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0193b32f56
Remove repeated word 'bit' in comments. Signed-off-by: Meng Yu <yumeng18@huawei.com> Signed-off-by: Herbert Xu <herbert@gondor.apana.org.au>
1665 lines
42 KiB
C
1665 lines
42 KiB
C
/*
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* Copyright (c) 2013, 2014 Kenneth MacKay. All rights reserved.
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* Copyright (c) 2019 Vitaly Chikunov <vt@altlinux.org>
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions are
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* met:
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* * Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* * Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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*
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* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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* A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
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* HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
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* LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*/
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#include <crypto/ecc_curve.h>
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#include <linux/module.h>
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#include <linux/random.h>
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#include <linux/slab.h>
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#include <linux/swab.h>
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#include <linux/fips.h>
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#include <crypto/ecdh.h>
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#include <crypto/rng.h>
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#include <asm/unaligned.h>
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#include <linux/ratelimit.h>
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#include "ecc.h"
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#include "ecc_curve_defs.h"
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typedef struct {
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u64 m_low;
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u64 m_high;
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} uint128_t;
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/* Returns curv25519 curve param */
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const struct ecc_curve *ecc_get_curve25519(void)
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{
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return &ecc_25519;
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}
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EXPORT_SYMBOL(ecc_get_curve25519);
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const struct ecc_curve *ecc_get_curve(unsigned int curve_id)
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{
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switch (curve_id) {
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/* In FIPS mode only allow P256 and higher */
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case ECC_CURVE_NIST_P192:
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return fips_enabled ? NULL : &nist_p192;
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case ECC_CURVE_NIST_P256:
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return &nist_p256;
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case ECC_CURVE_NIST_P384:
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return &nist_p384;
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default:
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return NULL;
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}
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}
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EXPORT_SYMBOL(ecc_get_curve);
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static u64 *ecc_alloc_digits_space(unsigned int ndigits)
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{
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size_t len = ndigits * sizeof(u64);
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if (!len)
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return NULL;
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return kmalloc(len, GFP_KERNEL);
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}
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static void ecc_free_digits_space(u64 *space)
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{
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kfree_sensitive(space);
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}
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static struct ecc_point *ecc_alloc_point(unsigned int ndigits)
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{
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struct ecc_point *p = kmalloc(sizeof(*p), GFP_KERNEL);
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if (!p)
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return NULL;
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p->x = ecc_alloc_digits_space(ndigits);
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if (!p->x)
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goto err_alloc_x;
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p->y = ecc_alloc_digits_space(ndigits);
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if (!p->y)
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goto err_alloc_y;
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p->ndigits = ndigits;
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return p;
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err_alloc_y:
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ecc_free_digits_space(p->x);
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err_alloc_x:
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kfree(p);
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return NULL;
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}
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static void ecc_free_point(struct ecc_point *p)
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{
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if (!p)
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return;
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kfree_sensitive(p->x);
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kfree_sensitive(p->y);
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kfree_sensitive(p);
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}
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static void vli_clear(u64 *vli, unsigned int ndigits)
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{
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int i;
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for (i = 0; i < ndigits; i++)
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vli[i] = 0;
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}
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/* Returns true if vli == 0, false otherwise. */
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bool vli_is_zero(const u64 *vli, unsigned int ndigits)
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{
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int i;
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for (i = 0; i < ndigits; i++) {
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if (vli[i])
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return false;
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}
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return true;
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}
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EXPORT_SYMBOL(vli_is_zero);
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/* Returns nonzero if bit of vli is set. */
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static u64 vli_test_bit(const u64 *vli, unsigned int bit)
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{
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return (vli[bit / 64] & ((u64)1 << (bit % 64)));
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}
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static bool vli_is_negative(const u64 *vli, unsigned int ndigits)
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{
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return vli_test_bit(vli, ndigits * 64 - 1);
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}
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/* Counts the number of 64-bit "digits" in vli. */
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static unsigned int vli_num_digits(const u64 *vli, unsigned int ndigits)
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{
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int i;
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/* Search from the end until we find a non-zero digit.
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* We do it in reverse because we expect that most digits will
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* be nonzero.
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*/
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for (i = ndigits - 1; i >= 0 && vli[i] == 0; i--);
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return (i + 1);
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}
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/* Counts the number of bits required for vli. */
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static unsigned int vli_num_bits(const u64 *vli, unsigned int ndigits)
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{
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unsigned int i, num_digits;
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u64 digit;
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num_digits = vli_num_digits(vli, ndigits);
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if (num_digits == 0)
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return 0;
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digit = vli[num_digits - 1];
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for (i = 0; digit; i++)
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digit >>= 1;
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return ((num_digits - 1) * 64 + i);
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}
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/* Set dest from unaligned bit string src. */
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void vli_from_be64(u64 *dest, const void *src, unsigned int ndigits)
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{
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int i;
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const u64 *from = src;
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for (i = 0; i < ndigits; i++)
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dest[i] = get_unaligned_be64(&from[ndigits - 1 - i]);
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}
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EXPORT_SYMBOL(vli_from_be64);
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void vli_from_le64(u64 *dest, const void *src, unsigned int ndigits)
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{
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int i;
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const u64 *from = src;
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for (i = 0; i < ndigits; i++)
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dest[i] = get_unaligned_le64(&from[i]);
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}
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EXPORT_SYMBOL(vli_from_le64);
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/* Sets dest = src. */
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static void vli_set(u64 *dest, const u64 *src, unsigned int ndigits)
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{
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int i;
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for (i = 0; i < ndigits; i++)
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dest[i] = src[i];
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}
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/* Returns sign of left - right. */
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int vli_cmp(const u64 *left, const u64 *right, unsigned int ndigits)
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{
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int i;
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for (i = ndigits - 1; i >= 0; i--) {
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if (left[i] > right[i])
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return 1;
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else if (left[i] < right[i])
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return -1;
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}
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return 0;
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}
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EXPORT_SYMBOL(vli_cmp);
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/* Computes result = in << c, returning carry. Can modify in place
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* (if result == in). 0 < shift < 64.
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*/
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static u64 vli_lshift(u64 *result, const u64 *in, unsigned int shift,
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unsigned int ndigits)
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{
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u64 carry = 0;
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int i;
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for (i = 0; i < ndigits; i++) {
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u64 temp = in[i];
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result[i] = (temp << shift) | carry;
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carry = temp >> (64 - shift);
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}
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return carry;
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}
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/* Computes vli = vli >> 1. */
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static void vli_rshift1(u64 *vli, unsigned int ndigits)
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{
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u64 *end = vli;
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u64 carry = 0;
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vli += ndigits;
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while (vli-- > end) {
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u64 temp = *vli;
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*vli = (temp >> 1) | carry;
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carry = temp << 63;
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}
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}
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/* Computes result = left + right, returning carry. Can modify in place. */
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static u64 vli_add(u64 *result, const u64 *left, const u64 *right,
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unsigned int ndigits)
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{
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u64 carry = 0;
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int i;
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for (i = 0; i < ndigits; i++) {
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u64 sum;
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sum = left[i] + right[i] + carry;
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if (sum != left[i])
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carry = (sum < left[i]);
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result[i] = sum;
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}
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return carry;
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}
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/* Computes result = left + right, returning carry. Can modify in place. */
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static u64 vli_uadd(u64 *result, const u64 *left, u64 right,
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unsigned int ndigits)
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{
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u64 carry = right;
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int i;
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for (i = 0; i < ndigits; i++) {
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u64 sum;
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sum = left[i] + carry;
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if (sum != left[i])
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carry = (sum < left[i]);
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else
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carry = !!carry;
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result[i] = sum;
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}
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return carry;
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}
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/* Computes result = left - right, returning borrow. Can modify in place. */
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u64 vli_sub(u64 *result, const u64 *left, const u64 *right,
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unsigned int ndigits)
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{
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u64 borrow = 0;
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int i;
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for (i = 0; i < ndigits; i++) {
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u64 diff;
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diff = left[i] - right[i] - borrow;
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if (diff != left[i])
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borrow = (diff > left[i]);
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result[i] = diff;
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}
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return borrow;
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}
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EXPORT_SYMBOL(vli_sub);
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/* Computes result = left - right, returning borrow. Can modify in place. */
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static u64 vli_usub(u64 *result, const u64 *left, u64 right,
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unsigned int ndigits)
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{
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u64 borrow = right;
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int i;
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for (i = 0; i < ndigits; i++) {
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u64 diff;
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diff = left[i] - borrow;
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if (diff != left[i])
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borrow = (diff > left[i]);
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result[i] = diff;
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}
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return borrow;
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}
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static uint128_t mul_64_64(u64 left, u64 right)
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{
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uint128_t result;
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#if defined(CONFIG_ARCH_SUPPORTS_INT128)
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unsigned __int128 m = (unsigned __int128)left * right;
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result.m_low = m;
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result.m_high = m >> 64;
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#else
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u64 a0 = left & 0xffffffffull;
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u64 a1 = left >> 32;
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u64 b0 = right & 0xffffffffull;
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u64 b1 = right >> 32;
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u64 m0 = a0 * b0;
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u64 m1 = a0 * b1;
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u64 m2 = a1 * b0;
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u64 m3 = a1 * b1;
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m2 += (m0 >> 32);
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m2 += m1;
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/* Overflow */
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if (m2 < m1)
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m3 += 0x100000000ull;
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result.m_low = (m0 & 0xffffffffull) | (m2 << 32);
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result.m_high = m3 + (m2 >> 32);
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#endif
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return result;
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}
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static uint128_t add_128_128(uint128_t a, uint128_t b)
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{
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uint128_t result;
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result.m_low = a.m_low + b.m_low;
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result.m_high = a.m_high + b.m_high + (result.m_low < a.m_low);
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return result;
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}
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static void vli_mult(u64 *result, const u64 *left, const u64 *right,
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unsigned int ndigits)
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{
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uint128_t r01 = { 0, 0 };
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u64 r2 = 0;
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unsigned int i, k;
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/* Compute each digit of result in sequence, maintaining the
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* carries.
