2 * Copyright (c) 2013, 2014 Kenneth MacKay. All rights reserved.
3 * Copyright (c) 2019 Vitaly Chikunov <vt@altlinux.org>
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions are
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.
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.
27 #include <linux/module.h>
28 #include <linux/random.h>
29 #include <linux/slab.h>
30 #include <linux/swab.h>
31 #include <linux/fips.h>
32 #include <crypto/ecdh.h>
33 #include <crypto/rng.h>
34 #include <asm/unaligned.h>
35 #include <linux/ratelimit.h>
38 #include "ecc_curve_defs.h"
45 static inline const struct ecc_curve *ecc_get_curve(unsigned int curve_id)
48 /* In FIPS mode only allow P256 and higher */
49 case ECC_CURVE_NIST_P192:
50 return fips_enabled ? NULL : &nist_p192;
51 case ECC_CURVE_NIST_P256:
58 static u64 *ecc_alloc_digits_space(unsigned int ndigits)
60 size_t len = ndigits * sizeof(u64);
65 return kmalloc(len, GFP_KERNEL);
68 static void ecc_free_digits_space(u64 *space)
70 kfree_sensitive(space);
73 static struct ecc_point *ecc_alloc_point(unsigned int ndigits)
75 struct ecc_point *p = kmalloc(sizeof(*p), GFP_KERNEL);
80 p->x = ecc_alloc_digits_space(ndigits);
84 p->y = ecc_alloc_digits_space(ndigits);
93 ecc_free_digits_space(p->x);
99 static void ecc_free_point(struct ecc_point *p)
104 kfree_sensitive(p->x);
105 kfree_sensitive(p->y);
109 static void vli_clear(u64 *vli, unsigned int ndigits)
113 for (i = 0; i < ndigits; i++)
117 /* Returns true if vli == 0, false otherwise. */
118 bool vli_is_zero(const u64 *vli, unsigned int ndigits)
122 for (i = 0; i < ndigits; i++) {
129 EXPORT_SYMBOL(vli_is_zero);
131 /* Returns nonzero if bit bit of vli is set. */
132 static u64 vli_test_bit(const u64 *vli, unsigned int bit)
134 return (vli[bit / 64] & ((u64)1 << (bit % 64)));
137 static bool vli_is_negative(const u64 *vli, unsigned int ndigits)
139 return vli_test_bit(vli, ndigits * 64 - 1);
142 /* Counts the number of 64-bit "digits" in vli. */
143 static unsigned int vli_num_digits(const u64 *vli, unsigned int ndigits)
147 /* Search from the end until we find a non-zero digit.
148 * We do it in reverse because we expect that most digits will
151 for (i = ndigits - 1; i >= 0 && vli[i] == 0; i--);
156 /* Counts the number of bits required for vli. */
157 static unsigned int vli_num_bits(const u64 *vli, unsigned int ndigits)
159 unsigned int i, num_digits;
162 num_digits = vli_num_digits(vli, ndigits);
166 digit = vli[num_digits - 1];
167 for (i = 0; digit; i++)
170 return ((num_digits - 1) * 64 + i);
173 /* Set dest from unaligned bit string src. */
174 void vli_from_be64(u64 *dest, const void *src, unsigned int ndigits)
177 const u64 *from = src;
179 for (i = 0; i < ndigits; i++)
180 dest[i] = get_unaligned_be64(&from[ndigits - 1 - i]);
182 EXPORT_SYMBOL(vli_from_be64);
184 void vli_from_le64(u64 *dest, const void *src, unsigned int ndigits)
187 const u64 *from = src;
189 for (i = 0; i < ndigits; i++)
190 dest[i] = get_unaligned_le64(&from[i]);
192 EXPORT_SYMBOL(vli_from_le64);
194 /* Sets dest = src. */
195 static void vli_set(u64 *dest, const u64 *src, unsigned int ndigits)
199 for (i = 0; i < ndigits; i++)
203 /* Returns sign of left - right. */
204 int vli_cmp(const u64 *left, const u64 *right, unsigned int ndigits)
208 for (i = ndigits - 1; i >= 0; i--) {
209 if (left[i] > right[i])
211 else if (left[i] < right[i])
217 EXPORT_SYMBOL(vli_cmp);
219 /* Computes result = in << c, returning carry. Can modify in place
220 * (if result == in). 0 < shift < 64.
