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 <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>
39 #include "ecc_curve_defs.h"
46 /* Returns curv25519 curve param */
47 const struct ecc_curve
*ecc_get_curve25519(void)
51 EXPORT_SYMBOL(ecc_get_curve25519
);
53 const struct ecc_curve
*ecc_get_curve(unsigned int 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
:
61 case ECC_CURVE_NIST_P384
:
67 EXPORT_SYMBOL(ecc_get_curve
);
69 static u64
*ecc_alloc_digits_space(unsigned int ndigits
)
71 size_t len
= ndigits
* sizeof(u64
);
76 return kmalloc(len
, GFP_KERNEL
);
79 static void ecc_free_digits_space(u64
*space
)
81 kfree_sensitive(space
);
84 struct ecc_point
*ecc_alloc_point(unsigned int ndigits
)
86 struct ecc_point
*p
= kmalloc(sizeof(*p
), GFP_KERNEL
);
91 p
->x
= ecc_alloc_digits_space(ndigits
);
95 p
->y
= ecc_alloc_digits_space(ndigits
);
104 ecc_free_digits_space(p
->x
);
109 EXPORT_SYMBOL(ecc_alloc_point
);
111 void ecc_free_point(struct ecc_point
*p
)
116 kfree_sensitive(p
->x
);
117 kfree_sensitive(p
->y
);
120 EXPORT_SYMBOL(ecc_free_point
);
122 static void vli_clear(u64
*vli
, unsigned int ndigits
)
126 for (i
= 0; i
< ndigits
; i
++)
130 /* Returns true if vli == 0, false otherwise. */
131 bool vli_is_zero(const u64
*vli
, unsigned int ndigits
)
135 for (i
= 0; i
< ndigits
; i
++) {
142 EXPORT_SYMBOL(vli_is_zero
);
144 /* Returns nonzero if bit of vli is set. */
145 static u64
vli_test_bit(const u64
*vli
, unsigned int bit
)
147 return (vli
[bit
/ 64] & ((u64
)1 << (bit
% 64)));
150 static bool vli_is_negative(const u64
*vli
, unsigned int ndigits
)
152 return vli_test_bit(vli
, ndigits
* 64 - 1);
155 /* Counts the number of 64-bit "digits" in vli. */
156 static unsigned int vli_num_digits(const u64
*vli
, unsigned int ndigits
)
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
164 for (i
= ndigits
- 1; i
>= 0 && vli
[i
] == 0; i
--);
169 /* Counts the number of bits required for vli. */
170 unsigned int vli_num_bits(const u64
*vli
, unsigned int ndigits
)
172 unsigned int i
, num_digits
;
175 num_digits
= vli_num_digits(vli
, ndigits
);
179 digit
= vli
[num_digits
- 1];
180 for (i
= 0; digit
; i
++)
183 return ((num_digits
- 1) * 64 + i
);
185 EXPORT_SYMBOL(vli_num_bits
);
187 /* Set dest from unaligned bit string src. */
188 void vli_from_be64(u64
*dest
, const void *src
, unsigned int ndigits
)
191 const u64
*from
= src
;
193 for (i
= 0; i
< ndigits
; i
++)
194 dest
[i
] = get_unaligned_be64(&from
[ndigits
- 1 - i
]);
196 EXPORT_SYMBOL(vli_from_be64
);
198 void vli_from_le64(u64
*dest
, const void *src
, unsigned int ndigits
)
201 const u64
*from
= src
;
203 for (i
= 0; i
< ndigits
; i
++)
204 dest
[i
] = get_unaligned_le64(&from
[i
]);
206 EXPORT_SYMBOL(vli_from_le64
);
208 /* Sets dest = src. */
209 static void vli_set(u64
*dest
, const u64
*src
, unsigned int ndigits
)
213 for (i
= 0; i
< ndigits
; i
++)
217 /* Returns sign of left - right. */
218 int vli_cmp(const u64
*left
, const u64
*right
, unsigned int ndigits
)
222 for (i
= ndigits
- 1; i
>= 0; i
--) {
223 if (left
[i
] > right
[i
])
225 else if (left
[i
] < right
[i
])
231 EXPORT_SYMBOL(vli_cmp
);
233 /* Computes result = in << c, returning carry. Can modify in place
234 * (if result == in). 0 < shift < 64.
