli_mod_sub(z1, z1, t5, curve_prime, ndigits);
1130         /* t3 = B^2 - 2A = x3 */
1131         vli_mod_sub(z1, z1, t5, curve_prime, ndigits);
1132         /* t5 = A - x3 */
1133         vli_mod_sub(t5, t5, z1, curve_prime, ndigits);
1134         /* t1 = B * (A - x3) */
1135         vli_mod_mult_fast(x1, x1, t5, curve);
1136         /* t4 = B * (A - x3) - y1^4 = y3 */
1137         vli_mod_sub(t4, x1, t4, curve_prime, ndigits);
1138 
1139         vli_set(x1, z1, ndigits);
1140         vli_set(z1, y1, ndigits);
1141         vli_set(y1, t4, ndigits);
1142 }
1143 
1144 /* Modify (x1, y1) => (x1 * z^2, y1 * z^3) */
1145 static void apply_z(u64 *x1, u64 *y1, u64 *z, const struct ecc_curve *curve)
1146 {
1147         u64 t1[ECC_MAX_DIGITS];
1148 
1149         vli_mod_square_fast(t1, z, curve);              /* z^2 */
1150         vli_mod_mult_fast(x1, x1, t1, curve);   /* x1 * z^2 */
1151         vli_mod_mult_fast(t1, t1, z, curve);    /* z^3 */
1152         vli_mod_mult_fast(y1, y1, t1, curve);   /* y1 * z^3 */
1153 }
1154 
1155 /* P = (x1, y1) => 2P, (x2, y2) => P' */
1156 static void xycz_initial_double(u64 *x1, u64 *y1, u64 *x2, u64 *y2,
1157                                 u64 *p_initial_z, const struct ecc_curve *curve)
1158 {
1159         u64 z[ECC_MAX_DIGITS];
1160         const unsigned int ndigits = curve->g.ndigits;
1161 
1162         vli_set(x2, x1, ndigits);
1163         vli_set(y2, y1, ndigits);
1164 
1165         vli_clear(z, ndigits);
1166         z[0] = 1;
1167 
1168         if (p_initial_z)
1169                 vli_set(z, p_initial_z, ndigits);
1170 
1171         apply_z(x1, y1, z, curve);
1172 
1173         ecc_point_double_jacobian(x1, y1, z, curve);
1174 
1175         apply_z(x2, y2, z, curve);
1176 }
1177 
1178 /* Input P = (x1, y1, Z), Q = (x2, y2, Z)
1179  * Output P' = (x1', y1', Z3), P + Q = (x3, y3, Z3)
1180  * or P => P', Q => P + Q
1181  */
1182 static void xycz_add(u64 *x1, u64 *y1, u64 *x2, u64 *y2,
1183                         const struct ecc_curve *curve)
1184 {
1185         /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
1186         u64 t5[ECC_MAX_DIGITS];
1187         const u64 *curve_prime = curve->p;
1188         const unsigned int ndigits = curve->g.ndigits;
1189 
1190         /* t5 = x2 - x1 */
1191         vli_mod_sub(t5, x2, x1, curve_prime, ndigits);
1192         /* t5 = (x2 - x1)^2 = A */
1193         vli_mod_square_fast(t5, t5, curve);
1194         /* t1 = x1*A = B */
1195         vli_mod_mult_fast(x1, x1, t5, curve);
1196         /* t3 = x2*A = C */
1197         vli_mod_mult_fast(x2, x2, t5, curve);
1198         /* t4 = y2 - y1 */
1199         vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
1200         /* t5 = (y2 - y1)^2 = D */
1201         vli_mod_square_fast(t5, y2, curve);
1202 
1203         /* t5 = D - B */
1204         vli_mod_sub(t5, t5, x1, curve_prime, ndigits);
1205         /* t5 = D - B - C = x3 */
1206         vli_mod_sub(t5, t5, x2, curve_prime, ndigits);
1207         /* t3 = C - B */
1208         vli_mod_sub(x2, x2, x1, curve_prime, ndigits);