222 static u64 vli_lshift(u64 *result, const u64 *in, unsigned int shift,
223 unsigned int ndigits)
228 for (i = 0; i < ndigits; i++) {
231 result[i] = (temp << shift) | carry;
232 carry = temp >> (64 - shift);
238 /* Computes vli = vli >> 1. */
239 static void vli_rshift1(u64 *vli, unsigned int ndigits)
246 while (vli-- > end) {
248 *vli = (temp >> 1) | carry;
253 /* Computes result = left + right, returning carry. Can modify in place. */
254 static u64 vli_add(u64 *result, const u64 *left, const u64 *right,
255 unsigned int ndigits)
260 for (i = 0; i < ndigits; i++) {
263 sum = left[i] + right[i] + carry;
265 carry = (sum < left[i]);
273 /* Computes result = left + right, returning carry. Can modify in place. */
274 static u64 vli_uadd(u64 *result, const u64 *left, u64 right,
275 unsigned int ndigits)
280 for (i = 0; i < ndigits; i++) {
283 sum = left[i] + carry;
285 carry = (sum < left[i]);
295 /* Computes result = left - right, returning borrow. Can modify in place. */
296 u64 vli_sub(u64 *result, const u64 *left, const u64 *right,
297 unsigned int ndigits)
302 for (i = 0; i < ndigits; i++) {
305 diff = left[i] - right[i] - borrow;
307 borrow = (diff > left[i]);
314 EXPORT_SYMBOL(vli_sub);
316 /* Computes result = left - right, returning borrow. Can modify in place. */
317 static u64 vli_usub(u64 *result, const u64 *left, u64 right,
318 unsigned int ndigits)
323 for (i = 0; i < ndigits; i++) {
326 diff = left[i] - borrow;
328 borrow = (diff > left[i]);
336 static uint128_t mul_64_64(u64 left, u64 right)
339 #if defined(CONFIG_ARCH_SUPPORTS_INT128)
340 unsigned __int128 m = (unsigned __int128)left * right;
343 result.m_high = m >> 64;
345 u64 a0 = left & 0xffffffffull;
347 u64 b0 = right & 0xffffffffull;
348 u64 b1 = right >> 32;
359 m3 += 0x100000000ull;
361 result.m_low = (m0 & 0xffffffffull) | (m2 << 32);
362 result.m_high = m3 + (m2 >> 32);
367 static uint128_t add_128_128(uint128_t a, uint128_t b)
371 result.m_low = a.m_low + b.m_low;
372 result.m_high = a.m_high + b.m_high + (result.m_low < a.m_low);
377 static void vli_mult(u64 *result, const u64 *left, const u64 *right,
378 unsigned int ndigits)
380 uint128_t r01 = { 0, 0 };
384 /* Compute each digit of result in sequence, maintaining the
387 for (k = 0; k < ndigits * 2 - 1; k++) {
393 min = (k + 1) - ndigits;
395 for (i = min; i <= k && i < ndigits; i++) {
398 product = mul_64_64(left[i], right[k - i]);
400 r01 = add_128_128(r01, product);
401 r2 += (r01.m_high < product.m_high);
404 result[k] = r01.m_low;
405 r01.m_low = r01.m_high;
410 result[ndigits * 2 - 1] = r01.m_low;
413 /* Compute product = left * right, for a small right value. */
414 static void vli_umult(u64 *result, const u64 *left, u32 right,
415 unsigned int ndigits)
417 uint128_t r01 = { 0 };
420 for (k = 0; k < ndigits; k++) {
423 product = mul_64_64(left[k], right);
424 r01 = add_128_128(r01, product);
426 result[k] = r01.m_low;
427 r01.m_low = r01.m_high;
430 result[k] = r01.m_low;
431 for (++k; k < ndigits * 2; k++)
435 static void vli_square(u64 *result, const u64 *left, unsigned int ndigits)
437 uint128_t r01 = { 0, 0 };
441 for (k = 0; k < ndigits * 2 - 1; k++) {
447 min = (k + 1) - ndigits;
449 for (i = min; i <= k && i <= k - i; i++) {
452 product = mul_64_64(left[i], left[k - i]);
455 r2 += product.m_high >> 63;
456 product.m_high = (product.m_high << 1) |
457 (product.m_low >> 63);
461 r01 = add_128_128(r01, product);
462 r2 += (r01.m_high < product.m_high);
465 result[k] = r01.m_low;
466 r01.m_low = r01.m_high;
471 result[ndigits * 2 - 1] = r01.m_low;
474 /* Computes result = (left + right) % mod.
475 * Assumes that left < mod and right < mod, result != mod.
477 static void vli_mod_add(u64 *result, const u64 *left, const u64 *right,
478 const u64 *mod, unsigned int ndigits)
482 carry = vli_add(result, left, right, ndigits);
484 /* result > mod (result = mod + remainder), so subtract mod to
487 if (carry || vli_cmp(result, mod, ndigits) >= 0)
488 vli_sub(result, result, mod, ndigits);
491 /* Computes result = (left - right) % mod.
492 * Assumes that left < mod and right < mod, result != mod.
494 static void vli_mod_sub(u64 *result, const u64 *left, const u64 *right,
495 const u64 *mod, unsigned int ndigits)
497 u64 borrow = vli_sub(result, left, right, ndigits);
499 /* In this case, p_result == -diff == (max int) - diff.
500 * Since -x % d == d - x, we can get the correct result from
501 * result + mod (with overflow).
504 vli_add(result, result, mod, ndigits);
508 * Computes result = product % mod
509 * for special form moduli: p = 2^k-c, for small c (note the minus sign)
512 * R. Crandall, C. Pomerance. Prime Numbers: A Computational Perspective.
513 * 9 Fast Algorithms for Large-Integer Arithmetic. 9.2.3 Moduli of special form
514 * Algorithm 9.2.13 (Fast mod operation for special-form moduli).
516 static void vli_mmod_special(u64 *result, const u64 *product,
517 const u64 *mod, unsigned int ndigits)
520 u64 t[ECC_MAX_DIGITS * 2];
521 u64 r[ECC_MAX_DIGITS * 2];
523 vli_set(r, product, ndigits * 2);
524 while (!vli_is_zero(r + ndigits, ndigits)) {
525 vli_umult(t, r + ndigits, c, ndigits);
526 vli_clear(r + ndigits, ndigits);
527 vli_add(r, r, t, ndigits * 2);
529 vli_set(t, mod, ndigits);
530 vli_clear(t + ndigits, ndigits);
531 while (vli_cmp(r, t, ndigits * 2) >= 0)
532 vli_sub(r, r, t, ndigits * 2);
533 vli_set(result, r, ndigits);
537 * Computes result = product % mod
538 * for special form moduli: p = 2^{k-1}+c, for small c (note the plus sign)
539 * where k-1 does not fit into qword boundary by -1 bit (such as 255).
541 * References (loosely based on):
542 * A. Menezes, P. van Oorschot, S. Vanstone. Handbook of Applied Cryptography.
543 * 14.3.4 Reduction methods for moduli of special form. Algorithm 14.47.
544 * URL: http://cacr.uwaterloo.ca/hac/about/chap14.pdf
546 * H. Cohen, G. Frey, R. Avanzi, C. Doche, T. Lange, K. Nguyen, F. Vercauteren.
547 * Handbook of Elliptic and Hyperelliptic Curve Cryptography.