236 static u64
vli_lshift(u64
*result
, const u64
*in
, unsigned int shift
,
237 unsigned int ndigits
)
242 for (i
= 0; i
< ndigits
; i
++) {
245 result
[i
] = (temp
<< shift
) | carry
;
246 carry
= temp
>> (64 - shift
);
252 /* Computes vli = vli >> 1. */
253 static void vli_rshift1(u64
*vli
, unsigned int ndigits
)
260 while (vli
-- > end
) {
262 *vli
= (temp
>> 1) | carry
;
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
)
274 for (i
= 0; i
< ndigits
; i
++) {
277 sum
= left
[i
] + right
[i
] + carry
;
279 carry
= (sum
< left
[i
]);
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
)
294 for (i
= 0; i
< ndigits
; i
++) {
297 sum
= left
[i
] + carry
;
299 carry
= (sum
< left
[i
]);
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
)
316 for (i
= 0; i
< ndigits
; i
++) {
319 diff
= left
[i
] - right
[i
] - borrow
;
321 borrow
= (diff
> left
[i
]);
328 EXPORT_SYMBOL(vli_sub
);
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
)
337 for (i
= 0; i
< ndigits
; i
++) {
340 diff
= left
[i
] - borrow
;
342 borrow
= (diff
> left
[i
]);
350 static uint128_t
mul_64_64(u64 left
, u64 right
)
353 #if defined(CONFIG_ARCH_SUPPORTS_INT128)
354 unsigned __int128 m
= (unsigned __int128
)left
* right
;
357 result
.m_high
= m
>> 64;
359 u64 a0
= left
& 0xffffffffull
;
361 u64 b0
= right
& 0xffffffffull
;
362 u64 b1
= right
>> 32;
373 m3
+= 0x100000000ull
;
375 result
.m_low
= (m0
& 0xffffffffull
) | (m2
<< 32);
376 result
.m_high
= m3
+ (m2
>> 32);
381 static uint128_t
add_128_128(uint128_t a
, uint128_t b
)
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
);
391 static void vli_mult(u64
*result
, const u64
*left
, const u64
*right
,
392 unsigned int ndigits
)
394 uint128_t r01
= { 0, 0 };
398 /* Compute each digit of result in sequence, maintaining the
401 for (k
= 0; k
< ndigits
* 2 - 1; k
++) {
407 min
= (k
+ 1) - ndigits
;
409 for (i
= min
; i
<= k
&& i
< ndigits
; i
++) {
412 product
= mul_64_64(left
[i
], right
[k
- i
]);
414 r01
= add_128_128(r01
, product
);
415 r2
+= (r01
.m_high
< product
.m_high
);
418 result
[k
] = r01
.m_low
;
419 r01
.m_low
= r01
.m_high
;
424 result
[ndigits
* 2 - 1] = r01
.m_low
;
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
)
431 uint128_t r01
= { 0 };
434 for (k
= 0; k
< ndigits
; k
++) {
437 product
= mul_64_64(left
[k
], right
);
438 r01
= add_128_128(r01
, product
);
440 result
[k
] = r01
.m_low
;
441 r01
.m_low
= r01
.m_high
;
444 result
[k
] = r01
.m_low
;
445 for (++k
; k
< ndigits
* 2; k
++)
449 static void vli_square(u64
*result
, const u64
*left
, unsigned int ndigits
)
451 uint128_t r01
= { 0, 0 };
455 for (k
= 0; k
< ndigits
* 2 - 1; k
++) {
461 min
= (k
+ 1) - ndigits
;
463 for (i
= min
; i
<= k
&& i
<= k
- i
; i
++) {
466 product
= mul_64_64(left
[i
], left
[k
- i
]);
469 r2
+= product
.m_high
>> 63;
470 product
.m_high
= (product
.m_high
<< 1) |
471 (product
.m_low
>> 63);
475 r01
= add_128_128(r01
, product
);
476 r2
+= (r01
.m_high
< product
.m_high
);
479 result
[k
] = r01
.m_low
;
480 r01
.m_low
= r01
.m_high
;
485 result
[ndigits
* 2 - 1] = r01
.m_low
;
488 /* Computes result = (left + right) % mod.
489 * Assumes that left < mod and right < mod, result != mod.