1209         /* t2 = y1*(C - B) */
1210         vli_mod_mult_fast(y1, y1, x2, curve);
1211         /* t3 = B - x3 */
1212         vli_mod_sub(x2, x1, t5, curve_prime, ndigits);
1213         /* t4 = (y2 - y1)*(B - x3) */
1214         vli_mod_mult_fast(y2, y2, x2, curve);
1215         /* t4 = y3 */
1216         vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
1217 
1218         vli_set(x2, t5, ndigits);
1219 }
1220 
1221 /* Input P = (x1, y1, Z), Q = (x2, y2, Z)
1222  * Output P + Q = (x3, y3, Z3), P - Q = (x3', y3', Z3)
1223  * or P => P - Q, Q => P + Q
1224  */
1225 static void xycz_add_c(u64 *x1, u64 *y1, u64 *x2, u64 *y2,
1226                         const struct ecc_curve *curve)
1227 {
1228         /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
1229         u64 t5[ECC_MAX_DIGITS];
1230         u64 t6[ECC_MAX_DIGITS];
1231         u64 t7[ECC_MAX_DIGITS];
1232         const u64 *curve_prime = curve->p;
1233         const unsigned int ndigits = curve->g.ndigits;
1234 
1235         /* t5 = x2 - x1 */
1236         vli_mod_sub(t5, x2, x1, curve_prime, ndigits);
1237         /* t5 = (x2 - x1)^2 = A */
1238         vli_mod_square_fast(t5, t5, curve);
1239         /* t1 = x1*A = B */
1240         vli_mod_mult_fast(x1, x1, t5, curve);
1241         /* t3 = x2*A = C */
1242         vli_mod_mult_fast(x2, x2, t5, curve);
1243         /* t4 = y2 + y1 */
1244         vli_mod_add(t5, y2, y1, curve_prime, ndigits);
1245         /* t4 = y2 - y1 */
1246         vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
1247 
1248         /* t6 = C - B */
1249         vli_mod_sub(t6, x2, x1, curve_prime, ndigits);
1250         /* t2 = y1 * (C - B) */
1251         vli_mod_mult_fast(y1, y1, t6, curve);
1252         /* t6 = B + C */
1253         vli_mod_add(t6, x1, x2, curve_prime, ndigits);
1254         /* t3 = (y2 - y1)^2 */
1255         vli_mod_square_fast(x2, y2, curve);
1256         /* t3 = x3 */
1257         vli_mod_sub(x2, x2, t6, curve_prime, ndigits);
1258 
1259         /* t7 = B - x3 */
1260         vli_mod_sub(t7, x1, x2, curve_prime, ndigits);
1261         /* t4 = (y2 - y1)*(B - x3) */
1262         vli_mod_mult_fast(y2, y2, t7, curve);
1263         /* t4 = y3 */
1264         vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
1265 
1266         /* t7 = (y2 + y1)^2 = F */
1267         vli_mod_square_fast(t7, t5, curve);
1268         /* t7 = x3' */
1269         vli_mod_sub(t7, t7, t6, curve_prime, ndigits);
1270         /* t6 = x3' - B */
1271         vli_mod_sub(t6, t7, x1, curve_prime, ndigits);
1272         /* t6 = (y2 + y1)*(x3' - B) */
1273         vli_mod_mult_fast(t6, t6, t5, curve);
1274         /* t2 = y3' */
1275         vli_mod_sub(y1, t6, y1, curve_prime, ndigits);
1276 
1277         vli_set(x1, t7, ndigits);
1278 }
1279 
1280 static void ecc_point_mult(struct ecc_point *result,
1281                            const struct ecc_point *point, const u64 *scalar,
1282                            u64 *initial_z, const struct ecc_curve *curve,
