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6755fd269d
Add support for generating ecc private keys. Generation of ecc private keys is helpful in a user-space to kernel ecdh offload because the keys are not revealed to user-space. Private key generation is also helpful to implement forward secrecy. If the user provides a NULL ecc private key, the kernel will generate it and further use it for ecdh. Move ecdh's object files below drbg's. drbg must be present in the kernel at the time of calling. Signed-off-by: Tudor Ambarus <tudor.ambarus@microchip.com> Reviewed-by: Stephan Müller <smueller@chronox.de> Signed-off-by: Herbert Xu <herbert@gondor.apana.org.au>
1071 lines
26 KiB
C
1071 lines
26 KiB
C
/*
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* Copyright (c) 2013, Kenneth MacKay
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* All rights reserved.
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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 <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 "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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static inline 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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default:
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return NULL;
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}
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}
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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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kzfree(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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kzfree(p->x);
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kzfree(p->y);
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kzfree(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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static 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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/* Returns nonzero if bit 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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/* 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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/* 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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static 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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/* 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 borrow. Can modify in place. */
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static 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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static uint128_t mul_64_64(u64 left, u64 right)
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{
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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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uint128_t result;
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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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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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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 };
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u64 r2 = 0;
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int i, k;
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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 <= k - i; i++) {
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uint128_t product;
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product = mul_64_64(left[i], left[k - i]);
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if (i < k - i) {
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r2 += product.m_high >> 63;
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product.m_high = (product.m_high << 1) |
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(product.m_low >> 63);
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product.m_low <<= 1;
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}
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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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/* Computes result = (left + right) % mod.
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* Assumes that left < mod and right < mod, result != mod.
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*/
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static void vli_mod_add(u64 *result, const u64 *left, const u64 *right,
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const u64 *mod, unsigned int ndigits)
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{
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u64 carry;
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carry = vli_add(result, left, right, ndigits);
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/* result > mod (result = mod + remainder), so subtract mod to
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* get remainder.
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*/
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if (carry || vli_cmp(result, mod, ndigits) >= 0)
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vli_sub(result, result, mod, ndigits);
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}
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/* Computes result = (left - right) % mod.
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* Assumes that left < mod and right < mod, result != mod.
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*/
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static void vli_mod_sub(u64 *result, const u64 *left, const u64 *right,
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const u64 *mod, unsigned int ndigits)
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{
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u64 borrow = vli_sub(result, left, right, ndigits);
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/* In this case, p_result == -diff == (max int) - diff.
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* Since -x % d == d - x, we can get the correct result from
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* result + mod (with overflow).
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*/