491 static void vli_mod_add(u64
*result
, const u64
*left
, const u64
*right
,
492 const u64
*mod
, unsigned int ndigits
)
496 carry
= vli_add(result
, left
, right
, ndigits
);
498 /* result > mod (result = mod + remainder), so subtract mod to
501 if (carry
|| vli_cmp(result
, mod
, ndigits
) >= 0)
502 vli_sub(result
, result
, mod
, ndigits
);
505 /* Computes result = (left - right) % mod.
506 * Assumes that left < mod and right < mod, result != mod.
508 static void vli_mod_sub(u64
*result
, const u64
*left
, const u64
*right
,
509 const u64
*mod
, unsigned int ndigits
)
511 u64 borrow
= vli_sub(result
, left
, right
, ndigits
);
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).
518 vli_add(result
, result
, mod
, ndigits
);
522 * Computes result = product % mod
523 * for special form moduli: p = 2^k-c, for small c (note the minus sign)
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).
530 static void vli_mmod_special(u64
*result
, const u64
*product
,
531 const u64
*mod
, unsigned int ndigits
)
534 u64 t
[ECC_MAX_DIGITS
* 2];
535 u64 r
[ECC_MAX_DIGITS
* 2];
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);
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
);
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).
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
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
564 static void vli_mmod_special2(u64
*result
, const u64
*product
,
565 const u64
*mod
, unsigned int ndigits
)
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 */
574 vli_set(m
, mod
, ndigits
);
575 vli_clear(m
+ ndigits
, ndigits
);
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
);
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];
587 vli_umult(qc
, q
, c2
, ndigits
);
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
);
594 qc
[ndigits
- 1] &= (1ull << 63) - 1;
596 vli_sub(r
, r
, qc
, ndigits
* 2);
598 vli_add(r
, r
, qc
, ndigits
* 2);
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);
605 vli_set(result
, r
, ndigits
);
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.
613 static void vli_mmod_slow(u64
*result
, u64
*product
, const u64
*mod
,
614 unsigned int ndigits
)
616 u64 mod_m
[2 * ECC_MAX_DIGITS
];
617 u64 tmp
[2 * ECC_MAX_DIGITS
];
618 u64
*v
[2] = { tmp
, product
};
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;
626 vli_clear(mod_m
, word_shift
);
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
);
633 vli_set(mod_m
+ word_shift
, mod
, ndigits
);
635 for (i
= 1; shift
>= 0; --shift
) {
639 for (j
= 0; j
< ndigits
* 2; ++j
) {
640 u64 diff
= v
[i
][j
] - mod_m
[j
] - borrow
;
643 borrow
= (diff
> v
[i
][j
]);
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
);
651 vli_set(result
, v
[i
], ndigits
);
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
660 * R. Brent, P. Zimmermann. Modern Computer Arithmetic. 2010.
661 * 2.4.1 Barrett's algorithm. Algorithm 2.5.
663 static void vli_mmod_barrett(u64
*result
, u64
*product
, const u64
*mod
,
664 unsigned int ndigits
)
666 u64 q
[ECC_MAX_DIGITS
* 2];
667 u64 r
[ECC_MAX_DIGITS
* 2];
668 const u64
*mu
= mod
+ ndigits
;
670 vli_mult(q
, product
+ ndigits
, 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) {
679 carry
= vli_sub(r
, r
, mod
, ndigits
);
680 vli_usub(r
+ ndigits
, r
+ ndigits
, carry
, ndigits
);
682 vli_set(result
, r
, ndigits
);
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
689 static void vli_mmod_fast_192(u64
*result
, const u64
*product
,
690 const u64
*curve_prime
, u64
*tmp
)
692 const unsigned int ndigits
= 3;
695 vli_set(result
, product
, ndigits
);
697 vli_set(tmp
, &product
[3], ndigits
);
698 carry
= vli_add(result
, result
, tmp
, ndigits
);
703 carry
+= vli_add(result
, result
, tmp
, ndigits
);
705 tmp
[0] = tmp
[1] = product
[5];
707 carry
+= vli_add(result
, result
, tmp
, ndigits
);
709 while (carry
|| vli_cmp(curve_prime
, result
, ndigits
) != 1)
710 carry