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*/
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for (k = 0; k < ndigits * 2 - 1; k++) {
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unsigned int min;
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if (k < ndigits)
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min = 0;
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else
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min = (k + 1) - ndigits;
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for (i = min; i <= k && i < ndigits; i++) {
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uint128_t product;
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product = mul_64_64(left[i], right[k - i]);
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r01 = add_128_128(r01, product);
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r2 += (r01.m_high < product.m_high);
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}
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result[k] = r01.m_low;
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r01.m_low = r01.m_high;
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r01.m_high = r2;
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r2 = 0;
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}
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result[ndigits * 2 - 1] = r01.m_low;
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}
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/* Compute product = left * right, for a small right value. */
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static void vli_umult(u64 *result, const u64 *left, u32 right,
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unsigned int ndigits)
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{
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uint128_t r01 = { 0 };
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unsigned int k;
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for (k = 0; k < ndigits; k++) {
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uint128_t product;
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product = mul_64_64(left[k], right);
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r01 = add_128_128(r01, product);
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/* no carry */
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result[k] = r01.m_low;
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r01.m_low = r01.m_high;
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r01.m_high = 0;
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}
|
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result[k] = r01.m_low;
|
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for (++k; k < ndigits * 2; k++)
|
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result[k] = 0;
|
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}
|
||
|
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static void vli_square(u64 *result, const u64 *left, unsigned int ndigits)
|
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{
|
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uint128_t r01 = { 0, 0 };
|
||
u64 r2 = 0;
|
||
int i, k;
|
||
|
||
for (k = 0; k < ndigits * 2 - 1; k++) {
|
||
unsigned int min;
|
||
|
||
if (k < ndigits)
|
||
min = 0;
|
||
else
|
||
min = (k + 1) - ndigits;
|
||
|
||
for (i = min; i <= k && i <= k - i; i++) {
|
||
uint128_t product;
|
||
|
||
product = mul_64_64(left[i], left[k - i]);
|
||
|
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if (i < k - i) {
|
||
r2 += product.m_high >> 63;
|
||
product.m_high = (product.m_high << 1) |
|
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(product.m_low >> 63);
|
||
product.m_low <<= 1;
|
||
}
|
||
|
||
r01 = add_128_128(r01, product);
|
||
r2 += (r01.m_high < product.m_high);
|
||
}
|
||
|
||
result[k] = r01.m_low;
|
||
r01.m_low = r01.m_high;
|
||
r01.m_high = r2;
|
||
r2 = 0;
|
||
}
|
||
|
||
result[ndigits * 2 - 1] = r01.m_low;
|
||
}
|
||
|
||
/* Computes result = (left + right) % mod.
|
||
* Assumes that left < mod and right < mod, result != mod.
|
||
*/
|
||
static void vli_mod_add(u64 *result, const u64 *left, const u64 *right,
|
||
const u64 *mod, unsigned int ndigits)
|
||
{
|
||
u64 carry;
|
||
|
||
carry = vli_add(result, left, right, ndigits);
|
||
|
||
/* result > mod (result = mod + remainder), so subtract mod to
|
||
* get remainder.
|
||
*/
|
||
if (carry || vli_cmp(result, mod, ndigits) >= 0)
|
||
vli_sub(result, result, mod, ndigits);
|
||
}
|
||
|
||
/* Computes result = (left - right) % mod.
|
||
* Assumes that left < mod and right < mod, result != mod.
|
||
*/
|
||
static void vli_mod_sub(u64 *result, const u64 *left, const u64 *right,
|
||
const u64 *mod, unsigned int ndigits)
|
||
{
|
||
u64 borrow = vli_sub(result, left, right, ndigits);
|
||
|
||
/* In this case, p_result == -diff == (max int) - diff.
|
||
* Since -x % d == d - x, we can get the correct result from
|
||
* result + mod (with overflow).
|
||
*/
|
||
if (borrow)
|
||
vli_add(result, result, mod, ndigits);
|
||
}
|
||
|
||
/*
|
||
* Computes result = product % mod
|
||
* for special form moduli: p = 2^k-c, for small c (note the minus sign)
|
||
*
|
||
* References:
|
||
* R. Crandall, C. Pomerance. Prime Numbers: A Computational Perspective.
|
||
* 9 Fast Algorithms for Large-Integer Arithmetic. 9.2.3 Moduli of special form
|
||
* Algorithm 9.2.13 (Fast mod operation for special-form moduli).
|
||
*/
|
||
static void vli_mmod_special(u64 *result, const u64 *product,
|
||
const u64 *mod, unsigned int ndigits)
|
||
{
|
||
u64 c = -mod[0];
|
||
u64 t[ECC_MAX_DIGITS * 2];
|
||
u64 r[ECC_MAX_DIGITS * 2];
|
||
|
||
vli_set(r, product, ndigits * 2);
|
||
while (!vli_is_zero(r + ndigits, ndigits)) {
|
||
vli_umult(t, r + ndigits, c, ndigits);
|
||
vli_clear(r + ndigits, ndigits);
|
||
vli_add(r, r, t, ndigits * 2);
|
||
}
|
||
vli_set(t, mod, ndigits);
|
||
vli_clear(t + ndigits, ndigits);
|
||
while (vli_cmp(r, t, ndigits * 2) >= 0)
|
||
vli_sub(r, r, t, ndigits * 2);
|
||
vli_set(result, r, ndigits);
|
||
}
|
||
|
||
/*
|
||
* Computes result = product % mod
|
||
* for special form moduli: p = 2^{k-1}+c, for small c (note the plus sign)
|
||
* where k-1 does not fit into qword boundary by -1 bit (such as 255).
|
||
|
||
* References (loosely based on):
|
||
* A. Menezes, P. van Oorschot, S. Vanstone. Handbook of Applied Cryptography.
|
||
* 14.3.4 Reduction methods for moduli of special form. Algorithm 14.47.
|
||
* URL: http://cacr.uwaterloo.ca/hac/about/chap14.pdf
|
||
*
|
||
* H. Cohen, G. Frey, R. Avanzi, C. Doche, T. Lange, K. Nguyen, F. Vercauteren.
|
||
* Handbook of Elliptic and Hyperelliptic Curve Cryptography.
