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 <asm/unaligned.h>
36 #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 static 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
);
110 static void ecc_free_point(struct ecc_point
*p
)
115 kfree_sensitive(p
->x
);
116 kfree_sensitive(p
->y
);
120 static void vli_clear(u64
*vli
, unsigned int ndigits
)
124 for (i
= 0; i
< ndigits
; i
++)
128 /* Returns true if vli == 0, false otherwise. */
129 bool vli_is_zero(const u64
*vli
, unsigned int ndigits
)
133 for (i
= 0; i
< ndigits
; i
++) {
140 EXPORT_SYMBOL(vli_is_zero
);
142 /* Returns nonzero if bit of vli is set. */
143 static u64
vli_test_bit(const u64
*vli
, unsigned int bit
)
145 return (vli
[bit
/ 64] & ((u64
)1 << (bit
% 64)));
148 static bool vli_is_negative(const u64
*vli
, unsigned int ndigits
)
150 return vli_test_bit(vli
, ndigits
* 64 - 1);
153 /* Counts the number of 64-bit "digits" in vli. */
154 static unsigned int vli_num_digits(const u64
*vli
, unsigned int ndigits
)
158 /* Search from the end until we find a non-zero digit.
159 * We do it in reverse because we expect that most digits will
162 for (i
= ndigits
- 1; i
>= 0 && vli
[i
] == 0; i
--);
167 /* Counts the number of bits required for vli. */
168 static unsigned int vli_num_bits(const u64
*vli
, unsigned int ndigits
)
170 unsigned int i
, num_digits
;
173 num_digits
= vli_num_digits(vli
, ndigits
);
177 digit
= vli
[num_digits
- 1];
178 for (i
= 0; digit
; i
++)
181 return ((num_digits
- 1) * 64 + i
);
184 /* Set dest from unaligned bit string src. */
185 void vli_from_be64(u64
*dest
, const void *src
, unsigned int ndigits
)
188 const u64
*from
= src
;
190 for (i
= 0; i
< ndigits
; i
++)
191 dest
[i
] = get_unaligned_be64(&from
[ndigits
- 1 - i
]);
193 EXPORT_SYMBOL(vli_from_be64
);
195 void vli_from_le64(u64
*dest
, const void *src
, unsigned int ndigits
)
198 const u64
*from
= src
;
200 for (i
= 0; i
< ndigits
; i
++)
201 dest
[i
] = get_unaligned_le64(&from
[i
]);
203 EXPORT_SYMBOL(vli_from_le64
);
205 /* Sets dest = src. */
206 static void vli_set(u64
*dest
, const u64
*src
, unsigned int ndigits
)
210 for (i
= 0; i
< ndigits
; i
++)
214 /* Returns sign of left - right. */
215 int vli_cmp(const u64
*left
, const u64
*right
, unsigned int ndigits
)
219 for (i
= ndigits
- 1; i
>= 0; i
--) {
220 if (left
[i
] > right
[i
])
222 else if (left
[i
] < right
[i
])
228 EXPORT_SYMBOL(vli_cmp
);
230 /* Computes result = in << c, returning carry. Can modify in place
231 * (if result == in). 0 < shift < 64.
233 static u64
vli_lshift(u64
*result
, const u64
*in
, unsigned int shift
,
234 unsigned int ndigits
)
239 for (i
= 0; i
< ndigits
; i
++) {
242 result
[i
] = (temp
<< shift
) | carry
;
243 carry
= temp
>> (64 - shift
);
249 /* Computes vli = vli >> 1. */
250 static void vli_rshift1(u64
*vli
, unsigned int ndigits
)
257 while (vli
-- > end
) {
259 *vli
= (temp
>> 1) | carry
;
264 /* Computes result = left + right, returning carry. Can modify in place. */
265 static u64
vli_add(u64
*result
, const u64
*left
, const u64
*right
,
266 unsigned int ndigits
)
271 for (i
= 0; i
< ndigits
; i
++) {
274 sum
= left
[i
] + right
[i
] + carry
;
276 carry
= (sum
< left
[i
]);
284 /* Computes result = left + right, returning carry. Can modify in place. */
285 static u64
vli_uadd(u64
*result
, const u64
*left
, u64 right
,
286 unsigned int ndigits
)
291 for (i
= 0; i
< ndigits
; i
++) {
294 sum
= left
[i
] + carry
;
296 carry
= (sum
< left
[i
]);
306 /* Computes result = left - right, returning borrow. Can modify in place. */
307 u64
vli_sub(u64
*result
, const u64
*left
, const u64
*right
,
308 unsigned int ndigits
)
313 for (i
= 0; i
< ndigits
; i
++) {
316 diff
= left
[i
] - right
[i
] - borrow
;
318 borrow
= (diff
> left
[i
]);
325 EXPORT_SYMBOL(vli_sub
);
327 /* Computes result = left - right, returning borrow. Can modify in place. */
328 static u64
vli_usub(u64
*result
, const u64
*left
, u64 right
,
329 unsigned int ndigits
)
334 for (i
= 0; i
< ndigits
; i
++) {
337 diff
= left
[i
] - borrow
;
339 borrow
= (diff
> left
[i
]);
347 static uint128_t
mul_64_64(u64 left
, u64 right
)
350 #if defined(CONFIG_ARCH_SUPPORTS_INT128)
351 unsigned __int128 m
= (unsigned __int128
)left
* right
;
354 result
.m_high
= m
>> 64;
356 u64 a0
= left
& 0xffffffffull
;
358 u64 b0
= right
& 0xffffffffull
;
359 u64 b1
= right
>> 32;
370 m3
+= 0x100000000ull
;
372 result
.m_low
= (m0
& 0xffffffffull
) | (m2
<< 32);
373 result
.m_high
= m3
+ (m2
>> 32);
378 static uint128_t
add_128_128(uint128_t a
, uint128_t b
)
382 result
.m_low
= a
.m_low
+ b
.m_low
;
383 result
.m_high
= a
.m_high
+ b
.m_high
+ (result
.m_low
< a
.m_low
);
388 static void vli_mult(u64
*result
, const u64
*left
, const u64
*right
,
389 unsigned int ndigits
)
391 uint128_t r01
= { 0, 0 };
395 /* Compute each digit of result in sequence, maintaining the
398 for (k
= 0; k
< ndigits
* 2 - 1; k
++) {
404 min
= (k
+ 1) - ndigits
;
406 for (i
= min
; i
<= k
&& i
< ndigits
; i
++) {
409 product
= mul_64_64(left
[i
], right
[k
- i
]);
411 r01
= add_128_128(r01
, product
);
412 r2
+= (r01
.m_high
< product
.m_high
);
415 result
[k
] = r01
.m_low
;
416 r01
.m_low
= r01
.m_high
;
421 result
[ndigits
* 2 - 1] = r01
.m_low
;
424 /* Compute product = left * right, for a small right value. */
425 static void vli_umult(u64
*result
, const u64
*left
, u32 right
,
426 unsigned int ndigits
)
428 uint128_t r01
= { 0 };
431 for (k
= 0; k
< ndigits
; k
++) {
434 product
= mul_64_64(left
[k
], right
);
435 r01
= add_128_128(r01
, product
);
437 result
[k
] = r01
.m_low
;
438 r01
.m_low
= r01
.m_high
;
441 result
[k
] = r01
.m_low
;
442 for (++k
; k
< ndigits
* 2; k
++)
446 static void vli_square(u64
*result
, const u64
*left
, unsigned int ndigits
)
448 uint128_t r01
= { 0, 0 };
452 for (k
= 0; k
< ndigits
* 2 - 1; k
++) {
458 min
= (k
+ 1) - ndigits
;
460 for (i
= min
; i
<= k
&& i
<= k
- i
; i
++) {
463 product
= mul_64_64(left
[i
], left
[k
- i
]);
466 r2
+= product
.m_high
>> 63;
467 product
.m_high
= (product
.m_high
<< 1) |
468 (product
.m_low
>> 63);
472 r01
= add_128_128(r01
, product
);
473 r2
+= (r01
.m_high
< product
.m_high
);
476 result
[k
] = r01
.m_low
;
477 r01
.m_low
= r01
.m_high
;
482 result
[ndigits
* 2 - 1] = r01
.m_low
;
485 /* Computes result = (left + right) % mod.