548 * Algorithm 10.25 Fast reduction for special form moduli
550 static void vli_mmod_special2(u64 *result, const u64 *product,
551 const u64 *mod, unsigned int ndigits)
554 u64 q[ECC_MAX_DIGITS];
555 u64 r[ECC_MAX_DIGITS * 2];
556 u64 m[ECC_MAX_DIGITS * 2]; /* expanded mod */
557 int carry; /* last bit that doesn't fit into q */
560 vli_set(m, mod, ndigits);
561 vli_clear(m + ndigits, ndigits);
563 vli_set(r, product, ndigits);
564 /* q and carry are top bits */
565 vli_set(q, product + ndigits, ndigits);
566 vli_clear(r + ndigits, ndigits);
567 carry = vli_is_negative(r, ndigits);
569 r[ndigits - 1] &= (1ull << 63) - 1;
570 for (i = 1; carry || !vli_is_zero(q, ndigits); i++) {
571 u64 qc[ECC_MAX_DIGITS * 2];
573 vli_umult(qc, q, c2, ndigits);
575 vli_uadd(qc, qc, mod[0], ndigits * 2);
576 vli_set(q, qc + ndigits, ndigits);
577 vli_clear(qc + ndigits, ndigits);
578 carry = vli_is_negative(qc, ndigits);
580 qc[ndigits - 1] &= (1ull << 63) - 1;
582 vli_sub(r, r, qc, ndigits * 2);
584 vli_add(r, r, qc, ndigits * 2);
586 while (vli_is_negative(r, ndigits * 2))
587 vli_add(r, r, m, ndigits * 2);
588 while (vli_cmp(r, m, ndigits * 2) >= 0)
589 vli_sub(r, r, m, ndigits * 2);
591 vli_set(result, r, ndigits);
595 * Computes result = product % mod, where product is 2N words long.
596 * Reference: Ken MacKay's micro-ecc.
597 * Currently only designed to work for curve_p or curve_n.
599 static void vli_mmod_slow(u64 *result, u64 *product, const u64 *mod,
600 unsigned int ndigits)
602 u64 mod_m[2 * ECC_MAX_DIGITS];
603 u64 tmp[2 * ECC_MAX_DIGITS];
604 u64 *v[2] = { tmp, product };
607 /* Shift mod so its highest set bit is at the maximum position. */
608 int shift = (ndigits * 2 * 64) - vli_num_bits(mod, ndigits);
609 int word_shift = shift / 64;
610 int bit_shift = shift % 64;
612 vli_clear(mod_m, word_shift);
614 for (i = 0; i < ndigits; ++i) {
615 mod_m[word_shift + i] = (mod[i] << bit_shift) | carry;
616 carry = mod[i] >> (64 - bit_shift);
619 vli_set(mod_m + word_shift, mod, ndigits);
621 for (i = 1; shift >= 0; --shift) {
625 for (j = 0; j < ndigits * 2; ++j) {
626 u64 diff = v[i][j] - mod_m[j] - borrow;
629 borrow = (diff > v[i][j]);
632 i = !(i ^ borrow); /* Swap the index if there was no borrow */
633 vli_rshift1(mod_m, ndigits);
634 mod_m[ndigits - 1] |= mod_m[ndigits] << (64 - 1);
635 vli_rshift1(mod_m + ndigits, ndigits);
637 vli_set(result, v[i], ndigits);
640 /* Computes result = product % mod using Barrett's reduction with precomputed
641 * value mu appended to the mod after ndigits, mu = (2^{2w} / mod) and have
642 * length ndigits + 1, where mu * (2^w - 1) should not overflow ndigits
646 * R. Brent, P. Zimmermann. Modern Computer Arithmetic. 2010.
647 * 2.4.1 Barrett's algorithm. Algorithm 2.5.
649 static void vli_mmod_barrett(u64 *result, u64 *product, const u64 *mod,
650 unsigned int ndigits)
652 u64 q[ECC_MAX_DIGITS * 2];
653 u64 r[ECC_MAX_DIGITS * 2];
654 const u64 *mu = mod + ndigits;
656 vli_mult(q, product + ndigits, mu, ndigits);
658 vli_add(q + ndigits, q + ndigits, product + ndigits, ndigits);
659 vli_mult(r, mod, q + ndigits, ndigits);
660 vli_sub(r, product, r, ndigits * 2);
661 while (!vli_is_zero(r + ndigits, ndigits) ||
662 vli_cmp(r, mod, ndigits) != -1) {
665 carry = vli_sub(r, r, mod, ndigits);
666 vli_usub(r + ndigits, r + ndigits, carry, ndigits);
668 vli_set(result, r, ndigits);
671 /* Computes p_result = p_product % curve_p.