|
||
* Algorithm 10.25 Fast reduction for special form moduli
|
||
*/
|
||
static void vli_mmod_special2(u64 *result, const u64 *product,
|
||
const u64 *mod, unsigned int ndigits)
|
||
{
|
||
u64 c2 = mod[0] * 2;
|
||
u64 q[ECC_MAX_DIGITS];
|
||
u64 r[ECC_MAX_DIGITS * 2];
|
||
u64 m[ECC_MAX_DIGITS * 2]; /* expanded mod */
|
||
int carry; /* last bit that doesn't fit into q */
|
||
int i;
|
||
|
||
vli_set(m, mod, ndigits);
|
||
vli_clear(m + ndigits, ndigits);
|
||
|
||
vli_set(r, product, ndigits);
|
||
/* q and carry are top bits */
|
||
vli_set(q, product + ndigits, ndigits);
|
||
vli_clear(r + ndigits, ndigits);
|
||
carry = vli_is_negative(r, ndigits);
|
||
if (carry)
|
||
r[ndigits - 1] &= (1ull << 63) - 1;
|
||
for (i = 1; carry || !vli_is_zero(q, ndigits); i++) {
|
||
u64 qc[ECC_MAX_DIGITS * 2];
|
||
|
||
vli_umult(qc, q, c2, ndigits);
|
||
if (carry)
|
||
vli_uadd(qc, qc, mod[0], ndigits * 2);
|
||
vli_set(q, qc + ndigits, ndigits);
|
||
vli_clear(qc + ndigits, ndigits);
|
||
carry = vli_is_negative(qc, ndigits);
|
||
if (carry)
|
||
qc[ndigits - 1] &= (1ull << 63) - 1;
|
||
if (i & 1)
|
||
vli_sub(r, r, qc, ndigits * 2);
|
||
else
|
||
vli_add(r, r, qc, ndigits * 2);
|
||
}
|
||
while (vli_is_negative(r, ndigits * 2))
|
||
vli_add(r, r, m, ndigits * 2);
|
||
while (vli_cmp(r, m, ndigits * 2) >= 0)
|
||
vli_sub(r, r, m, ndigits * 2);
|
||
|
||
vli_set(result, r, ndigits);
|
||
}
|
||
|
||
/*
|
||
* Computes result = product % mod, where product is 2N words long.
|
||
* Reference: Ken MacKay's micro-ecc.
|
||
* Currently only designed to work for curve_p or curve_n.
|
||
*/
|
||
static void vli_mmod_slow(u64 *result, u64 *product, const u64 *mod,
|
||
unsigned int ndigits)
|
||
{
|
||
u64 mod_m[2 * ECC_MAX_DIGITS];
|
||
u64 tmp[2 * ECC_MAX_DIGITS];
|
||
u64 *v[2] = { tmp, product };
|
||
u64 carry = 0;
|
||
unsigned int i;
|
||
/* Shift mod so its highest set bit is at the maximum position. */
|
||
int shift = (ndigits * 2 * 64) - vli_num_bits(mod, ndigits);
|
||
int word_shift = shift / 64;
|
||
int bit_shift = shift % 64;
|
||
|
||
vli_clear(mod_m, word_shift);
|
||
if (bit_shift > 0) {
|
||
for (i = 0; i < ndigits; ++i) {
|
||
mod_m[word_shift + i] = (mod[i] << bit_shift) | carry;
|
||
carry = mod[i] >> (64 - bit_shift);
|
||
}
|
||
} else
|
||
vli_set(mod_m + word_shift, mod, ndigits);
|
||
|
||
for (i = 1; shift >= 0; --shift) {
|
||
u64 borrow = 0;
|
||
unsigned int j;
|
||
|
||
for (j = 0; j < ndigits * 2; ++j) {
|
||
u64 diff = v[i][j] - mod_m[j] - borrow;
|
||
|
||
if (diff != v[i][j])
|
||
borrow = (diff > v[i][j]);
|
||
v[1 - i][j] = diff;
|
||
}
|
||
i = !(i ^ borrow); /* Swap the index if there was no borrow */
|
||
vli_rshift1(mod_m, ndigits);
|
||
mod_m[ndigits - 1] |= mod_m[ndigits] << (64 - 1);
|
||
vli_rshift1(mod_m + ndigits, ndigits);
|
||
}
|
||
vli_set(result, v[i], ndigits);
|
||
}
|
||
|
||
/* Computes result = product % mod using Barrett's reduction with precomputed
|
||
* value mu appended to the mod after ndigits, mu = (2^{2w} / mod) and have
|
||
* length ndigits + 1, where mu * (2^w - 1) should not overflow ndigits
|
||
* boundary.
|
||
*
|
||
* Reference:
|
||
* R. Brent, P. Zimmermann. Modern Computer Arithmetic. 2010.
|
||
* 2.4.1 Barrett's algorithm. Algorithm 2.5.
|
||
*/
|
||
static void vli_mmod_barrett(u64 *result, u64 *product, const u64 *mod,
|
||
unsigned int ndigits)
|
||
{
|
||
u64 q[ECC_MAX_DIGITS * 2];
|
||
u64 r[ECC_MAX_DIGITS * 2];
|
||
const u64 *mu = mod + ndigits;
|
||
|
||
vli_mult(q, product + ndigits, mu, ndigits);
|
||
if (mu[ndigits])
|
||
vli_add(q + ndigits, q + ndigits, product + ndigits, ndigits);
|
||
vli_mult(r, mod, q + ndigits, ndigits);
|
||
vli_sub(r, product, r, ndigits * 2);
|
||
while (!vli_is_zero(r + ndigits, ndigits) ||
|
||
vli_cmp(r, mod, ndigits) != -1) {
|
||
u64 carry;
|
||
|
||
carry = vli_sub(r, r, mod, ndigits);
|
||
vli_usub(r + ndigits, r + ndigits, carry, ndigits);
|
||
}
|
||
vli_set(result, r, ndigits);
|
||
}
|
||
|
||
/* Computes p_result = p_product % curve_p.
|
||
* See algorithm 5 and 6 from
|
||
* http://www.isys.uni-klu.ac.at/PDF/2001-0126-MT.pdf
|
||
*/
|
||
static void vli_mmod_fast_192(u64 *result, const u64 *product,
|
||
const u64 *curve_prime, u64 *tmp)
|
||
{
|
||
const unsigned int ndigits = 3;
|
||
int carry;
|
||
|
||
vli_set(result, product, ndigits);
|
||
|
||
vli_set(tmp, &product[3], ndigits);
|
||
carry = vli_add(result, result, tmp, ndigits);
|
||
|
||
tmp[0] = 0;
|
||
tmp[1] = product[3];
|
||
tmp[2] = product[4];
|
||
carry += vli_add(result, result, tmp, ndigits);
|
||
|
||
tmp[0] = tmp[1] = product[5];
|
||
tmp[2] = 0;
|
||
carry += vli_add(result, result, tmp, ndigits);
|
||
|
||
while (carry || vli_cmp(curve_prime, result, ndigits) != 1)
|
||
carry -= vli_sub(result, result, curve_prime, ndigits);
|
||
}
|
||
|
||
/* Computes result = product % curve_prime
|
||
* from http://www.nsa.gov/ia/_files/nist-routines.pdf
|
||
*/
|
||
static void vli_mmod_fast_256(u64 *result, const u64 *product,
|
||
const u64 *curve_prime, u64 *tmp)
|
||
{
|
||
int carry;
|
||
const unsigned int ndigits = 4;
|
||
|
||
/* t */
|
||
vli_set(result, product, ndigits);
|
||
|
||
/* s1 */
|
||
tmp[0] = 0;
|
||
tmp[1] = product[5] & 0xffffffff00000000ull;
|
||
tmp[2] = product[6];
|
||
tmp[3] = product[7];
|
||
carry = vli_lshift(tmp, tmp, 1, ndigits);
|
||
carry += vli_add(result, result, tmp, ndigits);
|
||
|
||
/* s2 */
|
||
tmp[1] = product[6] << 32;
|
||
tmp[2] = (product[6] >> 32) | (product[7] << 32);
|
||
tmp[3] = product[7] >> 32;
|
||
carry += vli_lshift(tmp, tmp, 1, ndigits);
|
||
carry += vli_add(result, result, tmp, ndigits);
|
||
|
||
/* s3 */
|
||
tmp[0] = product[4];
|
||