486 * Assumes that left < mod and right < mod, result != mod.
488 static void vli_mod_add(u64
*result
, const u64
*left
, const u64
*right
,
489 const u64
*mod
, unsigned int ndigits
)
493 carry
= vli_add(result
, left
, right
, ndigits
);
495 /* result > mod (result = mod + remainder), so subtract mod to
498 if (carry
|| vli_cmp(result
, mod
, ndigits
) >= 0)
499 vli_sub(result
, result
, mod
, ndigits
);
502 /* Computes result = (left - right) % mod.
503 * Assumes that left < mod and right < mod, result != mod.
505 static void vli_mod_sub(u64
*result
, const u64
*left
, const u64
*right
,
506 const u64
*mod
, unsigned int ndigits
)
508 u64 borrow
= vli_sub(result
, left
, right
, ndigits
);
510 /* In this case, p_result == -diff == (max int) - diff.
511 * Since -x % d == d - x, we can get the correct result from
512 * result + mod (with overflow).
515 vli_add(result
, result
, mod
, ndigits
);
519 * Computes result = product % mod
520 * for special form moduli: p = 2^k-c, for small c (note the minus sign)
523 * R. Crandall, C. Pomerance. Prime Numbers: A Computational Perspective.
524 * 9 Fast Algorithms for Large-Integer Arithmetic. 9.2.3 Moduli of special form
525 * Algorithm 9.2.13 (Fast mod operation for special-form moduli).
527 static void vli_mmod_special(u64
*result
, const u64
*product
,
528 const u64
*mod
, unsigned int ndigits
)
531 u64 t
[ECC_MAX_DIGITS
* 2];
532 u64 r
[ECC_MAX_DIGITS
* 2];
534 vli_set(r
, product
, ndigits
* 2);
535 while (!vli_is_zero(r
+ ndigits
, ndigits
)) {
536 vli_umult(t
, r
+ ndigits
, c
, ndigits
);
537 vli_clear(r
+ ndigits
, ndigits
);
538 vli_add(r
, r
, t
, ndigits
* 2);
540 vli_set(t
, mod
, ndigits
);
541 vli_clear(t
+ ndigits
, ndigits
);
542 while (vli_cmp(r
, t
, ndigits
* 2) >= 0)
543 vli_sub(r
, r
, t
, ndigits
* 2);
544 vli_set(result
, r
, ndigits
);
548 * Computes result = product % mod
549 * for special form moduli: p = 2^{k-1}+c, for small c (note the plus sign)
550 * where k-1 does not fit into qword boundary by -1 bit (such as 255).
552 * References (loosely based on):
553 * A. Menezes, P. van Oorschot, S. Vanstone. Handbook of Applied Cryptography.
554 * 14.3.4 Reduction methods for moduli of special form. Algorithm 14.47.
555 * URL: http://cacr.uwaterloo.ca/hac/about/chap14.pdf
557 * H. Cohen, G. Frey, R. Avanzi, C. Doche, T. Lange, K. Nguyen, F. Vercauteren.
558 * Handbook of Elliptic and Hyperelliptic Curve Cryptography.
559 * Algorithm 10.25 Fast reduction for special form moduli
561 static void vli_mmod_special2(u64
*result
, const u64
*product
,
562 const u64
*mod
, unsigned int ndigits
)
565 u64 q
[ECC_MAX_DIGITS
];
566 u64 r
[ECC_MAX_DIGITS
* 2];
567 u64 m
[ECC_MAX_DIGITS
* 2]; /* expanded mod */
568 int carry
; /* last bit that doesn't fit into q */
571 vli_set(m
, mod
, ndigits
);
572 vli_clear(m
+ ndigits
, ndigits
);
574 vli_set(r
, product
, ndigits
);
575 /* q and carry are top bits */
576 vli_set(q
, product
+ ndigits
, ndigits
);
577 vli_clear(r
+ ndigits
, ndigits
);
578 carry
= vli_is_negative(r
, ndigits
);
580 r
[ndigits
- 1] &= (1ull << 63) - 1;
581 for (i
= 1; carry
|| !vli_is_zero(q
, ndigits
); i
++) {
582 u64 qc
[ECC_MAX_DIGITS
* 2];
584 vli_umult(qc
, q
, c2
, ndigits
);
586 vli_uadd(qc
, qc
, mod
[0], ndigits
* 2);
587 vli_set(q
, qc
+ ndigits
, ndigits
);
588 vli_clear(qc
+ ndigits
, ndigits
);
589 carry
= vli_is_negative(qc
, ndigits
);
591 qc
[ndigits
- 1] &= (1ull << 63) - 1;
593 vli_sub(r
, r
, qc
, ndigits
* 2);
595 vli_add(r
, r
, qc
, ndigits
* 2);
597 while (vli_is_negative(r
, ndigits
* 2))
598 vli_add(r
, r
, m
, ndigits
* 2);
599 while (vli_cmp(r
, m
, ndigits
* 2) >= 0)
600 vli_sub(r
, r
, m
, ndigits
* 2);
602 vli_set(result
, r
, ndigits
);
606 * Computes result = product % mod, where product is 2N words long.
607 * Reference: Ken MacKay's micro-ecc.
608 * Currently only designed to work for curve_p or curve_n.