1283                            unsigned int ndigits)
1284 {
1285         /* R0 and R1 */
1286         u64 rx[2][ECC_MAX_DIGITS];
1287         u64 ry[2][ECC_MAX_DIGITS];
1288         u64 z[ECC_MAX_DIGITS];
1289         u64 sk[2][ECC_MAX_DIGITS];
1290         u64 *curve_prime = curve->p;
1291         int i, nb;
1292         int num_bits;
1293         int carry;
1294 
1295         carry = vli_add(sk[0], scalar, curve->n, ndigits);
1296         vli_add(sk[1], sk[0], curve->n, ndigits);
1297         scalar = sk[!carry];
1298         num_bits = sizeof(u64) * ndigits * 8 + 1;
1299 
1300         vli_set(rx[1], point->x, ndigits);
1301         vli_set(ry[1], point->y, ndigits);
1302 
1303         xycz_initial_double(rx[1], ry[1], rx[0], ry[0], initial_z, curve);
1304 
1305         for (i = num_bits - 2; i > 0; i--) {
1306                 nb = !vli_test_bit(scalar, i);
1307                 xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb], curve);
1308                 xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve);
1309         }
1310 
1311         nb = !vli_test_bit(scalar, 0);
1312         xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb], curve);
1313 
1314         /* Find final 1/Z value. */
1315         /* X1 - X0 */
1316         vli_mod_sub(z, rx[1], rx[0], curve_prime, ndigits);
1317         /* Yb * (X1 - X0) */
1318         vli_mod_mult_fast(z, z, ry[1 - nb], curve);
1319         /* xP * Yb * (X1 - X0) */
1320         vli_mod_mult_fast(z, z, point->x, curve);
1321 
1322         /* 1 / (xP * Yb * (X1 - X0)) */
1323         vli_mod_inv(z, z, curve_prime, point->ndigits);
1324 
1325         /* yP / (xP * Yb * (X1 - X0)) */
1326         vli_mod_mult_fast(z, z, point->y, curve);
1327         /* Xb * yP / (xP * Yb * (X1 - X0)) */
1328         vli_mod_mult_fast(z, z, rx[1 - nb], curve);
1329         /* End 1/Z calculation */
1330 
1331         xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve);
1332 
1333         apply_z(rx[0], ry[0], z, curve);
1334 
1335         vli_set(result->x, rx[0], ndigits);
1336         vli_set(result->y, ry[0], ndigits);
1337 }
1338 
1339 /* Computes R = P + Q mod p */
1340 static void ecc_point_add(const struct ecc_point *result,
1341                    const struct ecc_point *p, const struct ecc_point *q,
1342                    const struct ecc_curve *curve)
1343 {
1344         u64 z[ECC_MAX_DIGITS];
1345         u64 px[ECC_MAX_DIGITS];
1346         u64 py[ECC_MAX_DIGITS];
1347         unsigned int ndigits = curve->g.ndigits;
1348 
1349         vli_set(result->x, q->x, ndigits);
1350         vli_set(result->y, q->y, ndigits);
1351         vli_mod_sub(z, result->x, p->x, curve->p, ndigits);
1352         vli_set(px, p->x, ndigits);
1353         vli_set(py, p->y, ndigits);
1354         xycz_add(px, py, result->x, result->y, curve);
1355         vli_mod_inv(z, z, curve->p, ndigits);
1356         apply_z(result->x, result->y, z, curve);
1357 }
1358 
1359 /* Computes R = u1P + u2Q mod p using Shamir's trick.
1360  * Based on: Kenneth MacKay's micro-ecc (2014).