tmp[1] = product[5] & 0xffffffff;
|
||
tmp[2] = 0;
|
||
tmp[3] = product[7];
|
||
carry += vli_add(result, result, tmp, ndigits);
|
||
|
||
/* s4 */
|
||
tmp[0] = (product[4] >> 32) | (product[5] << 32);
|
||
tmp[1] = (product[5] >> 32) | (product[6] & 0xffffffff00000000ull);
|
||
tmp[2] = product[7];
|
||
tmp[3] = (product[6] >> 32) | (product[4] << 32);
|
||
carry += vli_add(result, result, tmp, ndigits);
|
||
|
||
/* d1 */
|
||
tmp[0] = (product[5] >> 32) | (product[6] << 32);
|
||
tmp[1] = (product[6] >> 32);
|
||
tmp[2] = 0;
|
||
tmp[3] = (product[4] & 0xffffffff) | (product[5] << 32);
|
||
carry -= vli_sub(result, result, tmp, ndigits);
|
||
|
||
/* d2 */
|
||
tmp[0] = product[6];
|
||
tmp[1] = product[7];
|
||
tmp[2] = 0;
|
||
tmp[3] = (product[4] >> 32) | (product[5] & 0xffffffff00000000ull);
|
||
carry -= vli_sub(result, result, tmp, ndigits);
|
||
|
||
/* d3 */
|
||
tmp[0] = (product[6] >> 32) | (product[7] << 32);
|
||
tmp[1] = (product[7] >> 32) | (product[4] << 32);
|
||
tmp[2] = (product[4] >> 32) | (product[5] << 32);
|
||
tmp[3] = (product[6] << 32);
|
||
carry -= vli_sub(result, result, tmp, ndigits);
|
||
|
||
/* d4 */
|
||
tmp[0] = product[7];
|
||
tmp[1] = product[4] & 0xffffffff00000000ull;
|
||
tmp[2] = product[5];
|
||
tmp[3] = product[6] & 0xffffffff00000000ull;
|
||
carry -= vli_sub(result, result, tmp, ndigits);
|
||
|
||
if (carry < 0) {
|
||
do {
|
||
carry += vli_add(result, result, curve_prime, ndigits);
|
||
} while (carry < 0);
|
||
} else {
|
||
while (carry || vli_cmp(curve_prime, result, ndigits) != 1)
|
||
carry -= vli_sub(result, result, curve_prime, ndigits);
|
||
}
|
||
}
|
||
|
||
#define SL32OR32(x32, y32) (((u64)x32 << 32) | y32)
|
||
#define AND64H(x64) (x64 & 0xffFFffFF00000000ull)
|
||
#define AND64L(x64) (x64 & 0x00000000ffFFffFFull)
|
||
|
||
/* Computes result = product % curve_prime
|
||
* from "Mathematical routines for the NIST prime elliptic curves"
|
||
*/
|
||
static void vli_mmod_fast_384(u64 *result, const u64 *product,
|
||
const u64 *curve_prime, u64 *tmp)
|
||
{
|
||
int carry;
|
||
const unsigned int ndigits = 6;
|
||
|
||
/* t */
|
||
vli_set(result, product, ndigits);
|
||
|
||
/* s1 */
|
||
tmp[0] = 0; // 0 || 0
|
||
tmp[1] = 0; // 0 || 0
|
||
tmp[2] = SL32OR32(product[11], (product[10]>>32)); //a22||a21
|
||
tmp[3] = product[11]>>32; // 0 ||a23
|
||
tmp[4] = 0; // 0 || 0
|
||
tmp[5] = 0; // 0 || 0
|
||
carry = vli_lshift(tmp, tmp, 1, ndigits);
|
||
carry += vli_add(result, result, tmp, ndigits);
|
||
|
||
/* s2 */
|
||
tmp[0] = product[6]; //a13||a12
|
||
tmp[1] = product[7]; //a15||a14
|
||
tmp[2] = product[8]; //a17||a16
|
||
tmp[3] = product[9]; //a19||a18
|
||
tmp[4] = product[10]; //a21||a20
|
||
tmp[5] = product[11]; //a23||a22
|
||
carry += vli_add(result, result, tmp, ndigits);
|
||
|
||
/* s3 */
|
||
tmp[0] = SL32OR32(product[11], (product[10]>>32)); //a22||a21
|
||
tmp[1] = SL32OR32(product[6], (product[11]>>32)); //a12||a23
|
||
tmp[2] = SL32OR32(product[7], (product[6])>>32); //a14||a13
|
||
tmp[3] = SL32OR32(product[8], (product[7]>>32)); //a16||a15
|
||
tmp[4] = SL32OR32(product[9], (product[8]>>32)); //a18||a17
|
||
tmp[5] = SL32OR32(product[10], (product[9]>>32)); //a20||a19
|
||
carry += vli_add(result, result, tmp, ndigits);
|
||
|
||
/* s4 */
|
||
tmp[0] = AND64H(product[11]); //a23|| 0
|
||
tmp[1] = (product[10]<<32); //a20|| 0
|
||
tmp[2] = product[6]; //a13||a12
|
||
tmp[3] = product[7]; //a15||a14
|
||
tmp[4] = product[8]; //a17||a16
|
||
tmp[5] = product[9]; //a19||a18
|
||
carry += vli_add(result, result, tmp, ndigits);
|
||
|
||
/* s5 */
|
||
tmp[0] = 0; // 0|| 0
|
||
tmp[1] = 0; // 0|| 0
|
||
tmp[2] = product[10]; //a21||a20
|
||
tmp[3] = product[11]; //a23||a22
|
||
tmp[4] = 0; // 0|| 0
|
||
tmp[5] = 0; // 0|| 0
|
||
carry += vli_add(result, result, tmp, ndigits);
|
||
|
||
/* s6 */
|
||
tmp[0] = AND64L(product[10]); // 0 ||a20
|
||
tmp[1] = AND64H(product[10]); //a21|| 0
|
||
tmp[2] = product[11]; //a23||a22
|
||
tmp[3] = 0; // 0 || 0
|
||
tmp[4] = 0; // 0 || 0
|
||
tmp[5] = 0; // 0 || 0
|
||
carry += vli_add(result, result, tmp, ndigits);
|
||
|
||
/* d1 */
|
||
tmp[0] = SL32OR32(product[6], (product[11]>>32)); //a12||a23
|
||
tmp[1] = SL32OR32(product[7], (product[6]>>32)); //a14||a13
|
||
tmp[2] = SL32OR32(product[8], (product[7]>>32)); //a16||a15
|
||
tmp[3] = SL32OR32(product[9], (product[8]>>32)); //a18||a17
|
||
tmp[4] = SL32OR32(product[10], (product[9]>>32)); //a20||a19
|
||
tmp[5] = SL32OR32(product[11], (product[10]>>32)); //a22||a21
|
||
carry -= vli_sub(result, result, tmp, ndigits);
|
||
|
||
/* d2 */
|
||
tmp[0] = (product[10]<<32); //a20|| 0
|
||
tmp[1] = SL32OR32(product[11], (product[10]>>32)); //a22||a21
|
||
tmp[2] = (product[11]>>32); // 0 ||a23
|
||
tmp[3] = 0; // 0 || 0
|
||
tmp[4] = 0; // 0 || 0
|
||
tmp[5] = 0; // 0 || 0
|
||
carry -= vli_sub(result, result, tmp, ndigits);
|
||
|
||
/* d3 */
|
||
tmp[0] = 0; // 0 || 0
|
||
tmp[1] = AND64H(product[11]); //a23|| 0
|
||
tmp[2] = product[11]>>32; // 0 ||a23
|
||
tmp[3] = 0; // 0 || 0
|
||
tmp[4] = 0; // 0 || 0
|
||
tmp[5] = 0; // 0 || 0
|
||
carry -= vli_sub(result, result, tmp, ndigits);
|
||
|
||
if (carry < 0) {
|
||
do {
|
||
carry += vli_add(result, result, curve_prime, ndigits);
|
||
} while (carry < 0);
|
||
} else {
|
||
while (carry || vli_cmp(curve_prime, result, ndigits) != 1)
|
||
carry -= vli_sub(result, result, curve_prime, ndigits);
|
||
}
|
||
|
||
}
|
||
|
||
#undef SL32OR32
|
||
#undef AND64H
|
||
#undef AND64L
|
||
|
||
/* Computes result = product % curve_prime for different curve_primes.
|
||
*
|
||
* Note that curve_primes are distinguished just by heuristic check and
|
||
* not by complete conformance check.