672 * See algorithm 5 and 6 from
673 * http://www.isys.uni-klu.ac.at/PDF/2001-0126-MT.pdf
675 static void vli_mmod_fast_192(u64 *result, const u64 *product,
676 const u64 *curve_prime, u64 *tmp)
678 const unsigned int ndigits = 3;
681 vli_set(result, product, ndigits);
683 vli_set(tmp, &product[3], ndigits);
684 carry = vli_add(result, result, tmp, ndigits);
689 carry += vli_add(result, result, tmp, ndigits);
691 tmp[0] = tmp[1] = product[5];
693 carry += vli_add(result, result, tmp, ndigits);
695 while (carry || vli_cmp(curve_prime, result, ndigits) != 1)
696 carry -= vli_sub(result, result, curve_prime, ndigits);
699 /* Computes result = product % curve_prime
700 * from http://www.nsa.gov/ia/_files/nist-routines.pdf
702 static void vli_mmod_fast_256(u64 *result, const u64 *product,
703 const u64 *curve_prime, u64 *tmp)
706 const unsigned int ndigits = 4;
709 vli_set(result, product, ndigits);
713 tmp[1] = product[5] & 0xffffffff00000000ull;
716 carry = vli_lshift(tmp, tmp, 1, ndigits);
717 carry += vli_add(result, result, tmp, ndigits);
720 tmp[1] = product[6] << 32;
721 tmp[2] = (product[6] >> 32) | (product[7] << 32);
722 tmp[3] = product[7] >> 32;
723 carry += vli_lshift(tmp, tmp, 1, ndigits);
724 carry += vli_add(result, result, tmp, ndigits);
728 tmp[1] = product[5] & 0xffffffff;
731 carry += vli_add(result, result, tmp, ndigits);
734 tmp[0] = (product[4] >> 32) | (product[5] << 32);
735 tmp[1] = (product[5] >> 32) | (product[6] & 0xffffffff00000000ull);
737 tmp[3] = (product[6] >> 32) | (product[4] << 32);
738 carry += vli_add(result, result, tmp, ndigits);
741 tmp[0] = (product[5] >> 32) | (product[6] << 32);
742 tmp[1] = (product[6] >> 32);
744 tmp[3] = (product[4] & 0xffffffff) | (product[5] << 32);
745 carry -= vli_sub(result, result, tmp, ndigits);
751 tmp[3] = (product[4] >> 32) | (product[5] & 0xffffffff00000000ull);
752 carry -= vli_sub(result, result, tmp, ndigits);
755 tmp[0] = (product[6] >> 32) | (product[7] << 32);
756 tmp[1] = (product[7] >> 32) | (product[4] << 32);
757 tmp[2] = (product[4] >> 32) | (product[5] << 32);
758 tmp[3] = (product[6] << 32);
759 carry -= vli_sub(result, result, tmp, ndigits);
763 tmp[1] = product[4] & 0xffffffff00000000ull;
765 tmp[3] = product[6] & 0xffffffff00000000ull;
766 carry -= vli_sub(result, result, tmp, ndigits);
770 carry += vli_add(result, result, curve_prime, ndigits);
773 while (carry || vli_cmp(curve_prime, result, ndigits) != 1)
774 carry -= vli_sub(result, result, curve_prime, ndigits);
778 /* Computes result = product % curve_prime for different curve_primes.
780 * Note that curve_primes are distinguished just by heuristic check and
781 * not by complete conformance check.
783 static bool vli_mmod_fast(u64 *result, u64 *product,
784 const u64 *curve_prime, unsigned int ndigits)
786 u64 tmp[2 * ECC_MAX_DIGITS];
788 /* Currently, both NIST primes have -1 in lowest qword. */
789 if (curve_prime[0] != -1ull) {
790 /* Try to handle Pseudo-Marsenne primes. */
791 if (curve_prime[ndigits - 1] == -1ull) {
792 vli_mmod_special(result, product, curve_prime,
795 } else if (curve_prime[ndigits - 1] == 1ull << 63 &&
796 curve_prime[ndigits - 2] == 0) {
797 vli_mmod_special2(result, product, curve_prime,
801 vli_mmod_barrett(result, product, curve_prime, ndigits);
807 vli_mmod_fast_192(result, product, curve_prime, tmp);
810 vli_mmod_fast_256(result, product, curve_prime, tmp);
813 pr_err_ratelimited("ecc: unsupported digits size!\n");
820 /* Computes result = (left * right) % mod.
821 * Assumes that mod is big enough curve order.
823 void vli_mod_mult_slow(u64 *result, const u64 *left, const u64 *right,
824 const u64 *mod, unsigned int ndigits)
826 u64 product[ECC_MAX_DIGITS * 2];
828 vli_mult(product, left, right, ndigits);
829 vli_mmod_slow(result, product, mod, ndigits);
831 EXPORT_SYMBOL(vli_mod_mult_slow);
833 /* Computes result = (left * right) % curve_prime. */
834 static void vli_mod_mult_fast(u64 *result, const u64 *left, const u64 *right,
835 const u64 *curve_prime, unsigned int ndigits)
837 u64 product[2 * ECC_MAX_DIGITS];
839 vli_mult(product, left, right, ndigits);
840 vli_mmod_fast(result, product, curve_prime, ndigits);
843 /* Computes result = left^2 % curve_prime. */
844 static void vli_mod_square_fast(u64 *result, const u64 *left,
845 const u64 *curve_prime, unsigned int ndigits)
847 u64 product[2 * ECC_MAX_DIGITS];
849 vli_square(product, left, ndigits);
850 vli_mmod_fast(result, product, curve_prime, ndigits);
853 #define EVEN(vli) (!(vli[0] & 1))
854 /* Computes result = (1 / p_input) % mod. All VLIs are the same size.