1361  */
1362 void ecc_point_mult_shamir(const struct ecc_point *result,
1363                            const u64 *u1, const struct ecc_point *p,
1364                            const u64 *u2, const struct ecc_point *q,
1365                            const struct ecc_curve *curve)
1366 {
1367         u64 z[ECC_MAX_DIGITS];
1368         u64 sump[2][ECC_MAX_DIGITS];
1369         u64 *rx = result->x;
1370         u64 *ry = result->y;
1371         unsigned int ndigits = curve->g.ndigits;
1372         unsigned int num_bits;
1373         struct ecc_point sum = ECC_POINT_INIT(sump[0], sump[1], ndigits);
1374         const struct ecc_point *points[4];
1375         const struct ecc_point *point;
1376         unsigned int idx;
1377         int i;
1378 
1379         ecc_point_add(&sum, p, q, curve);
1380         points[0] = NULL;
1381         points[1] = p;
1382         points[2] = q;
1383         points[3] = &sum;
1384 
1385         num_bits = max(vli_num_bits(u1, ndigits), vli_num_bits(u2, ndigits));
1386         i = num_bits - 1;
1387         idx = (!!vli_test_bit(u1, i)) | ((!!vli_test_bit(u2, i)) << 1);
1388         point = points[idx];
1389 
1390         vli_set(rx, point->x, ndigits);
1391         vli_set(ry, point->y, ndigits);
1392         vli_clear(z + 1, ndigits - 1);
1393         z[0] = 1;
1394 
1395         for (--i; i >= 0; i--) {
1396                 ecc_point_double_jacobian(rx, ry, z, curve);
1397                 idx = (!!vli_test_bit(u1, i)) | ((!!vli_test_bit(u2, i)) << 1);
1398                 point = points[idx];
1399                 if (point) {
1400                         u64 tx[ECC_MAX_DIGITS];
1401                         u64 ty[ECC_MAX_DIGITS];
1402                         u64 tz[ECC_MAX_DIGITS];
1403 
1404                         vli_set(tx, point->x, ndigits);
1405                         vli_set(ty, point->y, ndigits);
1406                         apply_z(tx, ty, z, curve);
1407                         vli_mod_sub(tz, rx, tx, curve->p, ndigits);
1408                         xycz_add(tx, ty, rx, ry, curve);
1409                         vli_mod_mult_fast(z, z, tz, curve);
1410                 }
1411         }
1412         vli_mod_inv(z, z, curve->p, ndigits);
1413         apply_z(rx, ry, z, curve);
1414 }
1415 EXPORT_SYMBOL(ecc_point_mult_shamir);
1416 
1417 static int __ecc_is_key_valid(const struct ecc_curve *curve,
1418                               const u64 *private_key, unsigned int ndigits)
1419 {
1420         u64 one[ECC_MAX_DIGITS] = { 1, };
1421         u64 res[ECC_MAX_DIGITS];
1422 
1423         if (!private_key)
1424                 return -EINVAL;
1425 
1426         if (curve->g.ndigits != ndigits)
1427                 return -EINVAL;
1428 
1429         /* Make sure the private key is in the range [2, n-3]. */
1430         if (vli_cmp(one, private_key, ndigits) != -1)
1431                 return -EINVAL;
1432         vli_sub(res, curve->n, one, ndigits);
1433         vli_sub(res, res, one, ndigits);
1434         if (vli_cmp(res, private_key, ndigits) != 1)
1435                 return -EINVAL;
1436 
1437         return 0;
1438 }
1439 
1440 int ecc_is_key_valid(unsigned int curve_id, unsigned int ndigits,
1441                      const u64 *private_key, unsigned int private_key_len)
1442 {
1443         int nbytes;
1444         const struct ecc_curve *curve = ecc_get_curve(curve_id);
1445 
1446         nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT;
1447 
1448         if (private_key_len != nbytes)
1449                 return -EINVAL;
1450 
1451         return __ecc_is_key_valid(curve, private_key, ndigits);
1452 }
1453 EXPORT_SYMBOL(ecc_is_key_valid);
1454 
1455 /*
1456  * ECC private keys are generated using the method of extra random bits,
1457  * equivalent to that described in FIPS 186-4, Appendix B.4.1.
1458  *
1459  * d = (c mod(n–1)) + 1    where c is a string of random bits, 64 bits longer
1460  *                         than requested
1461  * 0 <= c mod(n-1) <= n-2  and implies that
1462  * 1 <= d <= n-1
1463  *
1464  * This method generates a private key uniformly distributed in the range
1465  * [1, n-1].