610 static void vli_mmod_slow(u64
*result
, u64
*product
, const u64
*mod
,
611 unsigned int ndigits
)
613 u64 mod_m
[2 * ECC_MAX_DIGITS
];
614 u64 tmp
[2 * ECC_MAX_DIGITS
];
615 u64
*v
[2] = { tmp
, product
};
618 /* Shift mod so its highest set bit is at the maximum position. */
619 int shift
= (ndigits
* 2 * 64) - vli_num_bits(mod
, ndigits
);
620 int word_shift
= shift
/ 64;
621 int bit_shift
= shift
% 64;
623 vli_clear(mod_m
, word_shift
);
625 for (i
= 0; i
< ndigits
; ++i
) {
626 mod_m
[word_shift
+ i
] = (mod
[i
] << bit_shift
) | carry
;
627 carry
= mod
[i
] >> (64 - bit_shift
);
630 vli_set(mod_m
+ word_shift
, mod
, ndigits
);
632 for (i
= 1; shift
>= 0; --shift
) {
636 for (j
= 0; j
< ndigits
* 2; ++j
) {
637 u64 diff
= v
[i
][j
] - mod_m
[j
] - borrow
;
640 borrow
= (diff
> v
[i
][j
]);
643 i
= !(i
^ borrow
); /* Swap the index if there was no borrow */
644 vli_rshift1(mod_m
, ndigits
);
645 mod_m
[ndigits
- 1] |= mod_m
[ndigits
] << (64 - 1);
646 vli_rshift1(mod_m
+ ndigits
, ndigits
);
648 vli_set(result
, v
[i
], ndigits
);
651 /* Computes result = product % mod using Barrett's reduction with precomputed
652 * value mu appended to the mod after ndigits, mu = (2^{2w} / mod) and have
653 * length ndigits + 1, where mu * (2^w - 1) should not overflow ndigits
657 * R. Brent, P. Zimmermann. Modern Computer Arithmetic. 2010.
658 * 2.4.1 Barrett's algorithm. Algorithm 2.5.
660 static void vli_mmod_barrett(u64
*result
, u64
*product
, const u64
*mod
,
661 unsigned int ndigits
)
663 u64 q
[ECC_MAX_DIGITS
* 2];
664 u64 r
[ECC_MAX_DIGITS
* 2];
665 const u64
*mu
= mod
+ ndigits
;
667 vli_mult(q
, product
+ ndigits
, mu
, ndigits
);
669 vli_add(q
+ ndigits
, q
+ ndigits
, product
+ ndigits
, ndigits
);
670 vli_mult(r
, mod
, q
+ ndigits
, ndigits
);
671 vli_sub(r
, product
, r
, ndigits
* 2);
672 while (!vli_is_zero(r
+ ndigits
, ndigits
) ||
673 vli_cmp(r
, mod
, ndigits
) != -1) {
676 carry
= vli_sub(r
, r
, mod
, ndigits
);
677 vli_usub(r
+ ndigits
, r
+ ndigits
, carry
, ndigits
);
679 vli_set(result
, r
, ndigits
);
682 /* Computes p_result = p_product % curve_p.
683 * See algorithm 5 and 6 from
684 * http://www.isys.uni-klu.ac.at/PDF/2001-0126-MT.pdf
686 static void vli_mmod_fast_192(u64
*result
, const u64
*product
,
687 const u64
*curve_prime
, u64
*tmp
)
689 const unsigned int ndigits
= 3;
692 vli_set(result
, product
, ndigits
);
694 vli_set(tmp
, &product
[3], ndigits
);
695 carry
= vli_add(result
, result
, tmp
, ndigits
);
700 carry
+= vli_add(result
, result
, tmp
, ndigits
);
702 tmp
[0] = tmp
[1] = product
[5];
704 carry
+= vli_add(result
, result
, tmp
, ndigits
);
706 while (carry
|| vli_cmp(curve_prime
, result
, ndigits
) != 1)
707 carry
-= vli_sub(result
, result
, curve_prime
, ndigits
);
710 /* Computes result = product % curve_prime
711 * from http://www.nsa.gov/ia/_files/nist-routines.pdf
713 static void vli_mmod_fast_256(u64
*result
, const u64
*product
,
714 const u64
*curve_prime
, u64
*tmp
)
717 const unsigned int ndigits
= 4;
720 vli_set(result
, product
, ndigits
);
724 tmp
[1] = product
[5] & 0xffffffff00000000ull
;
727 carry
= vli_lshift(tmp
, tmp
, 1, ndigits
);
728 carry
+= vli_add(result
, result
, tmp
, ndigits
);
731 tmp
[1] = product
[6] << 32;
732 tmp
[2] = (product
[6] >> 32) | (product
[7] << 32);
733 tmp
[3] = product
[7] >> 32;
734 carry
+= vli_lshift(tmp
, tmp
, 1, ndigits
);
735 carry
+= vli_add(result
, result
, tmp
, ndigits
);
739 tmp
[1] = product
[5] & 0xffffffff;
742 carry
+= vli_add(result
, result
, tmp
, ndigits
);
745 tmp
[0] = (product
[4] >> 32) | (product
[5] << 32);
746 tmp
[1] = (product
[5] >> 32) | (product
[6] & 0xffffffff00000000ull
);
748 tmp
[3] = (product
[6] >> 32) | (product
[4] << 32);
749 carry
+= vli_add(result
, result
, tmp
, ndigits
);
752 tmp
[0] = (product
[5] >> 32) | (product
[6] << 32);
753 tmp
[1] = (product
[6] >> 32);
755 tmp
[3] = (product
[4] & 0xffffffff) | (product
[5] << 32);
756 carry
-= vli_sub(result
, result
, tmp
, ndigits
);
762 tmp
[3] = (product
[4] >> 32) | (product
[5] & 0xffffffff00000000ull
);
763 carry
-= vli_sub(result
, result
, tmp
, ndigits
);
766 tmp
[0] = (product
[6] >> 32) | (product
[7] << 32);
767 tmp
[1] = (product
[7] >> 32) | (product
[4] << 32);
768 tmp
[2] = (product
[4] >> 32) | (product
[5] << 32);
769 tmp
[3] = (product
[6] << 32);
770 carry
-= vli_sub(result
, result
, tmp
, ndigits
);
774 tmp
[1] = product
[4] & 0xffffffff00000000ull
;
776 tmp
[3] = product
[6] & 0xffffffff00000000ull
;
777 carry
-= vli_sub(result
, result
, tmp
, ndigits
);
781 carry
+= vli_add(result
, result
, curve_prime
, ndigits
);
784 while (carry
|| vli_cmp(curve_prime
, result
, ndigits
) != 1)
785 carry
-= vli_sub(result
, result
, curve_prime
, ndigits
);
789 #define SL32OR32(x32, y32) (((u64)x32 << 32) | y32)
790 #define AND64H(x64) (x64 & 0xffFFffFF00000000ull)
791 #define AND64L(x64) (x64 & 0x00000000ffFFffFFull)
793 /* Computes result = product % curve_prime
794 * from "Mathematical routines for the NIST prime elliptic curves"
796 static void vli_mmod_fast_384(u64
*result
, const u64
*product
,
797 const u64
*curve_prime
, u64
*tmp
)
800 const unsigned int ndigits
= 6;
803 vli_set(result
, product
, ndigits
);
806 tmp