855 * See "From Euclid's GCD to Montgomery Multiplication to the Great Divide"
856 * https://labs.oracle.com/techrep/2001/smli_tr-2001-95.pdf
858 void vli_mod_inv(u64 *result, const u64 *input, const u64 *mod,
859 unsigned int ndigits)
861 u64 a[ECC_MAX_DIGITS], b[ECC_MAX_DIGITS];
862 u64 u[ECC_MAX_DIGITS], v[ECC_MAX_DIGITS];
866 if (vli_is_zero(input, ndigits)) {
867 vli_clear(result, ndigits);
871 vli_set(a, input, ndigits);
872 vli_set(b, mod, ndigits);
873 vli_clear(u, ndigits);
875 vli_clear(v, ndigits);
877 while ((cmp_result = vli_cmp(a, b, ndigits)) != 0) {
881 vli_rshift1(a, ndigits);
884 carry = vli_add(u, u, mod, ndigits);
886 vli_rshift1(u, ndigits);
888 u[ndigits - 1] |= 0x8000000000000000ull;
889 } else if (EVEN(b)) {
890 vli_rshift1(b, ndigits);
893 carry = vli_add(v, v, mod, ndigits);
895 vli_rshift1(v, ndigits);
897 v[ndigits - 1] |= 0x8000000000000000ull;
898 } else if (cmp_result > 0) {
899 vli_sub(a, a, b, ndigits);
900 vli_rshift1(a, ndigits);
902 if (vli_cmp(u, v, ndigits) < 0)
903 vli_add(u, u, mod, ndigits);
905 vli_sub(u, u, v, ndigits);
907 carry = vli_add(u, u, mod, ndigits);
909 vli_rshift1(u, ndigits);
911 u[ndigits - 1] |= 0x8000000000000000ull;
913 vli_sub(b, b, a, ndigits);
914 vli_rshift1(b, ndigits);
916 if (vli_cmp(v, u, ndigits) < 0)
917 vli_add(v, v, mod, ndigits);
919 vli_sub(v, v, u, ndigits);
921 carry = vli_add(v, v, mod, ndigits);
923 vli_rshift1(v, ndigits);
925 v[ndigits - 1] |= 0x8000000000000000ull;
929 vli_set(result, u, ndigits);
931 EXPORT_SYMBOL(vli_mod_inv);
933 /* ------ Point operations ------ */
935 /* Returns true if p_point is the point at infinity, false otherwise. */
936 static bool ecc_point_is_zero(const struct ecc_point *point)
938 return (vli_is_zero(point->x, point->ndigits) &&
939 vli_is_zero(point->y, point->ndigits));
942 /* Point multiplication algorithm using Montgomery's ladder with co-Z
943 * coordinates. From https://eprint.iacr.org/2011/338.pdf
946 /* Double in place */
947 static void ecc_point_double_jacobian(u64 *x1, u64 *y1, u64 *z1,
948 u64 *curve_prime, unsigned int ndigits)
950 /* t1 = x, t2 = y, t3 = z */
951 u64 t4[ECC_MAX_DIGITS];
952 u64 t5[ECC_MAX_DIGITS];
954 if (vli_is_zero(z1, ndigits))
958 vli_mod_square_fast(t4, y1, curve_prime, ndigits);
959 /* t5 = x1*y1^2 = A */
960 vli_mod_mult_fast(t5, x1, t4, curve_prime, ndigits);
962 vli_mod_square_fast(t4, t4, curve_prime, ndigits);
963 /* t2 = y1*z1 = z3 */
964 vli_mod_mult_fast(y1, y1, z1, curve_prime, ndigits);
966 vli_mod_square_fast(z1, z1, curve_prime, ndigits);
969 vli_mod_add(x1, x1, z1, curve_prime, ndigits);
971 vli_mod_add(z1, z1, z1, curve_prime, ndigits);
973 vli_mod_sub(z1, x1, z1, curve_prime, ndigits);
974 /* t1 = x1^2 - z1^4 */
975 vli_mod_mult_fast(x1, x1, z1, curve_prime, ndigits);
977 /* t3 = 2*(x1^2 - z1^4) */
978 vli_mod_add(z1, x1, x1, curve_prime, ndigits);
979 /* t1 = 3*(x1^2 - z1^4) */
980 vli_mod_add(x1, x1, z1, curve_prime, ndigits);
981 if (vli_test_bit(x1, 0)) {
982 u64 carry = vli_add(x1, x1, curve_prime, ndigits);
984 vli_rshift1(x1, ndigits);
985 x1[ndigits - 1] |= carry << 63;
987 vli_rshift1(x1, ndigits);
989 /* t1 = 3/2*(x1^2 - z1^4) = B */
992 vli_mod_square_fast(z1, x1, curve_prime, ndigits);
994 vli_mod_sub(z1, z1, t5, curve_prime, ndigits);
995 /* t3 = B^2 - 2A = x3 */
996 vli_mod_sub(z1, z1, t5, curve_prime, ndigits);
998 vli_mod_sub(t5, t5, z1, curve_prime, ndigits);
999 /* t1 = B * (A - x3) */
1000 vli_mod_mult_fast(x1, x1, t5, curve_prime, ndigits);
1001 /* t4 = B * (A - x3) - y1^4 = y3 */
1002 vli_mod_sub(t4, x1, t4, curve_prime, ndigits);
1004 vli_set(x1, z1, ndigits);
1005 vli_set(z1, y1, ndigits);
1006 vli_set(y1, t4, ndigits);
1009 /* Modify (x1, y1) => (x1 * z^2, y1 * z^3) */
1010 static void apply_z(u64 *x1, u64 *y1, u64 *z, u64 *curve_prime,
1011 unsigned int ndigits)
1013 u64 t1[ECC_MAX_DIGITS];
1015 vli_mod_square_fast(t1, z, curve_prime, ndigits); /* z^2 */
1016 vli_mod_mult_fast(x1, x1, t1, curve_prime, ndigits); /* x1 * z^2 */
1017 vli_mod_mult_fast(t1, t1, z, curve_prime, ndigits); /* z^3 */
1018 vli_mod_mult_fast(y1, y1, t1, curve_prime, ndigits); /* y1 * z^3 */
1021 /* P = (x1, y1) => 2P, (x2, y2) => P' */
1022 static void xycz_initial_double(u64 *x1, u64 *y1, u64 *x2, u64 *y2,
1023 u64 *p_initial_z, u64 *curve_prime,
1024 unsigned int ndigits)
1026 u64 z[ECC_MAX_DIGITS];
1028 vli_set(x2, x1, ndigits);
1029 vli_set(y2, y1, ndigits);
1031 vli_clear(z, ndigits);
1035 vli_set(z, p_initial_z, ndigits);
1037 apply_z(x1, y1, z, curve_prime, ndigits);
1039 ecc_point_double_jacobian(x1, y1, z, curve_prime, ndigits);
1041 apply_z(x2, y2, z, curve_prime, ndigits);
1044 /* Input P = (x1, y1, Z), Q = (x2, y2, Z)
1045 * Output P' = (x1', y1', Z3), P + Q = (x3, y3, Z3)
1046 * or P => P', Q => P + Q
1048 static void xycz_add(u64 *x1, u64 *y1, u64 *x2, u64 *y2, u64 *curve_prime,
1049 unsigned int ndigits)
1051 /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
1052 u64 t5[ECC_MAX_DIGITS];
1055 vli_mod_sub(t5, x2, x1, curve_prime, ndigits);
1056 /* t5 = (x2 - x1)^2 = A */