|
||
*/
|
||
static bool vli_mmod_fast(u64 *result, u64 *product,
|
||
const struct ecc_curve *curve)
|
||
{
|
||
u64 tmp[2 * ECC_MAX_DIGITS];
|
||
const u64 *curve_prime = curve->p;
|
||
const unsigned int ndigits = curve->g.ndigits;
|
||
|
||
/* All NIST curves have name prefix 'nist_' */
|
||
if (strncmp(curve->name, "nist_", 5) != 0) {
|
||
/* Try to handle Pseudo-Marsenne primes. */
|
||
if (curve_prime[ndigits - 1] == -1ull) {
|
||
vli_mmod_special(result, product, curve_prime,
|
||
ndigits);
|
||
return true;
|
||
} else if (curve_prime[ndigits - 1] == 1ull << 63 &&
|
||
curve_prime[ndigits - 2] == 0) {
|
||
vli_mmod_special2(result, product, curve_prime,
|
||
ndigits);
|
||
return true;
|
||
}
|
||
vli_mmod_barrett(result, product, curve_prime, ndigits);
|
||
return true;
|
||
}
|
||
|
||
switch (ndigits) {
|
||
case 3:
|
||
vli_mmod_fast_192(result, product, curve_prime, tmp);
|
||
break;
|
||
case 4:
|
||
vli_mmod_fast_256(result, product, curve_prime, tmp);
|
||
break;
|
||
case 6:
|
||
vli_mmod_fast_384(result, product, curve_prime, tmp);
|
||
break;
|
||
default:
|
||
pr_err_ratelimited("ecc: unsupported digits size!\n");
|
||
return false;
|
||
}
|
||
|
||
return true;
|
||
}
|
||
|
||
/* Computes result = (left * right) % mod.
|
||
* Assumes that mod is big enough curve order.
|
||
*/
|
||
void vli_mod_mult_slow(u64 *result, const u64 *left, const u64 *right,
|
||
const u64 *mod, unsigned int ndigits)
|
||
{
|
||
u64 product[ECC_MAX_DIGITS * 2];
|
||
|
||
vli_mult(product, left, right, ndigits);
|
||
vli_mmod_slow(result, product, mod, ndigits);
|
||
}
|
||
EXPORT_SYMBOL(vli_mod_mult_slow);
|
||
|
||
/* Computes result = (left * right) % curve_prime. */
|
||
static void vli_mod_mult_fast(u64 *result, const u64 *left, const u64 *right,
|
||
const struct ecc_curve *curve)
|
||
{
|
||
u64 product[2 * ECC_MAX_DIGITS];
|
||
|
||
vli_mult(product, left, right, curve->g.ndigits);
|
||
vli_mmod_fast(result, product, curve);
|
||
}
|
||
|
||
/* Computes result = left^2 % curve_prime. */
|
||
static void vli_mod_square_fast(u64 *result, const u64 *left,
|
||
const struct ecc_curve *curve)
|
||
{
|
||
u64 product[2 * ECC_MAX_DIGITS];
|
||
|
||
vli_square(product, left, curve->g.ndigits);
|
||
vli_mmod_fast(result, product, curve);
|
||
}
|
||
|
||
#define EVEN(vli) (!(vli[0] & 1))
|
||
/* Computes result = (1 / p_input) % mod. All VLIs are the same size.
|
||
* See "From Euclid's GCD to Montgomery Multiplication to the Great Divide"
|
||
* https://labs.oracle.com/techrep/2001/smli_tr-2001-95.pdf
|
||
*/
|
||
void vli_mod_inv(u64 *result, const u64 *input, const u64 *mod,
|
||
unsigned int ndigits)
|
||
{
|
||
u64 a[ECC_MAX_DIGITS], b[ECC_MAX_DIGITS];
|
||
u64 u[ECC_MAX_DIGITS], v[ECC_MAX_DIGITS];
|
||
u64 carry;
|
||
int cmp_result;
|
||
|
||
if (vli_is_zero(input, ndigits)) {
|
||
vli_clear(result, ndigits);
|
||
return;
|
||
}
|
||
|
||
vli_set(a, input, ndigits);
|
||
vli_set(b, mod, ndigits);
|
||
vli_clear(u, ndigits);
|
||
u[0] = 1;
|
||
vli_clear(v, ndigits);
|
||
|
||
while ((cmp_result = vli_cmp(a, b, ndigits)) != 0) {
|
||
carry = 0;
|
||
|
||
if (EVEN(a)) {
|
||
vli_rshift1(a, ndigits);
|
||
|
||
if (!EVEN(u))
|
||
carry = vli_add(u, u, mod, ndigits);
|
||
|
||
vli_rshift1(u, ndigits);
|
||
if (carry)
|
||
u[ndigits - 1] |= 0x8000000000000000ull;
|
||
} else if (EVEN(b)) {
|
||
vli_rshift1(b, ndigits);
|
||
|
||
if (!EVEN(v))
|
||
carry = vli_add(v, v, mod, ndigits);
|
||
|
||
vli_rshift1(v, ndigits);
|
||
if (carry)
|
||
v[ndigits - 1] |= 0x8000000000000000ull;
|
||
} else if (cmp_result > 0) {
|
||
vli_sub(a, a, b, ndigits);
|
||
vli_rshift1(a, ndigits);
|
||
|
||
if (vli_cmp(u, v, ndigits) < 0)
|
||
vli_add(u, u, mod, ndigits);
|
||
|
||
vli_sub(u, u, v, ndigits);
|
||
if (!EVEN(u))
|
||
carry = vli_add(u, u, mod, ndigits);
|
||
|
||
vli_rshift1(u, ndigits);
|
||
if (carry)
|
||
u[ndigits - 1] |= 0x8000000000000000ull;
|
||
} else {
|
||
vli_sub(b, b, a, ndigits);
|
||
vli_rshift1(b, ndigits);
|
||
|
||
if (vli_cmp(v, u, ndigits) < 0)
|
||
vli_add(v, v, mod, ndigits);
|
||
|
||
vli_sub(v, v, u, ndigits);
|
||
if (!EVEN(v))
|
||
carry = vli_add(v, v, mod, ndigits);
|
||
|
||
vli_rshift1(v, ndigits);
|
||
if (carry)
|
||
v[ndigits - 1] |= 0x8000000000000000ull;
|
||
}
|
||
}
|
||
|
||
vli_set(result, u, ndigits);
|
||
}
|
||
EXPORT_SYMBOL(vli_mod_inv);
|
||
|
||
/* ------ Point operations ------ */
|
||
|
||
/* Returns true if p_point is the point at infinity, false otherwise. */
|
||
static bool ecc_point_is_zero(const struct ecc_point *point)
|
||
{
|
||
return (vli_is_zero(point->x, point->ndigits) &&
|
||
vli_is_zero(point->y, point->ndigits));
|
||
}
|
||
|
||
/* Point multiplication algorithm using Montgomery's ladder with co-Z
|
||
* coordinates. From https://eprint.iacr.org/2011/338.pdf
|
||
*/
|
||
|
||
/* Double in place */
|
||
static void ecc_point_double_jacobian(u64 *x1, u64 *y1, u64 *z1,
|
||
const struct ecc_curve *curve)
|
||
{
|
||
/* t1 = x, t2 = y, t3 = z */
|
||
u64 t4[ECC_MAX_DIGITS];
|
||
u64 t5[ECC_MAX_DIGITS];
|
||
const u64 *curve_prime = curve->p;
|
||
const unsigned int ndigits = curve->g.ndigits;
|
||
|
||
if (vli_is_zero(z1, ndigits))
|
||
return;
|
||
|
||
/* t4 = y1^2 */
|
||
vli_mod_square_fast(t4, y1, curve);
|
||
/* t5 = x1*y1^2 = A */
|
||
vli_mod_mult_fast(t5, x1, t4, curve);
|
||
/* t4 = y1^4 */
|
||
vli_mod_square_fast(t4, t4, curve);
|
||
/* t2 = y1*z1 = z3 */
|
||
vli_mod_mult_fast(y1, y1, z1, curve);
|
||
/* t3 = z1^2 */
|
||
vli_mod_square_fast(z1, z1, curve);
|
||
|
||
/* t1 = x1 + z1^2 */
|
||
vli_mod_add(x1, x1, z1, curve_prime, ndigits);
|
||
/* t3 = 2*z1^2 */
|
||
vli_mod_add(z1, z1, z1, curve_prime, ndigits);
|
||
/* t3 = x1 - z1^2 */
|
||