[0] = 0; // 0 || 0
807 tmp
[1] = 0; // 0 || 0
808 tmp
[2] = SL32OR32(product
[11], (product
[10]>>32)); //a22||a21
809 tmp
[3] = product
[11]>>32; // 0 ||a23
810 tmp
[4] = 0; // 0 || 0
811 tmp
[5] = 0; // 0 || 0
812 carry
= vli_lshift(tmp
, tmp
, 1, ndigits
);
813 carry
+= vli_add(result
, result
, tmp
, ndigits
);
816 tmp
[0] = product
[6]; //a13||a12
817 tmp
[1] = product
[7]; //a15||a14
818 tmp
[2] = product
[8]; //a17||a16
819 tmp
[3] = product
[9]; //a19||a18
820 tmp
[4] = product
[10]; //a21||a20
821 tmp
[5] = product
[11]; //a23||a22
822 carry
+= vli_add(result
, result
, tmp
, ndigits
);
825 tmp
[0] = SL32OR32(product
[11], (product
[10]>>32)); //a22||a21
826 tmp
[1] = SL32OR32(product
[6], (product
[11]>>32)); //a12||a23
827 tmp
[2] = SL32OR32(product
[7], (product
[6])>>32); //a14||a13
828 tmp
[3] = SL32OR32(product
[8], (product
[7]>>32)); //a16||a15
829 tmp
[4] = SL32OR32(product
[9], (product
[8]>>32)); //a18||a17
830 tmp
[5] = SL32OR32(product
[10], (product
[9]>>32)); //a20||a19
831 carry
+= vli_add(result
, result
, tmp
, ndigits
);
834 tmp
[0] = AND64H(product
[11]); //a23|| 0
835 tmp
[1] = (product
[10]<<32); //a20|| 0
836 tmp
[2] = product
[6]; //a13||a12
837 tmp
[3] = product
[7]; //a15||a14
838 tmp
[4] = product
[8]; //a17||a16
839 tmp
[5] = product
[9]; //a19||a18
840 carry
+= vli_add(result
, result
, tmp
, ndigits
);
845 tmp
[2] = product
[10]; //a21||a20
846 tmp
[3] = product
[11]; //a23||a22
849 carry
+= vli_add(result
, result
, tmp
, ndigits
);
852 tmp
[0] = AND64L(product
[10]); // 0 ||a20
853 tmp
[1] = AND64H(product
[10]); //a21|| 0
854 tmp
[2] = product
[11]; //a23||a22
855 tmp
[3] = 0; // 0 || 0
856 tmp
[4] = 0; // 0 || 0
857 tmp
[5] = 0; // 0 || 0
858 carry
+= vli_add(result
, result
, tmp
, ndigits
);
861 tmp
[0] = SL32OR32(product
[6], (product
[11]>>32)); //a12||a23
862 tmp
[1] = SL32OR32(product
[7], (product
[6]>>32)); //a14||a13
863 tmp
[2] = SL32OR32(product
[8], (product
[7]>>32)); //a16||a15
864 tmp
[3] = SL32OR32(product
[9], (product
[8]>>32)); //a18||a17
865 tmp
[4] = SL32OR32(product
[10], (product
[9]>>32)); //a20||a19
866 tmp
[5] = SL32OR32(product
[11], (product
[10]>>32)); //a22||a21
867 carry
-= vli_sub(result
, result
, tmp
, ndigits
);
870 tmp
[0] = (product
[10]<<32); //a20|| 0
871 tmp
[1] = SL32OR32(product
[11], (product
[10]>>32)); //a22||a21
872 tmp
[2] = (product
[11]>>32); // 0 ||a23
873 tmp
[3] = 0; // 0 || 0
874 tmp
[4] = 0; // 0 || 0
875 tmp
[5] = 0; // 0 || 0
876 carry
-= vli_sub(result
, result
, tmp
, ndigits
);
879 tmp
[0] = 0; // 0 || 0
880 tmp
[1] = AND64H(product
[11]); //a23|| 0
881 tmp
[2] = product
[11]>>32; // 0 ||a23
882 tmp
[3] = 0; // 0 || 0
883 tmp
[4] = 0; // 0 || 0
884 tmp
[5] = 0; // 0 || 0
885 carry
-= vli_sub(result
, result
, tmp
, ndigits
);
889 carry
+= vli_add(result
, result
, curve_prime
, ndigits
);
892 while (carry
|| vli_cmp(curve_prime
, result
, ndigits
) != 1)
893 carry
-= vli_sub(result
, result
, curve_prime
, ndigits
);
902 /* Computes result = product % curve_prime for different curve_primes.
904 * Note that curve_primes are distinguished just by heuristic check and
905 * not by complete conformance check.
907 static bool vli_mmod_fast(u64
*result
, u64
*product
,
908 const struct ecc_curve
*curve
)
910 u64 tmp
[2 * ECC_MAX_DIGITS
];
911 const u64
*curve_prime
= curve
->p
;
912 const unsigned int ndigits
= curve
->g
.ndigits
;
914 /* All NIST curves have name prefix 'nist_' */
915 if (strncmp(curve
->name
, "nist_", 5) != 0) {
916 /* Try to handle Pseudo-Marsenne primes. */
917 if (curve_prime
[ndigits
- 1] == -1ull) {
918 vli_mmod_special(result
, product
, curve_prime
,
921 } else if (curve_prime
[ndigits
- 1] == 1ull << 63 &&
922 curve_prime
[ndigits
- 2] == 0) {
923 vli_mmod_special2(result
, product
, curve_prime
,
927 vli_mmod_barrett(result
, product
, curve_prime
, ndigits
);
933 vli_mmod_fast_192(result
, product
, curve_prime
, tmp
);
936 vli_mmod_fast_256(result
, product
, curve_prime
, tmp
);
939 vli_mmod_fast_384(result
, product
, curve_prime
, tmp
);
942 pr_err_ratelimited("ecc: unsupported digits size!\n");
949 /* Computes result = (left * right) % mod.
950 * Assumes that mod is big enough curve order.
952 void vli_mod_mult_slow(u64
*result
, const u64
*left
, const u64
*right
,
953 const u64
*mod
, unsigned int ndigits
)
955 u64 product
[ECC_MAX_DIGITS
* 2];
957 vli_mult(product
, left
, right
, ndigits
);
958 vli_mmod_slow(result
, product
, mod
, ndigits
);
960 EXPORT_SYMBOL(vli_mod_mult_slow
);
962 /* Computes result = (left * right) % curve_prime. */
963 static void vli_mod_mult_fast(u64
*result
, const u64
*left
, const u64
*right
,
964 const struct ecc_curve
*curve
)
966 u64 product
[2 * ECC_MAX_DIGITS
];
968 vli_mult(product
, left
, right
, curve
->g
.ndigits
);
969 vli_mmod_fast(result
, product
, curve
);
972 /* Computes result = left^2 % curve_prime. */
973 static void vli_mod_square_fast(u64
*result
, const u64
*left
,
974 const struct ecc_curve
*curve
)
976 u64 product
[2 * ECC_MAX_DIGITS
];
978 vli_square(product
, left
, curve
->g
.ndigits
);
979 vli_mmod_fast(result
, product
, curve
);
982 #define EVEN(vli) (!(vli[0] & 1))
983 /* Computes result = (1 / p_input) % mod. All VLIs are the same size.