-= vli_sub(result
, result
, curve_prime
, ndigits
);
713 /* Computes result = product % curve_prime
714 * from http://www.nsa.gov/ia/_files/nist-routines.pdf
716 static void vli_mmod_fast_256(u64
*result
, const u64
*product
,
717 const u64
*curve_prime
, u64
*tmp
)
720 const unsigned int ndigits
= 4;
723 vli_set(result
, product
, ndigits
);
727 tmp
[1] = product
[5] & 0xffffffff00000000ull
;
730 carry
= vli_lshift(tmp
, tmp
, 1, ndigits
);
731 carry
+= vli_add(result
, result
, tmp
, ndigits
);
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
);
742 tmp
[1] = product
[5] & 0xffffffff;
745 carry
+= vli_add(result
, result
, tmp
, ndigits
);
748 tmp
[0] = (product
[4] >> 32) | (product
[5] << 32);
749 tmp
[1] = (product
[5] >> 32) | (product
[6] & 0xffffffff00000000ull
);
751 tmp
[3] = (product
[6] >> 32) | (product
[4] << 32);
752 carry
+= vli_add(result
, result
, tmp
, ndigits
);
755 tmp
[0] = (product
[5] >> 32) | (product
[6] << 32);
756 tmp
[1] = (product
[6] >> 32);
758 tmp
[3] = (product
[4] & 0xffffffff) | (product
[5] << 32);
759 carry
-= vli_sub(result
, result
, tmp
, ndigits
);
765 tmp
[3] = (product
[4] >> 32) | (product
[5] & 0xffffffff00000000ull
);
766 carry
-= vli_sub(result
, result
, tmp
, ndigits
);
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
);
777 tmp
[1] = product
[4] & 0xffffffff00000000ull
;
779 tmp
[3] = product
[6] & 0xffffffff00000000ull
;
780 carry
-= vli_sub(result
, result
, tmp
, ndigits
);
784 carry
+= vli_add(result
, result
, curve_prime
, ndigits
);
787 while (carry
|| vli_cmp(curve_prime
, result
, ndigits
) != 1)
788 carry
-= vli_sub(result
, result
, curve_prime
, ndigits
);
792 #define SL32OR32(x32, y32) (((u64)x32 << 32) | y32)
793 #define AND64H(x64) (x64 & 0xffFFffFF00000000ull)
794 #define AND64L(x64) (x64 & 0x00000000ffFFffFFull)
796 /* Computes result = product % curve_prime
797 * from "Mathematical routines for the NIST prime elliptic curves"
799 static void vli_mmod_fast_384(u64
*result
, const u64
*product
,
800 const u64
*curve_prime
, u64
*tmp
)
803 const unsigned int ndigits
= 6;
806 vli_set(result
, product
, ndigits
);
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
);
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
);
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
);
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
);
848 tmp
[2] = product
[10]; //a21||a20
849 tmp
[3] = product
[11]; //a23||a22
852 carry
+= vli_add(result
, result
, tmp
, ndigits
);
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
);
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
);
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
);
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
);
892 carry
+= vli_add(result
, result
, curve_prime
, ndigits
);
895 while (carry
|| vli_cmp(curve_prime
, result
, ndigits
) != 1)
896 carry
-= vli_sub(result
, result
, curve_prime
, ndigits
);
905 /* Computes result = product % curve_prime for different curve_primes.
907 * Note that curve_primes are distinguished just by heuristic check and
908 * not by complete conformance check.
910 static bool vli_mmod_fast(u64
*result
, u64
*product
,
911 const struct ecc_curve
*curve
)
913 u64 tmp
[2 * ECC_MAX_DIGITS
];
914 const u64
*curve_prime
= curve
->p
;
915 const unsigned int ndigits
= curve
->g
.ndigits
;
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
,
924 } else if (curve_prime
[ndigits
- 1] == 1ull << 63 &&
925 curve_prime
[ndigits
- 2] == 0) {
926 vli_mmod_special2(result
, product
, curve_prime
,
930 vli_mmod_barrett(result
, product
, curve_prime
, ndigits
);
936 vli_mmod_fast_192(result
, product
, curve_prime
, tmp
);
939 vli_mmod_fast_256(result
, product
, curve_prime
, tmp
);
942 vli_mmod_fast_384(result
, product
, curve_prime
, tmp
);
945 pr_err_ratelimited("ecc: unsupported digits size!\n");
952 /* Computes result = (left * right) % mod.
953 * Assumes that mod is big enough curve order.