vli_mod_sub(z1, x1, z1, curve_prime, ndigits);
|
||
/* t1 = x1^2 - z1^4 */
|
||
vli_mod_mult_fast(x1, x1, z1, curve);
|
||
|
||
/* t3 = 2*(x1^2 - z1^4) */
|
||
vli_mod_add(z1, x1, x1, curve_prime, ndigits);
|
||
/* t1 = 3*(x1^2 - z1^4) */
|
||
vli_mod_add(x1, x1, z1, curve_prime, ndigits);
|
||
if (vli_test_bit(x1, 0)) {
|
||
u64 carry = vli_add(x1, x1, curve_prime, ndigits);
|
||
|
||
vli_rshift1(x1, ndigits);
|
||
x1[ndigits - 1] |= carry << 63;
|
||
} else {
|
||
vli_rshift1(x1, ndigits);
|
||
}
|
||
/* t1 = 3/2*(x1^2 - z1^4) = B */
|
||
|
||
/* t3 = B^2 */
|
||
vli_mod_square_fast(z1, x1, curve);
|
||
/* t3 = B^2 - A */
|
||
vli_mod_sub(z1, z1, t5, curve_prime, ndigits);
|
||
/* t3 = B^2 - 2A = x3 */
|
||
vli_mod_sub(z1, z1, t5, curve_prime, ndigits);
|
||
/* t5 = A - x3 */
|
||
vli_mod_sub(t5, t5, z1, curve_prime, ndigits);
|
||
/* t1 = B * (A - x3) */
|
||
vli_mod_mult_fast(x1, x1, t5, curve);
|
||
/* t4 = B * (A - x3) - y1^4 = y3 */
|
||
vli_mod_sub(t4, x1, t4, curve_prime, ndigits);
|
||
|
||
vli_set(x1, z1, ndigits);
|
||
vli_set(z1, y1, ndigits);
|
||
vli_set(y1, t4, ndigits);
|
||
}
|
||
|
||
/* Modify (x1, y1) => (x1 * z^2, y1 * z^3) */
|
||
static void apply_z(u64 *x1, u64 *y1, u64 *z, const struct ecc_curve *curve)
|
||
{
|
||
u64 t1[ECC_MAX_DIGITS];
|
||
|
||
vli_mod_square_fast(t1, z, curve); /* z^2 */
|
||
vli_mod_mult_fast(x1, x1, t1, curve); /* x1 * z^2 */
|
||
vli_mod_mult_fast(t1, t1, z, curve); /* z^3 */
|
||
vli_mod_mult_fast(y1, y1, t1, curve); /* y1 * z^3 */
|
||
}
|
||
|
||
/* P = (x1, y1) => 2P, (x2, y2) => P' */
|
||
static void xycz_initial_double(u64 *x1, u64 *y1, u64 *x2, u64 *y2,
|
||
u64 *p_initial_z, const struct ecc_curve *curve)
|
||
{
|
||
u64 z[ECC_MAX_DIGITS];
|
||
const unsigned int ndigits = curve->g.ndigits;
|
||
|
||
vli_set(x2, x1, ndigits);
|
||
vli_set(y2, y1, ndigits);
|
||
|
||
vli_clear(z, ndigits);
|
||
z[0] = 1;
|
||
|
||
if (p_initial_z)
|
||
vli_set(z, p_initial_z, ndigits);
|
||
|
||
apply_z(x1, y1, z, curve);
|
||
|
||
ecc_point_double_jacobian(x1, y1, z, curve);
|
||
|
||
apply_z(x2, y2, z, curve);
|
||
}
|
||
|
||
/* Input P = (x1, y1, Z), Q = (x2, y2, Z)
|
||
* Output P' = (x1', y1', Z3), P + Q = (x3, y3, Z3)
|
||
* or P => P', Q => P + Q
|
||
*/
|
||
static void xycz_add(u64 *x1, u64 *y1, u64 *x2, u64 *y2,
|
||
const struct ecc_curve *curve)
|
||
{
|
||
/* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
|
||
u64 t5[ECC_MAX_DIGITS];
|
||
const u64 *curve_prime = curve->p;
|
||
const unsigned int ndigits = curve->g.ndigits;
|
||
|
||
/* t5 = x2 - x1 */
|
||
vli_mod_sub(t5, x2, x1, curve_prime, ndigits);
|
||
/* t5 = (x2 - x1)^2 = A */
|
||
vli_mod_square_fast(t5, t5, curve);
|
||
/* t1 = x1*A = B */
|
||
vli_mod_mult_fast(x1, x1, t5, curve);
|
||
/* t3 = x2*A = C */
|
||
vli_mod_mult_fast(x2, x2, t5, curve);
|
||
/* t4 = y2 - y1 */
|
||
vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
|
||
/* t5 = (y2 - y1)^2 = D */
|
||
vli_mod_square_fast(t5, y2, curve);
|
||
|
||
/* t5 = D - B */
|
||
vli_mod_sub(t5, t5, x1, curve_prime, ndigits);
|
||
/* t5 = D - B - C = x3 */
|
||
vli_mod_sub(t5, t5, x2, curve_prime, ndigits);
|
||
/* t3 = C - B */
|
||
vli_mod_sub(x2, x2, x1, curve_prime, ndigits);
|
||
/* t2 = y1*(C - B) */
|
||
vli_mod_mult_fast(y1, y1, x2, curve);
|
||
/* t3 = B - x3 */
|
||
vli_mod_sub(x2, x1, t5, curve_prime, ndigits);
|
||
/* t4 = (y2 - y1)*(B - x3) */
|
||
vli_mod_mult_fast(y2, y2, x2, curve);
|
||
/* t4 = y3 */
|
||
vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
|
||
|
||
vli_set(x2, t5, ndigits);
|
||
}
|
||
|
||
/* Input P = (x1, y1, Z), Q = (x2, y2, Z)
|
||
* Output P + Q = (x3, y3, Z3), P - Q = (x3', y3', Z3)
|
||
* or P => P - Q, Q => P + Q
|
||
*/
|
||
static void xycz_add_c(u64 *x1, u64 *y1, u64 *x2, u64 *y2,
|
||
const struct ecc_curve *curve)
|
||
{
|
||
/* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
|
||
u64 t5[ECC_MAX_DIGITS];
|
||
u64 t6[ECC_MAX_DIGITS];
|
||
u64 t7[ECC_MAX_DIGITS];
|
||
const u64 *curve_prime = curve->p;
|
||
const unsigned int ndigits = curve->g.ndigits;
|
||
|
||
/* t5 = x2 - x1 */
|
||
vli_mod_sub(t5, x2, x1, curve_prime, ndigits);
|
||
/* t5 = (x2 - x1)^2 = A */
|
||
vli_mod_square_fast(t5, t5, curve);
|
||
/* t1 = x1*A = B */
|
||
vli_mod_mult_fast(x1, x1, t5, curve);
|
||
/* t3 = x2*A = C */
|
||
vli_mod_mult_fast(x2, x2, t5, curve);
|
||
/* t4 = y2 + y1 */
|
||
vli_mod_add(t5, y2, y1, curve_prime, ndigits);
|
||
/* t4 = y2 - y1 */
|
||
vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
|
||
|
||
/* t6 = C - B */
|
||
vli_mod_sub(t6, x2, x1, curve_prime, ndigits);
|
||
/* t2 = y1 * (C - B) */
|
||
vli_mod_mult_fast(y1, y1, t6, curve);
|
||
/* t6 = B + C */
|
||
vli_mod_add(t6, x1, x2, curve_prime, ndigits);
|
||
/* t3 = (y2 - y1)^2 */
|
||
vli_mod_square_fast(x2, y2, curve);
|
||
/* t3 = x3 */
|
||
vli_mod_sub(x2, x2, t6, curve_prime, ndigits);
|
||
|
||
/* t7 = B - x3 */
|
||
vli_mod_sub(t7, x1, x2, curve_prime, ndigits);
|
||
/* t4 = (y2 - y1)*(B - x3) */
|
||
vli_mod_mult_fast(y2, y2, t7, curve);
|
||
/* t4 = y3 */
|
||
vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
|
||
|
||
/* t7 = (y2 + y1)^2 = F */
|
||
vli_mod_square_fast(t7, t5, curve);
|
||
/* t7 = x3' */
|
||
vli_mod_sub(t7, t7, t6, curve_prime, ndigits);
|
||
/* t6 = x3' - B */
|
||
vli_mod_sub(t6, t7, x1, curve_prime, ndigits);
|
||
/* t6 = (y2 + y1)*(x3' - B) */
|
||
vli_mod_mult_fast(t6, t6, t5, curve);
|
||
/* t2 = y3' */
|
||
vli_mod_sub(y1, t6, y1, curve_prime, ndigits);
|
||
|
||
vli_set(x1, t7, ndigits);
|
||
}
|
||
|
||
static void ecc_point_mult(struct ecc_point *result,
|
||
const struct ecc_point *point, const u64 *scalar,
|
||
u64 *initial_z, const struct ecc_curve *curve,
|
||
unsigned int ndigits)
|
||
{