984 * See "From Euclid's GCD to Montgomery Multiplication to the Great Divide"
985 * https://labs.oracle.com/techrep/2001/smli_tr-2001-95.pdf
987 void vli_mod_inv(u64
*result
, const u64
*input
, const u64
*mod
,
988 unsigned int ndigits
)
990 u64 a
[ECC_MAX_DIGITS
], b
[ECC_MAX_DIGITS
];
991 u64 u
[ECC_MAX_DIGITS
], v
[ECC_MAX_DIGITS
];
995 if (vli_is_zero(input
, ndigits
)) {
996 vli_clear(result
, ndigits
);
1000 vli_set(a
, input
, ndigits
);
1001 vli_set(b
, mod
, ndigits
);
1002 vli_clear(u
, ndigits
);
1004 vli_clear(v
, ndigits
);
1006 while ((cmp_result
= vli_cmp(a
, b
, ndigits
)) != 0) {
1010 vli_rshift1(a
, ndigits
);
1013 carry
= vli_add(u
, u
, mod
, ndigits
);
1015 vli_rshift1(u
, ndigits
);
1017 u
[ndigits
- 1] |= 0x8000000000000000ull
;
1018 } else if (EVEN(b
)) {
1019 vli_rshift1(b
, ndigits
);
1022 carry
= vli_add(v
, v
, mod
, ndigits
);
1024 vli_rshift1(v
, ndigits
);
1026 v
[ndigits
- 1] |= 0x8000000000000000ull
;
1027 } else if (cmp_result
> 0) {
1028 vli_sub(a
, a
, b
, ndigits
);
1029 vli_rshift1(a
, ndigits
);
1031 if (vli_cmp(u
, v
, ndigits
) < 0)
1032 vli_add(u
, u
, mod
, ndigits
);
1034 vli_sub(u
, u
, v
, ndigits
);
1036 carry
= vli_add(u
, u
, mod
, ndigits
);
1038 vli_rshift1(u
, ndigits
);
1040 u
[ndigits
- 1] |= 0x8000000000000000ull
;
1042 vli_sub(b
, b
, a
, ndigits
);
1043 vli_rshift1(b
, ndigits
);
1045 if (vli_cmp(v
, u
, ndigits
) < 0)
1046 vli_add(v
, v
, mod
, ndigits
);
1048 vli_sub(v
, v
, u
, ndigits
);
1050 carry
= vli_add(v
, v
, mod
, ndigits
);
1052 vli_rshift1(v
, ndigits
);
1054 v
[ndigits
- 1] |= 0x8000000000000000ull
;
1058 vli_set(result
, u
, ndigits
);
1060 EXPORT_SYMBOL(vli_mod_inv
);
1062 /* ------ Point operations ------ */
1064 /* Returns true if p_point is the point at infinity, false otherwise. */
1065 static bool ecc_point_is_zero(const struct ecc_point
*point
)
1067 return (vli_is_zero(point
->x
, point
->ndigits
) &&
1068 vli_is_zero(point
->y
, point
->ndigits
));
1071 /* Point multiplication algorithm using Montgomery's ladder with co-Z
1072 * coordinates. From https://eprint.iacr.org/2011/338.pdf
1075 /* Double in place */
1076 static void ecc_point_double_jacobian(u64
*x1
, u64
*y1
, u64
*z1
,
1077 const struct ecc_curve
*curve
)
1079 /* t1 = x, t2 = y, t3 = z */
1080 u64 t4
[ECC_MAX_DIGITS
];
1081 u64 t5
[ECC_MAX_DIGITS
];
1082 const u64
*curve_prime
= curve
->p
;
1083 const unsigned int ndigits
= curve
->g
.ndigits
;
1085 if (vli_is_zero(z1
, ndigits
))
1089 vli_mod_square_fast(t4
, y1
, curve
);
1090 /* t5 = x1*y1^2 = A */
1091 vli_mod_mult_fast(t5
, x1
, t4
, curve
);
1093 vli_mod_square_fast(t4
, t4
, curve
);
1094 /* t2 = y1*z1 = z3 */
1095 vli_mod_mult_fast(y1
, y1
, z1
, curve
);
1097 vli_mod_square_fast(z1
, z1
, curve
);
1099 /* t1 = x1 + z1^2 */
1100 vli_mod_add(x1
, x1
, z1
, curve_prime
, ndigits
);
1102 vli_mod_add(z1
, z1
, z1
, curve_prime
, ndigits
);
1103 /* t3 = x1 - z1^2 */
1104 vli_mod_sub(z1
, x1
, z1
, curve_prime
, ndigits
);
1105 /* t1 = x1^2 - z1^4 */
1106 vli_mod_mult_fast(x1
, x1
, z1
, curve
);
1108 /* t3 = 2*(x1^2 - z1^4) */
1109 vli_mod_add(z1
, x1
, x1
, curve_prime
, ndigits
);
1110 /* t1 = 3*(x1^2 - z1^4) */
1111 vli_mod_add(x1
, x1
, z1
, curve_prime
, ndigits
);
1112 if (vli_test_bit(x1
, 0)) {
1113 u64 carry
= vli_add(x1
, x1
, curve_prime
, ndigits
);
1115 vli_rshift1(x1
, ndigits
);
1116 x1
[ndigits
- 1] |= carry
<< 63;
1118 vli_rshift1(x1
, ndigits
);
1120 /* t1 = 3/2*(x1^2 - z1^4) = B */
1123 vli_mod_square_fast(z1
, x1
, curve
);
1125 vli_mod_sub(z1
, z1
, t5
, curve_prime
, ndigits
);
1126 /* t3 = B^2 - 2A = x3 */
1127 vli_mod_sub(z1
, z1
, t5
, curve_prime
, ndigits
);
1129 vli_mod_sub(t5
, t5
, z1
, curve_prime
, ndigits
);
1130 /* t1 = B * (A - x3) */
1131 vli_mod_mult_fast(x1
, x1
, t5
, curve
);
1132 /* t4 = B * (A - x3) - y1^4 = y3 */
1133 vli_mod_sub(t4
, x1
, t4
, curve_prime
, ndigits
);
1135 vli_set(x1
, z1
, ndigits
);
1136 vli_set(z1
, y1
, ndigits
);
1137 vli_set(y1
, t4
, ndigits
);
1140 /* Modify (x1, y1) => (x1 * z^2, y1 * z^3) */
1141 static void apply_z(u64
*x1
, u64
*y1
, u64
*z
, const struct ecc_curve
*curve
)
1143 u64 t1
[ECC_MAX_DIGITS
];
1145 vli_mod_square_fast(t1
, z
, curve
); /* z^2 */
1146 vli_mod_mult_fast(x1
, x1
, t1
, curve
); /* x1 * z^2 */
1147 vli_mod_mult_fast(t1
, t1
, z
, curve
); /* z^3 */
1148 vli_mod_mult_fast(y1
, y1
, t1
, curve
); /* y1 * z^3 */