1057 vli_mod_square_fast(t5, t5, curve_prime, ndigits);
1059 vli_mod_mult_fast(x1, x1, t5, curve_prime, ndigits);
1061 vli_mod_mult_fast(x2, x2, t5, curve_prime, ndigits);
1063 vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
1064 /* t5 = (y2 - y1)^2 = D */
1065 vli_mod_square_fast(t5, y2, curve_prime, ndigits);
1068 vli_mod_sub(t5, t5, x1, curve_prime, ndigits);
1069 /* t5 = D - B - C = x3 */
1070 vli_mod_sub(t5, t5, x2, curve_prime, ndigits);
1072 vli_mod_sub(x2, x2, x1, curve_prime, ndigits);
1073 /* t2 = y1*(C - B) */
1074 vli_mod_mult_fast(y1, y1, x2, curve_prime, ndigits);
1076 vli_mod_sub(x2, x1, t5, curve_prime, ndigits);
1077 /* t4 = (y2 - y1)*(B - x3) */
1078 vli_mod_mult_fast(y2, y2, x2, curve_prime, ndigits);
1080 vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
1082 vli_set(x2, t5, ndigits);
1085 /* Input P = (x1, y1, Z), Q = (x2, y2, Z)
1086 * Output P + Q = (x3, y3, Z3), P - Q = (x3', y3', Z3)
1087 * or P => P - Q, Q => P + Q
1089 static void xycz_add_c(u64 *x1, u64 *y1, u64 *x2, u64 *y2, u64 *curve_prime,
1090 unsigned int ndigits)
1092 /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
1093 u64 t5[ECC_MAX_DIGITS];
1094 u64 t6[ECC_MAX_DIGITS];
1095 u64 t7[ECC_MAX_DIGITS];
1098 vli_mod_sub(t5, x2, x1, curve_prime, ndigits);
1099 /* t5 = (x2 - x1)^2 = A */
1100 vli_mod_square_fast(t5, t5, curve_prime, ndigits);
1102 vli_mod_mult_fast(x1, x1, t5, curve_prime, ndigits);
1104 vli_mod_mult_fast(x2, x2, t5, curve_prime, ndigits);
1106 vli_mod_add(t5, y2, y1, curve_prime, ndigits);
1108 vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
1111 vli_mod_sub(t6, x2, x1, curve_prime, ndigits);
1112 /* t2 = y1 * (C - B) */
1113 vli_mod_mult_fast(y1, y1, t6, curve_prime, ndigits);
1115 vli_mod_add(t6, x1, x2, curve_prime, ndigits);
1116 /* t3 = (y2 - y1)^2 */
1117 vli_mod_square_fast(x2, y2, curve_prime, ndigits);
1119 vli_mod_sub(x2, x2, t6, curve_prime, ndigits);
1122 vli_mod_sub(t7, x1, x2, curve_prime, ndigits);
1123 /* t4 = (y2 - y1)*(B - x3) */
1124 vli_mod_mult_fast(y2, y2, t7, curve_prime, ndigits);
1126 vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
1128 /* t7 = (y2 + y1)^2 = F */
1129 vli_mod_square_fast(t7, t5, curve_prime, ndigits);
1131 vli_mod_sub(t7, t7, t6, curve_prime, ndigits);
1133 vli_mod_sub(t6, t7, x1, curve_prime, ndigits);
1134 /* t6 = (y2 + y1)*(x3' - B) */
1135 vli_mod_mult_fast(t6, t6, t5, curve_prime, ndigits);
1137 vli_mod_sub(y1, t6, y1, curve_prime, ndigits);
1139 vli_set(x1, t7, ndigits);
1142 static void ecc_point_mult(struct ecc_point *result,
1143 const struct ecc_point *point, const u64 *scalar,
1144 u64 *initial_z, const struct ecc_curve *curve,
1145 unsigned int ndigits)
1148 u64 rx[2][ECC_MAX_DIGITS];
1149 u64 ry[2][ECC_MAX_DIGITS];
1150 u64 z[ECC_MAX_DIGITS];
1151 u64 sk[2][ECC_MAX_DIGITS];
1152 u64 *curve_prime = curve->p;
1157 carry = vli_add(sk[0], scalar, curve->n, ndigits);
1158 vli_add(sk[1], sk[0], curve->n, ndigits);
1159 scalar = sk[!carry];
1160 num_bits = sizeof(u64) * ndigits * 8 + 1;
1162 vli_set(rx[1], point->x, ndigits);
1163 vli_set(ry[1], point->y, ndigits);
1165 xycz_initial_double(rx[1], ry[1], rx[0], ry[0], initial_z, curve_prime,
1168 for (i = num_bits - 2; i > 0; i--) {
1169 nb = !vli_test_bit(scalar, i);
1170 xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb], curve_prime,
1172 xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve_prime,
1176 nb = !vli_test_bit(scalar, 0);
1177 xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb], curve_prime,
1180 /* Find final 1/Z value. */
1182 vli_mod_sub(z, rx[1], rx[0], curve_prime, ndigits);
1183 /* Yb * (X1 - X0) */
1184 vli_mod_mult_fast(z, z, ry[1 - nb], curve_prime, ndigits);
1185 /* xP * Yb * (X1 - X0) */
1186 vli_mod_mult_fast(z, z, point->x, curve_prime, ndigits);
1188 /* 1 / (xP * Yb * (X1 - X0)) */
1189 vli_mod_inv(z, z, curve_prime, point->ndigits);
1191 /* yP / (xP * Yb * (X1 - X0)) */
1192 vli_mod_mult_fast(z, z, point->y, curve_prime, ndigits);
1193 /* Xb * yP / (xP * Yb * (X1 - X0)) */
1194 vli_mod_mult_fast(z, z, rx[1 - nb], curve_prime, ndigits);
1195 /* End 1/Z calculation */
1197 xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve_prime, ndigits);
1199 apply_z(rx[0], ry[0], z, curve_prime, ndigits);
1201 vli_set(result->x, rx[0], ndigits);
1202 vli_set(result->y, ry[0], ndigits);
1205 /* Computes R = P + Q mod p */
1206 static void ecc_point_add(const struct ecc_point *result,
1207 const struct ecc_point *p, const struct ecc_point *q,
1208 const struct ecc_curve *curve)
1210 u64 z[ECC_MAX_DIGITS];
1211 u64 px[ECC_MAX_DIGITS];
1212 u64 py[ECC_MAX_DIGITS];
1213 unsigned int ndigits = curve->g.ndigits;
1215 vli_set(result->x, q->x, ndigits);
1216 vli_set(result->y, q->y, ndigits);
1217 vli_mod_sub(z, result->x, p->x, curve->p, ndigits);
1218 vli_set(px, p->x, ndigits);
1219 vli_set(py, p->y, ndigits);
1220 xycz_add(px, py, result->x, result->y, curve->p, ndigits);
1221 vli_mod_inv(z, z, curve->p, ndigits);
1222 apply_z(result->x, result->y, z, curve->p, ndigits);
1225 /* Computes R = u1P + u2Q mod p using Shamir's trick.