|
||
/* R0 and R1 */
|
||
u64 rx[2][ECC_MAX_DIGITS];
|
||
u64 ry[2][ECC_MAX_DIGITS];
|
||
u64 z[ECC_MAX_DIGITS];
|
||
u64 sk[2][ECC_MAX_DIGITS];
|
||
u64 *curve_prime = curve->p;
|
||
int i, nb;
|
||
int num_bits;
|
||
int carry;
|
||
|
||
carry = vli_add(sk[0], scalar, curve->n, ndigits);
|
||
vli_add(sk[1], sk[0], curve->n, ndigits);
|
||
scalar = sk[!carry];
|
||
num_bits = sizeof(u64) * ndigits * 8 + 1;
|
||
|
||
vli_set(rx[1], point->x, ndigits);
|
||
vli_set(ry[1], point->y, ndigits);
|
||
|
||
xycz_initial_double(rx[1], ry[1], rx[0], ry[0], initial_z, curve);
|
||
|
||
for (i = num_bits - 2; i > 0; i--) {
|
||
nb = !vli_test_bit(scalar, i);
|
||
xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb], curve);
|
||
xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve);
|
||
}
|
||
|
||
nb = !vli_test_bit(scalar, 0);
|
||
xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb], curve);
|
||
|
||
/* Find final 1/Z value. */
|
||
/* X1 - X0 */
|
||
vli_mod_sub(z, rx[1], rx[0], curve_prime, ndigits);
|
||
/* Yb * (X1 - X0) */
|
||
vli_mod_mult_fast(z, z, ry[1 - nb], curve);
|
||
/* xP * Yb * (X1 - X0) */
|
||
vli_mod_mult_fast(z, z, point->x, curve);
|
||
|
||
/* 1 / (xP * Yb * (X1 - X0)) */
|
||
vli_mod_inv(z, z, curve_prime, point->ndigits);
|
||
|
||
/* yP / (xP * Yb * (X1 - X0)) */
|
||
vli_mod_mult_fast(z, z, point->y, curve);
|
||
/* Xb * yP / (xP * Yb * (X1 - X0)) */
|
||
vli_mod_mult_fast(z, z, rx[1 - nb], curve);
|
||
/* End 1/Z calculation */
|
||
|
||
xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve);
|
||
|
||
apply_z(rx[0], ry[0], z, curve);
|
||
|
||
vli_set(result->x, rx[0], ndigits);
|
||
vli_set(result->y, ry[0], ndigits);
|
||
}
|
||
|
||
/* Computes R = P + Q mod p */
|
||
static void ecc_point_add(const struct ecc_point *result,
|
||
const struct ecc_point *p, const struct ecc_point *q,
|
||
const struct ecc_curve *curve)
|
||
{
|
||
u64 z[ECC_MAX_DIGITS];
|
||
u64 px[ECC_MAX_DIGITS];
|
||
u64 py[ECC_MAX_DIGITS];
|
||
unsigned int ndigits = curve->g.ndigits;
|
||
|
||
vli_set(result->x, q->x, ndigits);
|
||
vli_set(result->y, q->y, ndigits);
|
||
vli_mod_sub(z, result->x, p->x, curve->p, ndigits);
|
||
vli_set(px, p->x, ndigits);
|
||
vli_set(py, p->y, ndigits);
|
||
xycz_add(px, py, result->x, result->y, curve);
|
||
vli_mod_inv(z, z, curve->p, ndigits);
|
||
apply_z(result->x, result->y, z, curve);
|
||
}
|
||
|
||
/* Computes R = u1P + u2Q mod p using Shamir's trick.
|
||
* Based on: Kenneth MacKay's micro-ecc (2014).
|
||
*/
|
||
void ecc_point_mult_shamir(const struct ecc_point *result,
|
||
const u64 *u1, const struct ecc_point *p,
|
||
const u64 *u2, const struct ecc_point *q,
|
||
const struct ecc_curve *curve)
|
||
{
|
||
u64 z[ECC_MAX_DIGITS];
|
||
u64 sump[2][ECC_MAX_DIGITS];
|
||
u64 *rx = result->x;
|
||
u64 *ry = result->y;
|
||
unsigned int ndigits = curve->g.ndigits;
|
||
unsigned int num_bits;
|
||
struct ecc_point sum = ECC_POINT_INIT(sump[0], sump[1], ndigits);
|
||
const struct ecc_point *points[4];
|
||
const struct ecc_point *point;
|
||
unsigned int idx;
|
||
int i;
|
||
|
||
ecc_point_add(&sum, p, q, curve);
|
||
points[0] = NULL;
|
||
points[1] = p;
|
||
points[2] = q;
|
||
points[3] = ∑
|
||
|
||
num_bits = max(vli_num_bits(u1, ndigits), vli_num_bits(u2, ndigits));
|
||
i = num_bits - 1;
|
||
idx = (!!vli_test_bit(u1, i)) | ((!!vli_test_bit(u2, i)) << 1);
|
||
point = points[idx];
|
||
|
||
vli_set(rx, point->x, ndigits);
|
||
vli_set(ry, point->y, ndigits);
|
||
vli_clear(z + 1, ndigits - 1);
|
||
z[0] = 1;
|
||
|
||
for (--i; i >= 0; i--) {
|
||
ecc_point_double_jacobian(rx, ry, z, curve);
|
||
idx = (!!vli_test_bit(u1, i)) | ((!!vli_test_bit(u2, i)) << 1);
|
||
point = points[idx];
|
||
if (point) {
|
||
u64 tx[ECC_MAX_DIGITS];
|
||
u64 ty[ECC_MAX_DIGITS];
|
||
u64 tz[ECC_MAX_DIGITS];
|
||
|
||
vli_set(tx, point->x, ndigits);
|
||
vli_set(ty, point->y, ndigits);
|
||
apply_z(tx, ty, z, curve);
|
||
vli_mod_sub(tz, rx, tx, curve->p, ndigits);
|
||
xycz_add(tx, ty, rx, ry, curve);
|
||
vli_mod_mult_fast(z, z, tz, curve);
|
||
}
|
||
}
|
||
vli_mod_inv(z, z, curve->p, ndigits);
|
||
apply_z(rx, ry, z, curve);
|
||
}
|
||
EXPORT_SYMBOL(ecc_point_mult_shamir);
|
||
|
||
static int __ecc_is_key_valid(const struct ecc_curve *curve,
|
||
const u64 *private_key, unsigned int ndigits)
|
||
{
|
||
u64 one[ECC_MAX_DIGITS] = { 1, };
|
||
u64 res[ECC_MAX_DIGITS];
|
||
|
||
if (!private_key)
|
||
return -EINVAL;
|
||
|
||
if (curve->g.ndigits != ndigits)
|
||
return -EINVAL;
|
||
|
||
/* Make sure the private key is in the range [2, n-3]. */
|
||
if (vli_cmp(one, private_key, ndigits) != -1)
|
||
return -EINVAL;
|
||
vli_sub(res, curve->n, one, ndigits);
|
||
vli_sub(res, res, one, ndigits);
|
||
if (vli_cmp(res, private_key, ndigits) != 1)
|
||
return -EINVAL;
|
||
|
||
return 0;
|
||
}
|
||
|
||
int ecc_is_key_valid(unsigned int curve_id, unsigned int ndigits,
|
||
const u64 *private_key, unsigned int private_key_len)
|
||
{
|
||
int nbytes;
|
||
const struct ecc_curve *curve = ecc_get_curve(curve_id);
|
||
|
||
nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT;
|
||
|
||
if (private_key_len != nbytes)
|
||
return -EINVAL;
|
||
|
||
return __ecc_is_key_valid(curve, private_key, ndigits);
|
||
}
|
||
EXPORT_SYMBOL(ecc_is_key_valid);
|
||
|
||
/*
|
||
* ECC private keys are generated using the method of extra random bits,
|
||
* equivalent to that described in FIPS 186-4, Appendix B.4.1.
|
||
*
|
||
* d = (c mod(n–1)) + 1 where c is a string of random bits, 64 bits longer
|
||
* than requested
|
||
* 0 <= c mod(n-1) <= n-2 and implies that
|
||
* 1 <= d <= n-1
|
||
*
|
||
* This method generates a private key uniformly distributed in the range
|
||
* [1, n-1].