1466  */
1467 int ecc_gen_privkey(unsigned int curve_id, unsigned int ndigits, u64 *privkey)
1468 {
1469         const struct ecc_curve *curve = ecc_get_curve(curve_id);
1470         u64 priv[ECC_MAX_DIGITS];
1471         unsigned int nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT;
1472         unsigned int nbits = vli_num_bits(curve->n, ndigits);
1473         int err;
1474 
1475         /* Check that N is included in Table 1 of FIPS 186-4, section 6.1.1 */
1476         if (nbits < 160 || ndigits > ARRAY_SIZE(priv))
1477                 return -EINVAL;
1478 
1479         /*
1480          * FIPS 186-4 recommends that the private key should be obtained from a
1481          * RBG with a security strength equal to or greater than the security
1482          * strength associated with N.
1483          *
1484          * The maximum security strength identified by NIST SP800-57pt1r4 for
1485          * ECC is 256 (N >= 512).
1486          *
1487          * This condition is met by the default RNG because it selects a favored
1488          * DRBG with a security strength of 256.
1489          */
1490         if (crypto_get_default_rng())
1491                 return -EFAULT;
1492 
1493         err = crypto_rng_get_bytes(crypto_default_rng, (u8 *)priv, nbytes);
1494         crypto_put_default_rng();
1495         if (err)
1496                 return err;
1497 
1498         /* Make sure the private key is in the valid range. */
1499         if (__ecc_is_key_valid(curve, priv, ndigits))
1500                 return -EINVAL;
1501 
1502         ecc_swap_digits(priv, privkey, ndigits);
1503 
1504         return 0;
1505 }
1506 EXPORT_SYMBOL(ecc_gen_privkey);
1507 
1508 int ecc_make_pub_key(unsigned int curve_id, unsigned int ndigits,
1509                      const u64 *private_key, u64 *public_key)
1510 {
1511         int ret = 0;
1512         struct ecc_point *pk;
1513         u64 priv[ECC_MAX_DIGITS];
1514         const struct ecc_curve *curve = ecc_get_curve(curve_id);
1515 
1516         if (!private_key || !curve || ndigits > ARRAY_SIZE(priv)) {
1517                 ret = -EINVAL;
1518                 goto out;
1519         }
1520 
1521         ecc_swap_digits(private_key, priv, ndigits);
1522 
1523         pk = ecc_alloc_point(ndigits);
1524         if (!pk) {
1525                 ret = -ENOMEM;
1526                 goto out;
1527         }
1528 
1529         ecc_point_mult(pk, &curve->g, priv, NULL, curve, ndigits);
1530 
1531         /* SP800-56A rev 3 5.6.2.1.3 key check */
1532         if (ecc_is_pubkey_valid_full(curve, pk)) {
1533                 ret = -EAGAIN;
1534                 goto err_free_point;
1535         }
1536 
1537         ecc_swap_digits(pk->x, public_key, ndigits);
1538         ecc_swap_digits(pk->y, &public_key[ndigits], ndigits);
1539 
1540 err_free_point:
1541         ecc_free_point(pk);
1542 out:
1543         return ret;
1544 }
1545 EXPORT_SYMBOL(ecc_make_pub_key);
1546 
1547 /* SP800-56A section 5.6.2.3.4 partial verification: ephemeral keys only */
1548 int ecc_is_pubkey_valid_partial(const struct ecc_curve *curve,
1549                                 struct ecc_point *pk)
1550 {
1551         u64 yy[ECC_MAX_DIGITS], xxx[ECC_MAX_DIGITS], w[ECC_MAX_DIGITS];
1552 
1553         if (WARN_ON(pk->ndigits != curve->g.ndigits))
1554                 return -EINVAL;
1555 
1556         /* Check 1: Verify key is not the zero point. */
1557         if (ecc_point_is_zero(pk))
1558                 return -EINVAL;
1559 
1560         /* Check 2: Verify key is in the range [1, p-1]. */
1561         if (vli_cmp(curve->p, pk->x, pk->ndigits) != 1)
1562                 return -EINVAL;
1563         if (vli_cmp(curve->p, pk->y, pk->ndigits) != 1)
1564                 return -EINVAL;