1226 * Based on: Kenneth MacKay's micro-ecc (2014).
1228 void ecc_point_mult_shamir(const struct ecc_point *result,
1229 const u64 *u1, const struct ecc_point *p,
1230 const u64 *u2, const struct ecc_point *q,
1231 const struct ecc_curve *curve)
1233 u64 z[ECC_MAX_DIGITS];
1234 u64 sump[2][ECC_MAX_DIGITS];
1235 u64 *rx = result->x;
1236 u64 *ry = result->y;
1237 unsigned int ndigits = curve->g.ndigits;
1238 unsigned int num_bits;
1239 struct ecc_point sum = ECC_POINT_INIT(sump[0], sump[1], ndigits);
1240 const struct ecc_point *points[4];
1241 const struct ecc_point *point;
1245 ecc_point_add(&sum, p, q, curve);
1251 num_bits = max(vli_num_bits(u1, ndigits),
1252 vli_num_bits(u2, ndigits));
1254 idx = (!!vli_test_bit(u1, i)) | ((!!vli_test_bit(u2, i)) << 1);
1255 point = points[idx];
1257 vli_set(rx, point->x, ndigits);
1258 vli_set(ry, point->y, ndigits);
1259 vli_clear(z + 1, ndigits - 1);
1262 for (--i; i >= 0; i--) {
1263 ecc_point_double_jacobian(rx, ry, z, curve->p, ndigits);
1264 idx = (!!vli_test_bit(u1, i)) | ((!!vli_test_bit(u2, i)) << 1);
1265 point = points[idx];
1267 u64 tx[ECC_MAX_DIGITS];
1268 u64 ty[ECC_MAX_DIGITS];
1269 u64 tz[ECC_MAX_DIGITS];
1271 vli_set(tx, point->x, ndigits);
1272 vli_set(ty, point->y, ndigits);
1273 apply_z(tx, ty, z, curve->p, ndigits);
1274 vli_mod_sub(tz, rx, tx, curve->p, ndigits);
1275 xycz_add(tx, ty, rx, ry, curve->p, ndigits);
1276 vli_mod_mult_fast(z, z, tz, curve->p, ndigits);
1279 vli_mod_inv(z, z, curve->p, ndigits);
1280 apply_z(rx, ry, z, curve->p, ndigits);
1282 EXPORT_SYMBOL(ecc_point_mult_shamir);
1284 static inline void ecc_swap_digits(const u64 *in, u64 *out,
1285 unsigned int ndigits)
1287 const __be64 *src = (__force __be64 *)in;
1290 for (i = 0; i < ndigits; i++)
1291 out[i] = be64_to_cpu(src[ndigits - 1 - i]);
1294 static int __ecc_is_key_valid(const struct ecc_curve *curve,
1295 const u64 *private_key, unsigned int ndigits)
1297 u64 one[ECC_MAX_DIGITS] = { 1, };
1298 u64 res[ECC_MAX_DIGITS];
1303 if (curve->g.ndigits != ndigits)
1306 /* Make sure the private key is in the range [2, n-3]. */
1307 if (vli_cmp(one, private_key, ndigits) != -1)
1309 vli_sub(res, curve->n, one, ndigits);
1310 vli_sub(res, res, one, ndigits);
1311 if (vli_cmp(res, private_key, ndigits) != 1)
1317 int ecc_is_key_valid(unsigned int curve_id, unsigned int ndigits,
1318 const u64 *private_key, unsigned int private_key_len)
1321 const struct ecc_curve *curve = ecc_get_curve(curve_id);
1323 nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT;
1325 if (private_key_len != nbytes)
1328 return __ecc_is_key_valid(curve, private_key, ndigits);
1330 EXPORT_SYMBOL(ecc_is_key_valid);
1333 * ECC private keys are generated using the method of extra random bits,
1334 * equivalent to that described in FIPS 186-4, Appendix B.4.1.
1336 * d = (c mod(n–1)) + 1 where c is a string of random bits, 64 bits longer
1338 * 0 <= c mod(n-1) <= n-2 and implies that
1341 * This method generates a private key uniformly distributed in the range
1344 int ecc_gen_privkey(unsigned int curve_id, unsigned int ndigits, u64 *privkey)
1346 const struct ecc_curve *curve = ecc_get_curve(curve_id);
1347 u64 priv[ECC_MAX_DIGITS];
1348 unsigned int nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT;
1349 unsigned int nbits = vli_num_bits(curve->n, ndigits);
1352 /* Check that N is included in Table 1 of FIPS 186-4, section 6.1.1 */
1353 if (nbits < 160 || ndigits > ARRAY_SIZE(priv))
1357 * FIPS 186-4 recommends that the private key should be obtained from a
1358 * RBG with a security strength equal to or greater than the security
1359 * strength associated with N.