955 void vli_mod_mult_slow(u64
*result
, const u64
*left
, const u64
*right
,
956 const u64
*mod
, unsigned int ndigits
)
958 u64 product
[ECC_MAX_DIGITS
* 2];
960 vli_mult(product
, left
, right
, ndigits
);
961 vli_mmod_slow(result
, product
, mod
, ndigits
);
963 EXPORT_SYMBOL(vli_mod_mult_slow
);
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
)
969 u64 product
[2 * ECC_MAX_DIGITS
];
971 vli_mult(product
, left
, right
, curve
->g
.ndigits
);
972 vli_mmod_fast(result
, product
, curve
);
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
)
979 u64 product
[2 * ECC_MAX_DIGITS
];
981 vli_square(product
, left
, curve
->g
.ndigits
);
982 vli_mmod_fast(result
, product
, curve
);
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
990 void vli_mod_inv(u64
*result
, const u64
*input
, const u64
*mod
,
991 unsigned int ndigits
)
993 u64 a
[ECC_MAX_DIGITS
], b
[ECC_MAX_DIGITS
];
994 u64 u
[ECC_MAX_DIGITS
], v
[ECC_MAX_DIGITS
];
998 if (vli_is_zero(input
, ndigits
)) {
999 vli_clear(result
, ndigits
);
1003 vli_set(a
, input
, ndigits
);
1004 vli_set(b
, mod
, ndigits
);
1005 vli_clear(u
, ndigits
);
1007 vli_clear(v
, ndigits
);
1009 while ((cmp_result
= vli_cmp(a
, b
, ndigits
)) != 0) {
1013 vli_rshift1(a
, ndigits
);
1016 carry
= vli_add(u
, u
, mod
, ndigits
);
1018 vli_rshift1(u
, ndigits
);
1020 u
[ndigits
- 1] |= 0x8000000000000000ull
;
1021 } else if (EVEN(b
)) {
1022 vli_rshift1(b
, ndigits
);
1025 carry
= vli_add(v
, v
, mod
, ndigits
);
1027 vli_rshift1(v
, ndigits
);
1029 v
[ndigits
- 1] |= 0x8000000000000000ull
;
1030 } else if (cmp_result
> 0) {
1031 vli_sub(a
, a
, b
, ndigits
);
1032 vli_rshift1(a
, ndigits
);
1034 if (vli_cmp(u
, v
, ndigits
) < 0)
1035 vli_add(u
, u
, mod
, ndigits
);
1037 vli_sub(u
, u
, v
, ndigits
);
1039 carry
= vli_add(u
, u
, mod
, ndigits
);
1041 vli_rshift1(u
, ndigits
);
1043 u
[ndigits
- 1] |= 0x8000000000000000ull
;
1045 vli_sub(b
, b
, a
, ndigits
);
1046 vli_rshift1(b
, ndigits
);
1048 if (vli_cmp(v
, u
, ndigits
) < 0)
1049 vli_add(v
, v
, mod
, ndigits
);
1051 vli_sub(v
, v
, u
, ndigits
);
1053 carry
= vli_add(v
, v
, mod
, ndigits
);
1055 vli_rshift1(v
, ndigits
);
1057 v
[ndigits
- 1] |= 0x8000000000000000ull
;
1061 vli_set(result
, u
, ndigits
);
1063 EXPORT_SYMBOL(vli_mod_inv
);
1065 /* ------ Point operations ------ */
1067 /* Returns true if p_point is the point at infinity, false otherwise. */
1068 bool ecc_point_is_zero(const struct ecc_point
*point
)
1070 return (vli_is_zero(point
->x
, point
->ndigits
) &&
1071 vli_is_zero(point
->y
, point
->ndigits
));
1073 EXPORT_SYMBOL(ecc_point_is_zero
);
1075 /* Point multiplication algorithm using Montgomery's ladder with co-Z
1076 * coordinates. From https://eprint.iacr.org/2011/338.pdf
1079 /* Double in place */
1080 static void ecc_point_double_jacobian(u64
*x1
, u64
*y1
, u64
*z1
,
1081 const struct ecc_curve
*curve
)
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
;
1089 if (vli_is_zero(z1
, ndigits
))
1093 vli_mod_square_fast(t4
, y1
, curve
);
1094 /* t5 = x1*y1^2 = A */
1095 vli_mod_mult_fast(t5
, x1
, t4
, curve
);
1097 vli_mod_square_fast(t4
, t4
, curve
);
1098 /* t2 = y1*z1 = z3 */
1099 vli_mod_mult_fast(y1
, y1
, z1
, curve
);
1101 vli_mod_square_fast(z1
, z1
, curve
);
1103 /* t1 = x1 + z1^2 */
1104 vli_mod_add(x1
, x1
, z1
, curve_prime
, ndigits
);
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
);