|
||
*/
|
||
int ecc_gen_privkey(unsigned int curve_id, unsigned int ndigits, u64 *privkey)
|
||
{
|
||
const struct ecc_curve *curve = ecc_get_curve(curve_id);
|
||
u64 priv[ECC_MAX_DIGITS];
|
||
unsigned int nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT;
|
||
unsigned int nbits = vli_num_bits(curve->n, ndigits);
|
||
int err;
|
||
|
||
/* Check that N is included in Table 1 of FIPS 186-4, section 6.1.1 */
|
||
if (nbits < 160 || ndigits > ARRAY_SIZE(priv))
|
||
return -EINVAL;
|
||
|
||
/*
|
||
* FIPS 186-4 recommends that the private key should be obtained from a
|
||
* RBG with a security strength equal to or greater than the security
|
||
* strength associated with N.
|
||
*
|
||
* The maximum security strength identified by NIST SP800-57pt1r4 for
|
||
* ECC is 256 (N >= 512).
|
||
*
|
||
* This condition is met by the default RNG because it selects a favored
|
||
* DRBG with a security strength of 256.
|
||
*/
|
||
if (crypto_get_default_rng())
|
||
return -EFAULT;
|
||
|
||
err = crypto_rng_get_bytes(crypto_default_rng, (u8 *)priv, nbytes);
|
||
crypto_put_default_rng();
|
||
if (err)
|
||
return err;
|
||
|
||
/* Make sure the private key is in the valid range. */
|
||
if (__ecc_is_key_valid(curve, priv, ndigits))
|
||
return -EINVAL;
|
||
|
||
ecc_swap_digits(priv, privkey, ndigits);
|
||
|
||
return 0;
|
||
}
|
||
EXPORT_SYMBOL(ecc_gen_privkey);
|
||
|
||
int ecc_make_pub_key(unsigned int curve_id, unsigned int ndigits,
|
||
const u64 *private_key, u64 *public_key)
|
||
{
|
||
int ret = 0;
|
||
struct ecc_point *pk;
|
||
u64 priv[ECC_MAX_DIGITS];
|
||
const struct ecc_curve *curve = ecc_get_curve(curve_id);
|
||
|
||
if (!private_key || !curve || ndigits > ARRAY_SIZE(priv)) {
|
||
ret = -EINVAL;
|
||
goto out;
|
||
}
|
||
|
||
ecc_swap_digits(private_key, priv, ndigits);
|
||
|
||
pk = ecc_alloc_point(ndigits);
|
||
if (!pk) {
|
||
ret = -ENOMEM;
|
||
goto out;
|
||
}
|
||
|
||
ecc_point_mult(pk, &curve->g, priv, NULL, curve, ndigits);
|
||
|
||
/* SP800-56A rev 3 5.6.2.1.3 key check */
|
||
if (ecc_is_pubkey_valid_full(curve, pk)) {
|
||
ret = -EAGAIN;
|
||
goto err_free_point;
|
||
}
|
||
|
||
ecc_swap_digits(pk->x, public_key, ndigits);
|
||
ecc_swap_digits(pk->y, &public_key[ndigits], ndigits);
|
||
|
||
err_free_point:
|
||
ecc_free_point(pk);
|
||
out:
|
||
return ret;
|
||
}
|
||
EXPORT_SYMBOL(ecc_make_pub_key);
|
||
|
||
/* SP800-56A section 5.6.2.3.4 partial verification: ephemeral keys only */
|
||
int ecc_is_pubkey_valid_partial(const struct ecc_curve *curve,
|
||
struct ecc_point *pk)
|
||
{
|
||
u64 yy[ECC_MAX_DIGITS], xxx[ECC_MAX_DIGITS], w[ECC_MAX_DIGITS];
|
||
|
||
if (WARN_ON(pk->ndigits != curve->g.ndigits))
|
||
return -EINVAL;
|
||
|
||
/* Check 1: Verify key is not the zero point. */
|
||
if (ecc_point_is_zero(pk))
|
||
return -EINVAL;
|
||
|
||
/* Check 2: Verify key is in the range [1, p-1]. */
|
||
if (vli_cmp(curve->p, pk->x, pk->ndigits) != 1)
|
||
return -EINVAL;
|
||
if (vli_cmp(curve->p, pk->y, pk->ndigits) != 1)
|
||
return -EINVAL;
|
||
|
||
/* Check 3: Verify that y^2 == (x^3 + a·x + b) mod p */
|
||
vli_mod_square_fast(yy, pk->y, curve); /* y^2 */
|
||
vli_mod_square_fast(xxx, pk->x, curve); /* x^2 */
|
||
vli_mod_mult_fast(xxx, xxx, pk->x, curve); /* x^3 */
|
||
vli_mod_mult_fast(w, curve->a, pk->x, curve); /* a·x */
|
||
vli_mod_add(w, w, curve->b, curve->p, pk->ndigits); /* a·x + b */
|
||
vli_mod_add(w, w, xxx, curve->p, pk->ndigits); /* x^3 + a·x + b */
|
||
if (vli_cmp(yy, w, pk->ndigits) != 0) /* Equation */
|
||
return -EINVAL;
|
||
|
||
return 0;
|
||
}
|
||
EXPORT_SYMBOL(ecc_is_pubkey_valid_partial);
|
||
|
||
/* SP800-56A section 5.6.2.3.3 full verification */
|
||
int ecc_is_pubkey_valid_full(const struct ecc_curve *curve,
|
||
struct ecc_point *pk)
|
||
{
|
||
struct ecc_point *nQ;
|
||
|
||
/* Checks 1 through 3 */
|
||
int ret = ecc_is_pubkey_valid_partial(curve, pk);
|
||
|
||
if (ret)
|
||
return ret;
|
||
|
||
/* Check 4: Verify that nQ is the zero point. */
|
||
nQ = ecc_alloc_point(pk->ndigits);
|
||
if (!nQ)
|
||
return -ENOMEM;
|
||
|
||
ecc_point_mult(nQ, pk, curve->n, NULL, curve, pk->ndigits);
|
||
if (!ecc_point_is_zero(nQ))
|
||
ret = -EINVAL;
|
||
|
||
ecc_free_point(nQ);
|
||
|
||
return ret;
|
||
}
|
||
EXPORT_SYMBOL(ecc_is_pubkey_valid_full);
|
||
|
||
int crypto_ecdh_shared_secret(unsigned int curve_id, unsigned int ndigits,
|
||
const u64 *private_key, const u64 *public_key,
|
||
u64 *secret)
|
||
{
|
||
int ret = 0;
|
||
struct ecc_point *product, *pk;
|
||
u64 priv[ECC_MAX_DIGITS];
|
||
u64 rand_z[ECC_MAX_DIGITS];
|
||
unsigned int nbytes;
|
||
const struct ecc_curve *curve = ecc_get_curve(curve_id);
|
||
|
||
if (!private_key || !public_key || !curve ||
|
||
ndigits > ARRAY_SIZE(priv) || ndigits > ARRAY_SIZE(rand_z)) {
|
||
ret = -EINVAL;
|
||
goto out;
|
||
}
|
||
|
||
nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT;
|
||
|
||
get_random_bytes(rand_z, nbytes);
|
||
|
||
pk = ecc_alloc_point(ndigits);
|
||
if (!pk) {
|
||
ret = -ENOMEM;
|
||
goto out;
|
||
}
|
||
|
||
ecc_swap_digits(public_key, pk->x, ndigits);
|
||
ecc_swap_digits(&public_key[ndigits], pk->y, ndigits);
|
||
ret = ecc_is_pubkey_valid_partial(curve, pk);
|
||
if (ret)
|
||
goto err_alloc_product;
|
||
|
||
ecc_swap_digits(private_key, priv, ndigits);
|
||
|
||
product = ecc_alloc_point(ndigits);
|
||
if (!product) {
|
||
ret = -ENOMEM;
|
||
goto err_alloc_product;
|
||
}
|
||
|
||
ecc_point_mult(product, pk, priv, rand_z, curve, ndigits);
|
||
|
||
if (ecc_point_is_zero(product)) {
|
||
ret = -EFAULT;
|
||
goto err_validity;
|
||
}
|
||
|
||
ecc_swap_digits(product->x, secret, ndigits);
|
||
|
||
err_validity:
|
||
memzero_explicit(priv, sizeof(priv));
|
||
memzero_explicit(rand_z, sizeof(rand_z));
|
||
ecc_free_point(product);
|
||
err_alloc_product:
|
||
ecc_free_point(pk);
|
||
out:
|
||
return ret;
|
||
}
|
||
EXPORT_SYMBOL(crypto_ecdh_shared_secret);
|
||
|
||
MODULE_LICENSE("Dual BSD/GPL");
|