1361 * The maximum security strength identified by NIST SP800-57pt1r4 for
1362 * ECC is 256 (N >= 512).
1364 * This condition is met by the default RNG because it selects a favored
1365 * DRBG with a security strength of 256.
1367 if (crypto_get_default_rng())
1370 err = crypto_rng_get_bytes(crypto_default_rng, (u8 *)priv, nbytes);
1371 crypto_put_default_rng();
1375 /* Make sure the private key is in the valid range. */
1376 if (__ecc_is_key_valid(curve, priv, ndigits))
1379 ecc_swap_digits(priv, privkey, ndigits);
1383 EXPORT_SYMBOL(ecc_gen_privkey);
1385 int ecc_make_pub_key(unsigned int curve_id, unsigned int ndigits,
1386 const u64 *private_key, u64 *public_key)
1389 struct ecc_point *pk;
1390 u64 priv[ECC_MAX_DIGITS];
1391 const struct ecc_curve *curve = ecc_get_curve(curve_id);
1393 if (!private_key || !curve || ndigits > ARRAY_SIZE(priv)) {
1398 ecc_swap_digits(private_key, priv, ndigits);
1400 pk = ecc_alloc_point(ndigits);
1406 ecc_point_mult(pk, &curve->g, priv, NULL, curve, ndigits);
1408 /* SP800-56A rev 3 5.6.2.1.3 key check */
1409 if (ecc_is_pubkey_valid_full(curve, pk)) {
1411 goto err_free_point;
1414 ecc_swap_digits(pk->x, public_key, ndigits);
1415 ecc_swap_digits(pk->y, &public_key[ndigits], ndigits);
1422 EXPORT_SYMBOL(ecc_make_pub_key);
1424 /* SP800-56A section 5.6.2.3.4 partial verification: ephemeral keys only */
1425 int ecc_is_pubkey_valid_partial(const struct ecc_curve *curve,
1426 struct ecc_point *pk)
1428 u64 yy[ECC_MAX_DIGITS], xxx[ECC_MAX_DIGITS], w[ECC_MAX_DIGITS];
1430 if (WARN_ON(pk->ndigits != curve->g.ndigits))
1433 /* Check 1: Verify key is not the zero point. */
1434 if (ecc_point_is_zero(pk))
1437 /* Check 2: Verify key is in the range [1, p-1]. */
1438 if (vli_cmp(curve->p, pk->x, pk->ndigits) != 1)
1440 if (vli_cmp(curve->p, pk->y, pk->ndigits) != 1)
1443 /* Check 3: Verify that y^2 == (x^3 + a·x + b) mod p */
1444 vli_mod_square_fast(yy, pk->y, curve->p, pk->ndigits); /* y^2 */
1445 vli_mod_square_fast(xxx, pk->x, curve->p, pk->ndigits); /* x^2 */
1446 vli_mod_mult_fast(xxx, xxx, pk->x, curve->p, pk->ndigits); /* x^3 */
1447 vli_mod_mult_fast(w, curve->a, pk->x, curve->p, pk->ndigits); /* a·x */
1448 vli_mod_add(w, w, curve->b, curve->p, pk->ndigits); /* a·x + b */
1449 vli_mod_add(w, w, xxx, curve->p, pk->ndigits); /* x^3 + a·x + b */
1450 if (vli_cmp(yy, w, pk->ndigits) != 0) /* Equation */
1455 EXPORT_SYMBOL(ecc_is_pubkey_valid_partial);
1457 /* SP800-56A section 5.6.2.3.3 full verification */
1458 int ecc_is_pubkey_valid_full(const struct ecc_curve *curve,
1459 struct ecc_point *pk)
1461 struct ecc_point *nQ;
1463 /* Checks 1 through 3 */
1464 int ret = ecc_is_pubkey_valid_partial(curve, pk);
1469 /* Check 4: Verify that nQ is the zero point. */
1470 nQ = ecc_alloc_point(pk->ndigits);
1474 ecc_point_mult(nQ, pk, curve->n, NULL, curve, pk->ndigits);
1475 if (!ecc_point_is_zero(nQ))
1482 EXPORT_SYMBOL(ecc_is_pubkey_valid_full);
1484 int crypto_ecdh_shared_secret(unsigned int curve_id, unsigned int ndigits,
1485 const u64 *private_key, const u64 *public_key,
1489 struct ecc_point *product, *pk;
1490 u64 priv[ECC_MAX_DIGITS];
1491 u64 rand_z[ECC_MAX_DIGITS];
1492 unsigned int nbytes;
1493 const struct ecc_curve *curve = ecc_get_curve(curve_id);
1495 if (!private_key || !public_key || !curve ||
1496 ndigits > ARRAY_SIZE(priv) || ndigits > ARRAY_SIZE(rand_z)) {
1501 nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT;
1503 get_random_bytes(rand_z, nbytes);
1505 pk = ecc_alloc_point(ndigits);
1511 ecc_swap_digits(public_key, pk->x, ndigits);
1512 ecc_swap_digits(&public_key[ndigits], pk->y, ndigits);
1513 ret = ecc_is_pubkey_valid_partial(curve, pk);
1515 goto err_alloc_product;
1517 ecc_swap_digits(private_key, priv, ndigits);
1519 product = ecc_alloc_point(ndigits);
1522 goto err_alloc_product;
1525 ecc_point_mult(product, pk, priv, rand_z, curve, ndigits);
1527 if (ecc_point_is_zero(product)) {
1532 ecc_swap_digits(product->x, secret, ndigits);
1535 memzero_explicit(priv, sizeof(priv));
1536 memzero_explicit(rand_z, sizeof(rand_z));
1537 ecc_free_point(product);
1543 EXPORT_SYMBOL(crypto_ecdh_shared_secret);
1545 MODULE_LICENSE("Dual BSD/GPL");