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
);
1119 vli_rshift1(x1
, ndigits
);
1120 x1
[ndigits
- 1] |= carry
<< 63;
1122 vli_rshift1(x1
, ndigits
);
1124 /* t1 = 3/2*(x1^2 - z1^4) = B */
1127 vli_mod_square_fast(z1
, x1
, curve
);
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
);
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
);
1139 vli_set(x1
, z1
, ndigits
);
1140 vli_set(z1
, y1
, ndigits
);
1141 vli_set(y1
, t4
, ndigits
);
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
)
1147 u64 t1
[ECC_MAX_DIGITS
];
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 */
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
)
1159 u64 z
[ECC_MAX_DIGITS
];
1160 const unsigned int ndigits
= curve
->g
.ndigits
;
1162 vli_set(x2
, x1
, ndigits
);
1163 vli_set(y2
, y1
, ndigits
);
1165 vli_clear(z
, ndigits
);
1169 vli_set(z
, p_initial_z
, ndigits
);
1171 apply_z(x1
, y1
, z
, curve
);
1173 ecc_point_double_jacobian(x1
, y1
, z
, curve
);
1175 apply_z(x2
, y2
, z
, curve
);
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
1182 static void xycz_add(u64
*x1
, u64
*y1
, u64
*x2
, u64
*y2
,
1183 const struct ecc_curve
*curve
)
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
;
1191 vli_mod_sub(t5
, x2
, x1
, curve_prime
, ndigits
);
1192 /* t5 = (x2 - x1)^2 = A */
1193 vli_mod_square_fast(t5
, t5
, curve
);
1195 vli_mod_mult_fast(x1
, x1
, t5
, curve
);
1197 vli_mod_mult_fast(x2
, x2
, t5
, curve
);
1199 vli_mod_sub(y2
, y2
, y1
, curve_prime
, ndigits
);
1200 /* t5 = (y2 - y1)^2 = D */
1201 vli_mod_square_fast(t5
, y2
, curve
);
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
);
1208 vli_mod_sub(x2
, x2
, x1
, curve_prime
, ndigits
);
1209 /* t2 = y1*(C - B) */
1210 vli_mod_mult_fast(y1
, y1
, x2
, curve
);
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
);
1216 vli_mod_sub(y2
, y2
, y1
, curve_prime
, ndigits
);
1218 vli_set(x2
, t5
, ndigits
);
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
1225 static void xycz_add_c(u64
*x1
, u64
*y1
, u64
*x2
, u64
*y2
,
1226 const struct ecc_curve
*curve
)
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
;
1236 vli_mod_sub(t5
, x2
, x1
, curve_prime
, ndigits
);
1237 /* t5 = (x2 - x1)^2 = A */
1238 vli_mod_square_fast(t5
, t5
, curve
);
1240 vli_mod_mult_fast(x1
, x1
, t5
, curve
);
1242 vli_mod_mult_fast(x2
, x2
, t5
, curve
);
1244 vli_mod_add(t5
, y2
, y1
, curve_prime
, ndigits
);
1246 vli_mod_sub(y2
, y2
, y1
, curve_prime
, ndigits
);
1249 vli_mod_sub(t6
, x2
, x1
, curve_prime
, ndigits
);
1250 /* t2 = y1 * (C - B) */
1251 vli_mod_mult_fast(y1
, y1
, t6
, curve
);
1253 vli_mod_add(t6
, x1
, x2
, curve_prime
, ndigits
);
1254 /* t3 = (y2 - y1)^2 */
1255 vli_mod_square_fast(x2
, y2
, curve
);
1257 vli_mod_sub(x2
, x2
, t6
, curve_prime
, ndigits
);
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
);
1264 vli_mod_sub(y2
, y2
, y1
, curve_prime
, ndigits
);
1266 /* t7 = (y2 + y1)^2 = F */
1267 vli_mod_square_fast(t7
, t5
, curve
);
1269 vli_mod_sub(t7
, t7
, t6
, curve_prime
, ndigits
);
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
);
1275 vli_mod_sub(y1
, t6
, y1
, curve_prime
, ndigits
);
1277 vli_set(x1
, t7
, ndigits
);
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
)
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
;
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;
1300 vli_set(rx
[1], point
->x
, ndigits
);
1301 vli_set(ry
