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![Vitaly Chikunov](/assets/img/avatar_default.png)
Add Elliptic Curve Russian Digital Signature Algorithm (GOST R 34.10-2012, RFC 7091, ISO/IEC 14888-3) is one of the Russian (and since 2018 the CIS countries) cryptographic standard algorithms (called GOST algorithms). Only signature verification is supported, with intent to be used in the IMA. Summary of the changes: * crypto/Kconfig: - EC-RDSA is added into Public-key cryptography section. * crypto/Makefile: - ecrdsa objects are added. * crypto/asymmetric_keys/x509_cert_parser.c: - Recognize EC-RDSA and Streebog OIDs. * include/linux/oid_registry.h: - EC-RDSA OIDs are added to the enum. Also, a two currently not implemented curve OIDs are added for possible extension later (to not change numbering and grouping). * crypto/ecc.c: - Kenneth MacKay copyright date is updated to 2014, because vli_mmod_slow, ecc_point_add, ecc_point_mult_shamir are based on his code from micro-ecc. - Functions needed for ecrdsa are EXPORT_SYMBOL'ed. - New functions: vli_is_negative - helper to determine sign of vli; vli_from_be64 - unpack big-endian array into vli (used for a signature); vli_from_le64 - unpack little-endian array into vli (used for a public key); vli_uadd, vli_usub - add/sub u64 value to/from vli (used for increment/decrement); mul_64_64 - optimized to use __int128 where appropriate, this speeds up point multiplication (and as a consequence signature verification) by the factor of 1.5-2; vli_umult - multiply vli by a small value (speeds up point multiplication by another factor of 1.5-2, depending on vli sizes); vli_mmod_special - module reduction for some form of Pseudo-Mersenne primes (used for the curves A); vli_mmod_special2 - module reduction for another form of Pseudo-Mersenne primes (used for the curves B); vli_mmod_barrett - module reduction using pre-computed value (used for the curve C); vli_mmod_slow - more general module reduction which is much slower (used when the modulus is subgroup order); vli_mod_mult_slow - modular multiplication; ecc_point_add - add two points; ecc_point_mult_shamir - add two points multiplied by scalars in one combined multiplication (this gives speed up by another factor 2 in compare to two separate multiplications). ecc_is_pubkey_valid_partial - additional samity check is added. - Updated vli_mmod_fast with non-strict heuristic to call optimal module reduction function depending on the prime value; - All computations for the previously defined (two NIST) curves should not unaffected. * crypto/ecc.h: - Newly exported functions are documented. * crypto/ecrdsa_defs.h - Five curves are defined. * crypto/ecrdsa.c: - Signature verification is implemented. * crypto/ecrdsa_params.asn1, crypto/ecrdsa_pub_key.asn1: - Templates for BER decoder for EC-RDSA parameters and public key. Cc: linux-integrity@vger.kernel.org Signed-off-by: Vitaly Chikunov <vt@altlinux.org> Signed-off-by: Herbert Xu <herbert@gondor.apana.org.au>
1510 lines
38 KiB
C
1510 lines
38 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 <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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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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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 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) && defined(__SIZEOF_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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|
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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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|
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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;
|
||
|
||
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]);
|
||
|
||
if (i < k - i) {
|
||
r2 += product.m_high >> 63;
|
||
product.m_high = (product.m_high << 1) |
|
||
(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);
|
||
}
|
||
}
|
||
|
||
/* 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 u64 *curve_prime, unsigned int ndigits)
|
||
{
|
||
u64 tmp[2 * ECC_MAX_DIGITS];
|
||
|
||
/* Currently, both NIST primes have -1 in lowest qword. */
|
||
if (curve_prime[0] != -1ull) {
|
||
/* 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;
|
||
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 u64 *curve_prime, unsigned int ndigits)
|
||
{
|
||
u64 product[2 * ECC_MAX_DIGITS];
|
||
|
||
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 * ECC_MAX_DIGITS];
|
||
|
||
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
|
||
*/
|
||
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 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[ECC_MAX_DIGITS];
|
||
u64 t5[ECC_MAX_DIGITS];
|
||
|
||
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[ECC_MAX_DIGITS];
|
||
|
||
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[ECC_MAX_DIGITS];
|
||
|
||
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[ECC_MAX_DIGITS];
|
||
|
||
/* 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[ECC_MAX_DIGITS];
|
||
u64 t6[ECC_MAX_DIGITS];
|
||
u64 t7[ECC_MAX_DIGITS];
|
||
|
||
/* 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, 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_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);
|
||
}
|
||
|
||
/* 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->p, ndigits);
|
||
vli_mod_inv(z, z, curve->p, ndigits);
|
||
apply_z(result->x, result->y, z, curve->p, ndigits);
|
||
}
|
||
|
||
/* 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->p, ndigits);
|
||
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->p, ndigits);
|
||
vli_mod_sub(tz, rx, tx, curve->p, ndigits);
|
||
xycz_add(tx, ty, rx, ry, curve->p, ndigits);
|
||
vli_mod_mult_fast(z, z, tz, curve->p, ndigits);
|
||
}
|
||
}
|
||
vli_mod_inv(z, z, curve->p, ndigits);
|
||
apply_z(rx, ry, z, curve->p, ndigits);
|
||
}
|
||
EXPORT_SYMBOL(ecc_point_mult_shamir);
|
||
|
||
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]);
|
||
}
|
||
|
||
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);
|
||
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;
|
||
}
|
||
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->p, pk->ndigits); /* y^2 */
|
||
vli_mod_square_fast(xxx, pk->x, curve->p, pk->ndigits); /* x^2 */
|
||
vli_mod_mult_fast(xxx, xxx, pk->x, curve->p, pk->ndigits); /* x^3 */
|
||
vli_mod_mult_fast(w, curve->a, pk->x, curve->p, pk->ndigits); /* 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);
|
||
|
||
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);
|
||
|
||
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;
|
||
}
|
||
EXPORT_SYMBOL(crypto_ecdh_shared_secret);
|
||
|
||
MODULE_LICENSE("Dual BSD/GPL");
|