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if (borrow)
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vli_add(result, result, mod, ndigits);
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}
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/* Computes p_result = p_product % curve_p.
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* See algorithm 5 and 6 from
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* http://www.isys.uni-klu.ac.at/PDF/2001-0126-MT.pdf
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*/
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static void vli_mmod_fast_192(u64 *result, const u64 *product,
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const u64 *curve_prime, u64 *tmp)
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{
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const unsigned int ndigits = 3;
|
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int carry;
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vli_set(result, product, ndigits);
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vli_set(tmp, &product[3], ndigits);
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carry = vli_add(result, result, tmp, ndigits);
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tmp[0] = 0;
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tmp[1] = product[3];
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tmp[2] = product[4];
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carry += vli_add(result, result, tmp, ndigits);
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tmp[0] = tmp[1] = product[5];
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tmp[2] = 0;
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carry += vli_add(result, result, tmp, ndigits);
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while (carry || vli_cmp(curve_prime, result, ndigits) != 1)
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carry -= vli_sub(result, result, curve_prime, ndigits);
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}
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/* Computes result = product % curve_prime
|
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* from http://www.nsa.gov/ia/_files/nist-routines.pdf
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*/
|
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static void vli_mmod_fast_256(u64 *result, const u64 *product,
|
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const u64 *curve_prime, u64 *tmp)
|
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{
|
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int carry;
|
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const unsigned int ndigits = 4;
|
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|
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/* t */
|
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vli_set(result, product, ndigits);
|
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|
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/* s1 */
|
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tmp[0] = 0;
|
||
tmp[1] = product[5] & 0xffffffff00000000ull;
|
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tmp[2] = product[6];
|
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tmp[3] = product[7];
|
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carry = vli_lshift(tmp, tmp, 1, ndigits);
|
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carry += vli_add(result, result, tmp, ndigits);
|
||
|
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/* s2 */
|
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tmp[1] = product[6] << 32;
|
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tmp[2] = (product[6] >> 32) | (product[7] << 32);
|
||
tmp[3] = product[7] >> 32;
|
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carry += vli_lshift(tmp, tmp, 1, ndigits);
|
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carry += vli_add(result, result, tmp, ndigits);
|
||
|
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/* s3 */
|
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tmp[0] = product[4];
|
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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);
|
||
}
|
||
}
|
||
|
||
/* Computes result = product % curve_prime
|
||
* from http://www.nsa.gov/ia/_files/nist-routines.pdf
|
||
*/
|
||
static bool vli_mmod_fast(u64 *result, u64 *product,
|
||
const u64 *curve_prime, unsigned int ndigits)
|
||
{
|
||
u64 tmp[2 * ndigits];
|
||
|
||
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;
|
||
default:
|
||
pr_err("unsupports digits size!\n");
|
||
return false;
|
||
}
|
||
|
||
return true;
|
||
}
|
||
|
||
/* Computes result = (left * right) % curve_prime. */
|
||
static void vli_mod_mult_fast(u64 *result, const u64 *left, const u64 *right,
|
||
const u64 *curve_prime, unsigned int ndigits)
|
||
{
|
||
u64 product[2 * ndigits];
|
||
|
||
vli_mult(product, left, right, ndigits);
|
||
vli_mmod_fast(result, product, curve_prime, ndigits);
|
||
}
|
||
|
||
/* Computes result = left^2 % curve_prime. */
|
||
static void vli_mod_square_fast(u64 *result, const u64 *left,
|
||
const u64 *curve_prime, unsigned int ndigits)
|
||
{
|
||
u64 product[2 * ndigits];
|
||
|
||
vli_square(product, left, ndigits);
|
||
vli_mmod_fast(result, product, curve_prime, ndigits);
|
||
}
|
||
|
||
#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
|
||
*/
|
||
static void vli_mod_inv(u64 *result, const u64 *input, const u64 *mod,
|
||
unsigned int ndigits)
|
||
{
|
||
u64 a[ndigits], b[ndigits];
|
||
u64 u[ndigits], v[ndigits];
|
||
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);
|
||
}
|
||
|
||
/* ------ 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 http://eprint.iacr.org/2011/338.pdf
|
||
*/
|
||
|
||
/* Double in place */
|
||
static void ecc_point_double_jacobian(u64 *x1, u64 *y1, u64 *z1,
|
||
u64 *curve_prime, unsigned int ndigits)
|
||
{
|
||
/* t1 = x, t2 = y, t3 = z */
|
||
u64 t4[ndigits];
|
||
u64 t5[ndigits];
|
||
|
||
if (vli_is_zero(z1, ndigits))
|
||
return;
|
||
|
||
/* t4 = y1^2 */
|
||
vli_mod_square_fast(t4, y1, curve_prime, ndigits);
|
||
/* t5 = x1*y1^2 = A */
|
||
vli_mod_mult_fast(t5, x1, t4, curve_prime, ndigits);
|
||
/* t4 = y1^4 */
|
||
vli_mod_square_fast(t4, t4, curve_prime, ndigits);
|
||
/* t2 = y1*z1 = z3 */
|
||
vli_mod_mult_fast(y1, y1, z1, curve_prime, ndigits);
|
||
/* t3 = z1^2 */
|
||
vli_mod_square_fast(z1, z1, curve_prime, ndigits);
|
||
|
||
/* 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_prime, ndigits);