1151 /* P = (x1, y1) => 2P, (x2, y2) => P' */
1152 static void xycz_initial_double(u64
*x1
, u64
*y1
, u64
*x2
, u64
*y2
,
1153 u64
*p_initial_z
, const struct ecc_curve
*curve
)
1155 u64 z
[ECC_MAX_DIGITS
];
1156 const unsigned int ndigits
= curve
->g
.ndigits
;
1158 vli_set(x2
, x1
, ndigits
);
1159 vli_set(y2
, y1
, ndigits
);
1161 vli_clear(z
, ndigits
);
1165 vli_set(z
, p_initial_z
, ndigits
);
1167 apply_z(x1
, y1
, z
, curve
);
1169 ecc_point_double_jacobian(x1
, y1
, z
, curve
);
1171 apply_z(x2
, y2
, z
, curve
);
1174 /* Input P = (x1, y1, Z), Q = (x2, y2, Z)
1175 * Output P' = (x1', y1', Z3), P + Q = (x3, y3, Z3)
1176 * or P => P', Q => P + Q
1178 static void xycz_add(u64
*x1
, u64
*y1
, u64
*x2
, u64
*y2
,
1179 const struct ecc_curve
*curve
)
1181 /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
1182 u64 t5
[ECC_MAX_DIGITS
];
1183 const u64
*curve_prime
= curve
->p
;
1184 const unsigned int ndigits
= curve
->g
.ndigits
;
1187 vli_mod_sub(t5
, x2
, x1
, curve_prime
, ndigits
);
1188 /* t5 = (x2 - x1)^2 = A */
1189 vli_mod_square_fast(t5
, t5
, curve
);
1191 vli_mod_mult_fast(x1
, x1
, t5
, curve
);
1193 vli_mod_mult_fast(x2
, x2
, t5
, curve
);
1195 vli_mod_sub(y2
, y2
, y1
, curve_prime
, ndigits
);
1196 /* t5 = (y2 - y1)^2 = D */
1197 vli_mod_square_fast(t5
, y2
, curve
);
1200 vli_mod_sub(t5
, t5
, x1
, curve_prime
, ndigits
);
1201 /* t5 = D - B - C = x3 */
1202 vli_mod_sub(t5
, t5
, x2
, curve_prime
, ndigits
);
1204 vli_mod_sub(x2
, x2
, x1
, curve_prime
, ndigits
);
1205 /* t2 = y1*(C - B) */
1206 vli_mod_mult_fast(y1
, y1
, x2
, curve
);
1208 vli_mod_sub(x2
, x1
, t5
, curve_prime
, ndigits
);
1209 /* t4 = (y2 - y1)*(B - x3) */
1210 vli_mod_mult_fast(y2
, y2
, x2
, curve
);
1212 vli_mod_sub(y2
, y2
, y1
, curve_prime
, ndigits
);
1214 vli_set(x2
, t5
, ndigits
);
1217 /* Input P = (x1, y1, Z), Q = (x2, y2, Z)
1218 * Output P + Q = (x3, y3, Z3), P - Q = (x3', y3', Z3)
1219 * or P => P - Q, Q => P + Q
1221 static void xycz_add_c(u64
*x1
, u64
*y1
, u64
*x2
, u64
*y2
,
1222 const struct ecc_curve
*curve
)
1224 /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
1225 u64 t5
[ECC_MAX_DIGITS
];
1226 u64 t6
[ECC_MAX_DIGITS
];
1227 u64 t7
[ECC_MAX_DIGITS
];
1228 const u64
*curve_prime
= curve
->p
;
1229 const unsigned int ndigits
= curve
->g
.ndigits
;
1232 vli_mod_sub(t5
, x2
, x1
, curve_prime
, ndigits
);
1233 /* t5 = (x2 - x1)^2 = A */
1234 vli_mod_square_fast(t5
, t5
, curve
);
1236 vli_mod_mult_fast(x1
, x1
, t5
, curve
);
1238 vli_mod_mult_fast(x2
, x2
, t5
, curve
);
1240 vli_mod_add(t5
, y2
, y1
, curve_prime
, ndigits
);
1242 vli_mod_sub(y2
, y2
, y1
, curve_prime
, ndigits
);
1245 vli_mod_sub(t6
, x2
, x1
, curve_prime
, ndigits
);
1246 /* t2 = y1 * (C - B) */
1247 vli_mod_mult_fast(y1
, y1
, t6
, curve
);
1249 vli_mod_add(t6
, x1
, x2
, curve_prime
, ndigits
);
1250 /* t3 = (y2 - y1)^2 */
1251 vli_mod_square_fast(x2
, y2
, curve
);
1253 vli_mod_sub(x2
, x2
, t6
, curve_prime
, ndigits
);
1256 vli_mod_sub(t7
, x1
, x2
, curve_prime
, ndigits
);
1257 /* t4 = (y2 - y1)*(B - x3) */
1258 vli_mod_mult_fast(y2
, y2
, t7
, curve
);
1260 vli_mod_sub(y2
, y2
, y1
, curve_prime
, ndigits
);
1262 /* t7 = (y2 + y1)^2 = F */
1263 vli_mod_square_fast(t7
, t5
, curve
);
1265 vli_mod_sub(t7
, t7
, t6
, curve_prime
, ndigits
);
1267 vli_mod_sub(t6
, t7
, x1
, curve_prime
, ndigits
);
1268 /* t6 = (y2 + y1)*(x3' - B) */
1269 vli_mod_mult_fast(t6
, t6
, t5
, curve
);
1271 vli_mod_sub(y1
, t6
, y1
, curve_prime
, ndigits
);
1273 vli_set(x1
, t7
, ndigits
);
1276 static void ecc_point_mult(struct ecc_point
*result
,
1277 const struct ecc_point
*point
, const u64
*scalar
,
1278 u64
*initial_z
, const struct ecc_curve
*curve
,
1279 unsigned int ndigits
)
1282 u64 rx
[2][ECC_MAX_DIGITS
];
1283 u64 ry
[2][ECC_MAX_DIGITS
];
1284 u64 z
[ECC_MAX_DIGITS
];
1285 u64 sk
[2][ECC_MAX_DIGITS
];
1286 u64
*curve_prime
= curve
->p
;
1291 carry
= vli_add(sk
[0], scalar
, curve
->n
, ndigits
);
1292 vli_add(sk
[1], sk
[0], curve
->n
, ndigits
);
1293 scalar
= sk
[!carry
];
1294 num_bits
= sizeof(u64
) * ndigits
* 8 + 1;
1296 vli_set(rx
[1], point
->x
, ndigits
);
1297 vli_set(ry
[1], point
->y
, ndigits
);
1299 xycz_initial_double(rx
[1], ry
[1], rx
[0], ry
[0], initial_z
, curve
);
1301 for (i
= num_bits
- 2; i
> 0; i
--) {
1302 nb
= !vli_test_bit(scalar
, i
);
1303 xycz_add_c(rx
[1 - nb
], ry
[1 - nb
], rx
[nb
], ry
[nb