[1], point
->y
, ndigits
);
1303 xycz_initial_double(rx
[1], ry
[1], rx
[0], ry
[0], initial_z
, curve
);
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
);
1311 nb
= !vli_test_bit(scalar
, 0);
1312 xycz_add_c(rx
[1 - nb
], ry
[1 - nb
], rx
[nb
], ry
[nb
], curve
);
1314 /* Find final 1/Z value. */
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
);
1322 /* 1 / (xP * Yb * (X1 - X0)) */
1323 vli_mod_inv(z
, z
, curve_prime
, point
->ndigits
);
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 */
1331 xycz_add(rx
[nb
], ry
[nb
], rx
[1 - nb
], ry
[1 - nb
], curve
);
1333 apply_z(rx
[0], ry
[0], z
, curve
);
1335 vli_set(result
->x
, rx
[0], ndigits
);
1336 vli_set(result
->y
, ry
[0], ndigits
);
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
)
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
;
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
);
1359 /* Computes R = u1P + u2Q mod p using Shamir's trick.
1360 * Based on: Kenneth MacKay's micro-ecc (2014).
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
)
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
;
1379 ecc_point_add(&sum
, p
, q
, curve
);
1385 num_bits
= max(vli_num_bits(u1
, ndigits
), vli_num_bits(u2
, ndigits
));
1387 idx
= (!!vli_test_bit(u1
, i
)) | ((!!vli_test_bit(u2
, i
)) << 1);
1388 point
= points
[idx
];
1390 vli_set(rx
, point
->x
, ndigits
);
1391 vli_set(ry
, point
->y
, ndigits
);
1392 vli_clear(z
+ 1, ndigits
- 1);
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
];
1400 u64 tx
[ECC_MAX_DIGITS
];
1401 u64 ty
[ECC_MAX_DIGITS
];
1402 u64 tz
[ECC_MAX_DIGITS
];
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
);
1412 vli_mod_inv(z
, z
, curve
->p
, ndigits
);
1413 apply_z(rx
, ry
, z
, curve
);
1415 EXPORT_SYMBOL(ecc_point_mult_shamir
);
1417 static int __ecc_is_key_valid(const struct ecc_curve
*curve
,
1418 const u64
*private_key
, unsigned int ndigits
)
1420 u64 one
[ECC_MAX_DIGITS
] = { 1, };
1421 u64 res
[ECC_MAX_DIGITS
];
1426 if (curve
->g
.ndigits
!= ndigits
)
1429 /* Make sure the private key is in the range [2, n-3]. */
1430 if (vli_cmp(one
, private_key
, ndigits
) != -1)
1432 vli_sub(res
, curve
->n
, one
, ndigits
);
1433 vli_sub(res
, res
, one
, ndigits
);
1434 if (vli_cmp(res
, private_key
, ndigits
) != 1)
1440 int ecc_is_key_valid(unsigned int curve_id
, unsigned int ndigits
,
1441 const u64
*private_key
, unsigned int private_key_len
)
1444 const struct ecc_curve
*curve
= ecc_get_curve(curve_id
);
1446 nbytes
= ndigits
<< ECC_DIGITS_TO_BYTES_SHIFT
;
1448 if (private_key_len
!= nbytes
)
1451 return __ecc_is_key_valid(curve
, private_key
, ndigits
);
1453 EXPORT_SYMBOL(ecc_is_key_valid
);
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.
1459 * d = (c mod(n–1)) + 1 where c is a string of random bits, 64 bits longer
1461 * 0 <= c mod(n-1) <= n-2 and implies that
1464 * This method generates a private key uniformly distributed in the range
1467 int ecc_gen_privkey(unsigned int curve_id
, unsigned int ndigits
, u64
*privkey
)
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
);
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
))
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.
1484 * The maximum security strength identified by NIST SP800-57pt1r4 for
1485 * ECC is 256 (N >= 512).
1487 * This condition is met by the default RNG because it selects a favored
1488 * DRBG with a security strength of 256.