1565 
1566         /* Check 3: Verify that y^2 == (x^3 + a·x + b) mod p */
1567         vli_mod_square_fast(yy, pk->y, curve); /* y^2 */
1568         vli_mod_square_fast(xxx, pk->x, curve); /* x^2 */
1569         vli_mod_mult_fast(xxx, xxx, pk->x, curve); /* x^3 */
1570         vli_mod_mult_fast(w, curve->a, pk->x, curve); /* a·x */
1571         vli_mod_add(w, w, curve->b, curve->p, pk->ndigits); /* a·x + b */
1572         vli_mod_add(w, w, xxx, curve->p, pk->ndigits); /* x^3 + a·x + b */
1573         if (vli_cmp(yy, w, pk->ndigits) != 0) /* Equation */
1574                 return -EINVAL;
1575 
1576         return 0;
1577 }
1578 EXPORT_SYMBOL(ecc_is_pubkey_valid_partial);
1579 
1580 /* SP800-56A section 5.6.2.3.3 full verification */
1581 int ecc_is_pubkey_valid_full(const struct ecc_curve *curve,
1582                              struct ecc_point *pk)
1583 {
1584         struct ecc_point *nQ;
1585 
1586         /* Checks 1 through 3 */
1587         int ret = ecc_is_pubkey_valid_partial(curve, pk);
1588 
1589         if (ret)
1590                 return ret;
1591 
1592         /* Check 4: Verify that nQ is the zero point. */
1593         nQ = ecc_alloc_point(pk->ndigits);
1594         if (!nQ)
1595                 return -ENOMEM;
1596 
1597         ecc_point_mult(nQ, pk, curve->n, NULL, curve, pk->ndigits);
1598         if (!ecc_point_is_zero(nQ))
1599                 ret = -EINVAL;
1600 
1601         ecc_free_point(nQ);
1602 
1603         return ret;
1604 }
1605 EXPORT_SYMBOL(ecc_is_pubkey_valid_full);
1606 
1607 int crypto_ecdh_shared_secret(unsigned int curve_id, unsigned int ndigits,
1608                               const u64 *private_key, const u64 *public_key,
1609                               u64 *secret)
1610 {
1611         int ret = 0;
1612         struct ecc_point *product, *pk;
1613         u64 priv[ECC_MAX_DIGITS];
1614         u64 rand_z[ECC_MAX_DIGITS];
1615         unsigned int nbytes;
1616         const struct ecc_curve *curve = ecc_get_curve(curve_id);
1617 
1618         if (!private_key || !public_key || !curve ||
1619             ndigits > ARRAY_SIZE(priv) || ndigits > ARRAY_SIZE(rand_z)) {
1620                 ret = -EINVAL;
1621                 goto out;
1622         }
1623 
1624         nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT;
1625 
1626         get_random_bytes(rand_z, nbytes);
1627 
1628         pk = ecc_alloc_point(ndigits);
1629         if (!pk) {
1630                 ret = -ENOMEM;
1631                 goto out;
1632         }
1633 
1634         ecc_swap_digits(public_key, pk->x, ndigits);
1635         ecc_swap_digits(&public_key[ndigits], pk->y, ndigits);
1636         ret = ecc_is_pubkey_valid_partial(curve, pk);
1637         if (ret)
1638                 goto err_alloc_product;
1639 
1640         ecc_swap_digits(private_key, priv, ndigits);
1641 
1642         product = ecc_alloc_point(ndigits);
1643         if (!product) {
1644                 ret = -ENOMEM;
1645                 goto err_alloc_product;
1646         }
1647 
1648         ecc_point_mult(product, pk, priv, rand_z, curve, ndigits);
1649 
1650         if (ecc_point_is_zero(product)) {
1651                 ret = -EFAULT;
1652                 goto err_validity;
1653         }
1654 
1655         ecc_swap_digits(product->x, secret, ndigits);
1656 
1657 err_validity:
1658         memzero_explicit(priv, sizeof(priv));
1659         memzero_explicit(rand_z, sizeof(rand_z));
1660         ecc_free_point(product);
1661 err_alloc_product:
1662         ecc_free_point(pk);
1663 out:
1664         return ret;
1665 }
1666 EXPORT_SYMBOL(crypto_ecdh_shared_secret);
1667 
1668 MODULE_LICENSE("Dual BSD/GPL");
1669 

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