], curve
);
1304 xycz_add(rx
[nb
], ry
[nb
], rx
[1 - nb
], ry
[1 - nb
], curve
);
1307 nb
= !vli_test_bit(scalar
, 0);
1308 xycz_add_c(rx
[1 - nb
], ry
[1 - nb
], rx
[nb
], ry
[nb
], curve
);
1310 /* Find final 1/Z value. */
1312 vli_mod_sub(z
, rx
[1], rx
[0], curve_prime
, ndigits
);
1313 /* Yb * (X1 - X0) */
1314 vli_mod_mult_fast(z
, z
, ry
[1 - nb
], curve
);
1315 /* xP * Yb * (X1 - X0) */
1316 vli_mod_mult_fast(z
, z
, point
->x
, curve
);
1318 /* 1 / (xP * Yb * (X1 - X0)) */
1319 vli_mod_inv(z
, z
, curve_prime
, point
->ndigits
);
1321 /* yP / (xP * Yb * (X1 - X0)) */
1322 vli_mod_mult_fast(z
, z
, point
->y
, curve
);
1323 /* Xb * yP / (xP * Yb * (X1 - X0)) */
1324 vli_mod_mult_fast(z
, z
, rx
[1 - nb
], curve
);
1325 /* End 1/Z calculation */
1327 xycz_add(rx
[nb
], ry
[nb
], rx
[1 - nb
], ry
[1 - nb
], curve
);
1329 apply_z(rx
[0], ry
[0], z
, curve
);
1331 vli_set(result
->x
, rx
[0], ndigits
);
1332 vli_set(result
->y
, ry
[0], ndigits
);
1335 /* Computes R = P + Q mod p */
1336 static void ecc_point_add(const struct ecc_point
*result
,
1337 const struct ecc_point
*p
, const struct ecc_point
*q
,
1338 const struct ecc_curve
*curve
)
1340 u64 z
[ECC_MAX_DIGITS
];
1341 u64 px
[ECC_MAX_DIGITS
];
1342 u64 py
[ECC_MAX_DIGITS
];
1343 unsigned int ndigits
= curve
->g
.ndigits
;
1345 vli_set(result
->x
, q
->x
, ndigits
);
1346 vli_set(result
->y
, q
->y
, ndigits
);
1347 vli_mod_sub(z
, result
->x
, p
->x
, curve
->p
, ndigits
);
1348 vli_set(px
, p
->x
, ndigits
);
1349 vli_set(py
, p
->y
, ndigits
);
1350 xycz_add(px
, py
, result
->x
, result
->y
, curve
);
1351 vli_mod_inv(z
, z
, curve
->p
, ndigits
);
1352 apply_z(result
->x
, result
->y
, z
, curve
);
1355 /* Computes R = u1P + u2Q mod p using Shamir's trick.
1356 * Based on: Kenneth MacKay's micro-ecc (2014).
1358 void ecc_point_mult_shamir(const struct ecc_point
*result
,
1359 const u64
*u1
, const struct ecc_point
*p
,
1360 const u64
*u2
, const struct ecc_point
*q
,
1361 const struct ecc_curve
*curve
)
1363 u64 z
[ECC_MAX_DIGITS
];
1364 u64 sump
[2][ECC_MAX_DIGITS
];
1365 u64
*rx
= result
->x
;
1366 u64
*ry
= result
->y
;
1367 unsigned int ndigits
= curve
->g
.ndigits
;
1368 unsigned int num_bits
;
1369 struct ecc_point sum
= ECC_POINT_INIT(sump
[0], sump
[1], ndigits
);
1370 const struct ecc_point
*points
[4];
1371 const struct ecc_point
*point
;
1375 ecc_point_add(&sum
, p
, q
, curve
);
1381 num_bits
= max(vli_num_bits(u1
, ndigits
), vli_num_bits(u2
, ndigits
));
1383 idx
= (!!vli_test_bit(u1
, i
)) | ((!!vli_test_bit(u2
, i
)) << 1);
1384 point
= points
[idx
];
1386 vli_set(rx
, point
->x
, ndigits
);
1387 vli_set(ry
, point
->y
, ndigits
);
1388 vli_clear(z
+ 1, ndigits
- 1);
1391 for (--i
; i
>= 0; i
--) {
1392 ecc_point_double_jacobian(rx
, ry
, z
, curve
);
1393 idx
= (!!vli_test_bit(u1
, i
)) | ((!!vli_test_bit(u2
, i
)) << 1);
1394 point
= points
[idx
];
1396 u64 tx
[ECC_MAX_DIGITS
];
1397 u64 ty
[ECC_MAX_DIGITS
];
1398 u64 tz
[ECC_MAX_DIGITS
];
1400 vli_set(tx
, point
->x
, ndigits
);
1401 vli_set(ty
, point
->y
, ndigits
);
1402 apply_z(tx
, ty
, z
, curve
);
1403 vli_mod_sub(tz
, rx
, tx
, curve
->p
, ndigits
);
1404 xycz_add(tx
, ty
, rx
, ry
, curve
);
1405 vli_mod_mult_fast(z
, z
, tz
, curve
);
1408 vli_mod_inv(z
, z
, curve
->p
, ndigits
);
1409 apply_z(rx
, ry
, z
, curve
);
1411 EXPORT_SYMBOL(ecc_point_mult_shamir
);
1413 static int __ecc_is_key_valid(const struct ecc_curve
*curve
,
1414 const u64
*private_key
, unsigned int ndigits
)
1416 u64 one
[ECC_MAX_DIGITS
] = { 1, };
1417 u64 res
[ECC_MAX_DIGITS
];
1422 if (curve
->g
.ndigits
!= ndigits
)
1425 /* Make sure the private key is in the range [2, n-3]. */
1426 if (vli_cmp(one
, private_key
, ndigits
) != -1)
1428 vli_sub(res
, curve
->n
, one
, ndigits
);
1429 vli_sub(res
, res
, one
, ndigits
);
1430 if (vli_cmp(res
, private_key
, ndigits
) != 1)
1436 int ecc_is_key_valid(unsigned int curve_id
, unsigned int ndigits
,
1437 const u64
*private_key
, unsigned int private_key_len
)
1440 const struct ecc_curve
*curve
= ecc_get_curve(curve_id
);
1442 nbytes
= ndigits
<< ECC_DIGITS_TO_BYTES_SHIFT
;
1444 if (private_key_len
!= nbytes
)
1447 return __ecc_is_key_valid(curve
, private_key
, ndigits
);
1449 EXPORT_SYMBOL(ecc_is_key_valid
);
1452 * ECC private keys are generated using the method of extra random bits,
1453 * equivalent to that described in FIPS 186-4, Appendix B.4.1.