1490 if (crypto_get_default_rng())
1493 err
= crypto_rng_get_bytes(crypto_default_rng
, (u8
*)priv
, nbytes
);
1494 crypto_put_default_rng();
1498 /* Make sure the private key is in the valid range. */
1499 if (__ecc_is_key_valid(curve
, priv
, ndigits
))
1502 ecc_swap_digits(priv
, privkey
, ndigits
);
1506 EXPORT_SYMBOL(ecc_gen_privkey
);
1508 int ecc_make_pub_key(unsigned int curve_id
, unsigned int ndigits
,
1509 const u64
*private_key
, u64
*public_key
)
1512 struct ecc_point
*pk
;
1513 u64 priv
[ECC_MAX_DIGITS
];
1514 const struct ecc_curve
*curve
= ecc_get_curve(curve_id
);
1516 if (!private_key
|| !curve
|| ndigits
> ARRAY_SIZE(priv
)) {
1521 ecc_swap_digits(private_key
, priv
, ndigits
);
1523 pk
= ecc_alloc_point(ndigits
);
1529 ecc_point_mult(pk
, &curve
->g
, priv
, NULL
, curve
, ndigits
);
1531 /* SP800-56A rev 3 5.6.2.1.3 key check */
1532 if (ecc_is_pubkey_valid_full(curve
, pk
)) {
1534 goto err_free_point
;
1537 ecc_swap_digits(pk
->x
, public_key
, ndigits
);
1538 ecc_swap_digits(pk
->y
, &public_key
[ndigits
], ndigits
);
1545 EXPORT_SYMBOL(ecc_make_pub_key
);
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
)
1551 u64 yy
[ECC_MAX_DIGITS
], xxx
[ECC_MAX_DIGITS
], w
[ECC_MAX_DIGITS
];
1553 if (WARN_ON(pk
->ndigits
!= curve
->g
.ndigits
))
1556 /* Check 1: Verify key is not the zero point. */
1557 if (ecc_point_is_zero(pk
))
1560 /* Check 2: Verify key is in the range [1, p-1]. */
1561 if (vli_cmp(curve
->p
, pk
->x
, pk
->ndigits
) != 1)
1563 if (vli_cmp(curve
->p
, pk
->y
, pk
->ndigits
) != 1)
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 */
1578 EXPORT_SYMBOL(ecc_is_pubkey_valid_partial
);
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
)
1584 struct ecc_point
*nQ
;
1586 /* Checks 1 through 3 */
1587 int ret
= ecc_is_pubkey_valid_partial(curve
, pk
);
1592 /* Check 4: Verify that nQ is the zero point. */
1593 nQ
= ecc_alloc_point(pk
->ndigits
);
1597 ecc_point_mult(nQ
, pk
, curve
->n
, NULL
, curve
, pk
->ndigits
);
1598 if (!ecc_point_is_zero(nQ
))
1605 EXPORT_SYMBOL(ecc_is_pubkey_valid_full
);
1607 int crypto_ecdh_shared_secret(unsigned int curve_id
, unsigned int ndigits
,
1608 const u64
*private_key
, const u64
*public_key
,
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
);
1618 if (!private_key
|| !public_key
|| !curve
||
1619 ndigits
> ARRAY_SIZE(priv
) || ndigits
> ARRAY_SIZE(rand_z
)) {
1624 nbytes
= ndigits
<< ECC_DIGITS_TO_BYTES_SHIFT
;
1626 get_random_bytes(rand_z
, nbytes
);
1628 pk
= ecc_alloc_point(ndigits
);
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
);
1638 goto err_alloc_product
;
1640 ecc_swap_digits(private_key
, priv
, ndigits
);
1642 product
= ecc_alloc_point(ndigits
);
1645 goto err_alloc_product
;
1648 ecc_point_mult(product
, pk
, priv
, rand_z
, curve
, ndigits
);
1650 if (ecc_point_is_zero(product
)) {
1655 ecc_swap_digits(product
->x
, secret
, ndigits
);
1658 memzero_explicit(priv
, sizeof(priv
));
1659 memzero_explicit(rand_z
, sizeof(rand_z
));
1660 ecc_free_point(product
);
1666 EXPORT_SYMBOL(crypto_ecdh_shared_secret
);
1668 MODULE_LICENSE("Dual BSD/GPL");