|
||
|
||
/* 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_prime, ndigits);
|
||
/* 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_prime, ndigits);
|
||
/* 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, u64 *curve_prime,
|
||
unsigned int ndigits)
|
||
{
|
||
u64 t1[ndigits];
|
||
|
||
vli_mod_square_fast(t1, z, curve_prime, ndigits); /* z^2 */
|
||
vli_mod_mult_fast(x1, x1, t1, curve_prime, ndigits); /* x1 * z^2 */
|
||
vli_mod_mult_fast(t1, t1, z, curve_prime, ndigits); /* z^3 */
|
||
vli_mod_mult_fast(y1, y1, t1, curve_prime, ndigits); /* 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, u64 *curve_prime,
|
||
unsigned int ndigits)
|
||
{
|
||
u64 z[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_prime, ndigits);
|
||
|
||
ecc_point_double_jacobian(x1, y1, z, curve_prime, ndigits);
|
||
|
||
apply_z(x2, y2, z, curve_prime, ndigits);
|
||
}
|
||
|
||
/* 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, u64 *curve_prime,
|
||
unsigned int ndigits)
|
||
{
|
||
/* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
|
||
u64 t5[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_prime, ndigits);
|
||
/* t1 = x1*A = B */
|
||
vli_mod_mult_fast(x1, x1, t5, curve_prime, ndigits);
|
||
/* t3 = x2*A = C */
|
||
vli_mod_mult_fast(x2, x2, t5, curve_prime, ndigits);
|
||
/* t4 = y2 - y1 */
|
||
vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
|
||
/* t5 = (y2 - y1)^2 = D */
|
||
vli_mod_square_fast(t5, y2, curve_prime, ndigits);
|
||
|
||
/* 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_prime, ndigits);
|
||
/* 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_prime, ndigits);
|
||
/* 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, u64 *curve_prime,
|
||
unsigned int ndigits)
|
||
{
|
||
/* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
|
||
u64 t5[ndigits];
|
||
u64 t6[ndigits];
|
||
u64 t7[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_prime, ndigits);
|
||
/* t1 = x1*A = B */
|
||
vli_mod_mult_fast(x1, x1, t5, curve_prime, ndigits);
|
||
/* t3 = x2*A = C */
|
||
vli_mod_mult_fast(x2, x2, t5, curve_prime, ndigits);
|
||
/* 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_prime, ndigits);
|
||
/* t6 = B + C */
|
||
vli_mod_add(t6, x1, x2, curve_prime, ndigits);
|
||
/* t3 = (y2 - y1)^2 */
|
||
vli_mod_square_fast(x2, y2, curve_prime, ndigits);
|
||
/* 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_prime, ndigits);
|
||
/* t4 = y3 */
|
||
vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
|
||
|
||
/* t7 = (y2 + y1)^2 = F */
|
||
vli_mod_square_fast(t7, t5, curve_prime, ndigits);
|
||
/* 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_prime, ndigits);
|
||
/* 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, u64 *curve_prime,
|
||
unsigned int ndigits)
|
||
{
|
||
/* R0 and R1 */
|
||
u64 rx[2][ndigits];
|
||
u64 ry[2][ndigits];
|
||
u64 z[ndigits];
|
||
int i, nb;
|
||
int num_bits = vli_num_bits(scalar, ndigits);
|
||
|
||
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_prime,
|
||
ndigits);
|
||
|
||
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_prime,
|
||
ndigits);
|
||
xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve_prime,
|
||
ndigits);
|
||
}
|
||
|
||
nb = !vli_test_bit(scalar, 0);
|
||
xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb], curve_prime,
|
||
ndigits);
|
||
|
||
/* 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_prime, ndigits);
|
||
/* xP * Yb * (X1 - X0) */
|
||
vli_mod_mult_fast(z, z, point->x, curve_prime, ndigits);
|
||
|
||
/* 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_prime, ndigits);
|
||
/* Xb * yP / (xP * Yb * (X1 - X0)) */
|
||
vli_mod_mult_fast(z, z, rx[1 - nb], curve_prime, ndigits);
|
||
/* End 1/Z calculation */
|
||
|
||
xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve_prime, ndigits);
|
||
|
||
apply_z(rx[0], ry[0], z, curve_prime, ndigits);
|
||
|
||
vli_set(result->x, rx[0], ndigits);
|
||
vli_set(result->y, ry[0], ndigits);
|
||
}
|
||
|
||
static inline void ecc_swap_digits(const u64 *in, u64 *out,
|
||
unsigned int ndigits)
|
||
{
|
||
int i;
|
||
|
||
for (i = 0; i < ndigits; i++)
|
||
out[i] = __swab64(in[ndigits - 1 - i]);
|
||
}
|
||
|
||
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);
|
||
|
||
if (!private_key)
|
||
return -EINVAL;
|
||
|
||
nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT;
|
||
|
||
if (private_key_len != nbytes)
|
||
return -EINVAL;
|
||
|
||
if (vli_is_zero(private_key, ndigits))
|
||
return -EINVAL;
|
||
|
||
/* Make sure the private key is in the range [1, n-1]. */
|
||
if (vli_cmp(curve->n, private_key, ndigits) != 1)
|
||
return -EINVAL;
|
||
|
||
return 0;
|
||
}
|
||
|
||
/*
|
||
* 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[ndigits];
|
||
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)
|
||
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())
|
||
err = -EFAULT;
|
||
|
||
err = crypto_rng_get_bytes(crypto_default_rng, (u8 *)priv, nbytes);
|
||
crypto_put_default_rng();
|
||
if (err)
|
||
return err;
|
||
|
||
if (vli_is_zero(priv, ndigits))
|
||
return -EINVAL;
|
||
|
||
/* Make sure the private key is in the range [1, n-1]. */
|
||
if (vli_cmp(curve->n, priv, ndigits) != 1)
|
||
return -EINVAL;
|
||
|
||
ecc_swap_digits(priv, privkey, ndigits);
|
||
|
||
return 0;
|
||
}
|
||
|
||
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[ndigits];
|
||
const struct ecc_curve *curve = ecc_get_curve(curve_id);
|
||
|
||
if (!private_key || !curve) {
|
||
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->p, ndigits);
|
||
if (ecc_point_is_zero(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;
|
||
}
|
||
|
||
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[ndigits];
|
||
u64 rand_z[ndigits];
|
||
unsigned int nbytes;
|
||
const struct ecc_curve *curve = ecc_get_curve(curve_id);
|
||
|
||
if (!private_key || !public_key || !curve) {
|
||
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;
|
||
}
|
||
|
||
product = ecc_alloc_point(ndigits);
|
||
if (!product) {
|
||
ret = -ENOMEM;
|
||
goto err_alloc_product;
|
||
}
|
||
|
||
ecc_swap_digits(public_key, pk->x, ndigits);
|
||
ecc_swap_digits(&public_key[ndigits], pk->y, ndigits);
|
||
ecc_swap_digits(private_key, priv, ndigits);
|
||
|
||
ecc_point_mult(product, pk, priv, rand_z, curve->p, ndigits);
|
||
|
||
ecc_swap_digits(product->x, secret, ndigits);
|
||
|
||
if (ecc_point_is_zero(product))
|
||
ret = -EFAULT;
|
||
|
||
ecc_free_point(product);
|
||
err_alloc_product:
|
||
ecc_free_point(pk);
|
||
out:
|
||
return ret;
|
||
}
|