1455 * d = (c mod(n–1)) + 1 where c is a string of random bits, 64 bits longer
1457 * 0 <= c mod(n-1) <= n-2 and implies that
1460 * This method generates a private key uniformly distributed in the range
1463 int ecc_gen_privkey(unsigned int curve_id
, unsigned int ndigits
, u64
*privkey
)
1465 const struct ecc_curve
*curve
= ecc_get_curve(curve_id
);
1466 u64 priv
[ECC_MAX_DIGITS
];
1467 unsigned int nbytes
= ndigits
<< ECC_DIGITS_TO_BYTES_SHIFT
;
1468 unsigned int nbits
= vli_num_bits(curve
->n
, ndigits
);
1471 /* Check that N is included in Table 1 of FIPS 186-4, section 6.1.1 */
1472 if (nbits
< 160 || ndigits
> ARRAY_SIZE(priv
))
1476 * FIPS 186-4 recommends that the private key should be obtained from a
1477 * RBG with a security strength equal to or greater than the security
1478 * strength associated with N.
1480 * The maximum security strength identified by NIST SP800-57pt1r4 for
1481 * ECC is 256 (N >= 512).
1483 * This condition is met by the default RNG because it selects a favored
1484 * DRBG with a security strength of 256.
1486 if (crypto_get_default_rng())
1489 err
= crypto_rng_get_bytes(crypto_default_rng
, (u8
*)priv
, nbytes
);
1490 crypto_put_default_rng();
1494 /* Make sure the private key is in the valid range. */
1495 if (__ecc_is_key_valid(curve
, priv
, ndigits
))
1498 ecc_swap_digits(priv
, privkey
, ndigits
);
1502 EXPORT_SYMBOL(ecc_gen_privkey
);
1504 int ecc_make_pub_key(unsigned int curve_id
, unsigned int ndigits
,
1505 const u64
*private_key
, u64
*public_key
)
1508 struct ecc_point
*pk
;
1509 u64 priv
[ECC_MAX_DIGITS
];
1510 const struct ecc_curve
*curve
= ecc_get_curve(curve_id
);
1512 if (!private_key
|| !curve
|| ndigits
> ARRAY_SIZE(priv
)) {
1517 ecc_swap_digits(private_key
, priv
, ndigits
);
1519 pk
= ecc_alloc_point(ndigits
);
1525 ecc_point_mult(pk
, &curve
->g
, priv
, NULL
, curve
, ndigits
);
1527 /* SP800-56A rev 3 5.6.2.1.3 key check */
1528 if (ecc_is_pubkey_valid_full(curve
, pk
)) {
1530 goto err_free_point
;
1533 ecc_swap_digits(pk
->x
, public_key
, ndigits
);
1534 ecc_swap_digits(pk
->y
, &public_key
[ndigits
], ndigits
);
1541 EXPORT_SYMBOL(ecc_make_pub_key
);
1543 /* SP800-56A section 5.6.2.3.4 partial verification: ephemeral keys only */
1544 int ecc_is_pubkey_valid_partial(const struct ecc_curve
*curve
,
1545 struct ecc_point
*pk
)
1547 u64 yy
[ECC_MAX_DIGITS
], xxx
[ECC_MAX_DIGITS
], w
[ECC_MAX_DIGITS
];
1549 if (WARN_ON(pk
->ndigits
!= curve
->g
.ndigits
))
1552 /* Check 1: Verify key is not the zero point. */
1553 if (ecc_point_is_zero(pk
))
1556 /* Check 2: Verify key is in the range [1, p-1]. */
1557 if (vli_cmp(curve
->p
, pk
->x
, pk
->ndigits
) != 1)
1559 if (vli_cmp(curve
->p
, pk
->y
, pk
->ndigits
) != 1)
1562 /* Check 3: Verify that y^2 == (x^3 + a·x + b) mod p */
1563 vli_mod_square_fast(yy
, pk
->y
, curve
); /* y^2 */
1564 vli_mod_square_fast(xxx
, pk
->x
, curve
); /* x^2 */
1565 vli_mod_mult_fast(xxx
, xxx
, pk
->x
, curve
); /* x^3 */
1566 vli_mod_mult_fast(w
, curve
->a
, pk
->x
, curve
); /* a·x */
1567 vli_mod_add(w
, w
, curve
->b
, curve
->p
, pk
->ndigits
); /* a·x + b */
1568 vli_mod_add(w
, w
, xxx
, curve
->p
, pk
->ndigits
); /* x^3 + a·x + b */
1569 if (vli_cmp(yy
, w
, pk
->ndigits
) != 0) /* Equation */
1574 EXPORT_SYMBOL(ecc_is_pubkey_valid_partial
);
1576 /* SP800-56A section 5.6.2.3.3 full verification */
1577 int ecc_is_pubkey_valid_full(const struct ecc_curve
*curve
,
1578 struct ecc_point
*pk
)
1580 struct ecc_point
*nQ
;
1582 /* Checks 1 through 3 */
1583 int ret
= ecc_is_pubkey_valid_partial(curve
, pk
);
1588 /* Check 4: Verify that nQ is the zero point. */
1589 nQ
= ecc_alloc_point(pk
->ndigits
);
1593 ecc_point_mult(nQ
, pk
, curve
->n
, NULL
, curve
, pk
->ndigits
);
1594 if (!ecc_point_is_zero(nQ
))
1601 EXPORT_SYMBOL(ecc_is_pubkey_valid_full
);
1603 int crypto_ecdh_shared_secret(unsigned int curve_id
, unsigned int ndigits
,
1604 const u64
*private_key
, const u64
*public_key
,
1608 struct ecc_point
*product
, *pk
;
1609 u64 priv
[ECC_MAX_DIGITS
];
1610 u64 rand_z
[ECC_MAX_DIGITS
];
1611 unsigned int nbytes
;
1612 const struct ecc_curve
*curve
= ecc_get_curve(curve_id
);
1614 if (!private_key
|| !public_key
|| !curve
||
1615 ndigits
> ARRAY_SIZE(priv
) || ndigits
> ARRAY_SIZE(rand_z
)) {
1620 nbytes
= ndigits
<< ECC_DIGITS_TO_BYTES_SHIFT
;
1622 get_random_bytes(rand_z
, nbytes
);
1624 pk
= ecc_alloc_point(ndigits
);
1630 ecc_swap_digits(public_key
, pk
->x
, ndigits
);
1631 ecc_swap_digits(&public_key
[ndigits
], pk
->y
, ndigits
);
1632 ret
= ecc_is_pubkey_valid_partial(curve
, pk
);
1634 goto err_alloc_product
;
1636 ecc_swap_digits(private_key
, priv
, ndigits
);
1638 product
= ecc_alloc_point(ndigits
);
1641 goto err_alloc_product
;
1644 ecc_point_mult(product
, pk
, priv
, rand_z
, curve
, ndigits
);
1646 if (ecc_point_is_zero(product
)) {
1651 ecc_swap_digits(product
->x
, secret
, ndigits
);
1654 memzero_explicit(priv
, sizeof(priv
));
1655 memzero_explicit(rand_z
, sizeof(rand_z
));
1656 ecc_free_point(product
);
1662 EXPORT_SYMBOL(crypto_ecdh_shared_secret
);
1664 MODULE_LICENSE("Dual BSD/GPL");