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1664 lines
42 KiB
1664 lines
42 KiB
/* |
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* Copyright (c) 2013, 2014 Kenneth MacKay. All rights reserved. |
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* Copyright (c) 2019 Vitaly Chikunov <[email protected]> |
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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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|
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#include <crypto/ecc_curve.h> |
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#include <linux/module.h> |
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#include <linux/random.h> |
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#include <linux/slab.h> |
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#include <linux/swab.h> |
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#include <linux/fips.h> |
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#include <crypto/ecdh.h> |
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#include <crypto/rng.h> |
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#include <asm/unaligned.h> |
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#include <linux/ratelimit.h> |
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|
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#include "ecc.h" |
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#include "ecc_curve_defs.h" |
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|
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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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|
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/* Returns curv25519 curve param */ |
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const struct ecc_curve *ecc_get_curve25519(void) |
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{ |
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return &ecc_25519; |
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} |
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EXPORT_SYMBOL(ecc_get_curve25519); |
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|
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const struct ecc_curve *ecc_get_curve(unsigned int curve_id) |
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{ |
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switch (curve_id) { |
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/* In FIPS mode only allow P256 and higher */ |
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case ECC_CURVE_NIST_P192: |
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return fips_enabled ? NULL : &nist_p192; |
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case ECC_CURVE_NIST_P256: |
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return &nist_p256; |
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case ECC_CURVE_NIST_P384: |
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return &nist_p384; |
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default: |
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return NULL; |
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} |
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} |
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EXPORT_SYMBOL(ecc_get_curve); |
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|
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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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|
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if (!len) |
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return NULL; |
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|
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return kmalloc(len, GFP_KERNEL); |
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} |
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|
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static void ecc_free_digits_space(u64 *space) |
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{ |
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kfree_sensitive(space); |
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} |
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|
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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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|
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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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|
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static void ecc_free_point(struct ecc_point *p) |
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{ |
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if (!p) |
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return; |
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kfree_sensitive(p->x); |
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kfree_sensitive(p->y); |
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kfree_sensitive(p); |
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} |
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|
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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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|
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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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|
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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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|
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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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|
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return true; |
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} |
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EXPORT_SYMBOL(vli_is_zero); |
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|
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/* Returns nonzero if bit of vli is set. */ |
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static u64 vli_test_bit(const u64 *vli, unsigned int bit) |
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{ |
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return (vli[bit / 64] & ((u64)1 << (bit % 64))); |
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} |
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static bool vli_is_negative(const u64 *vli, unsigned int ndigits) |
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{ |
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return vli_test_bit(vli, ndigits * 64 - 1); |
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} |
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|
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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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|
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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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|
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return (i + 1); |
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} |
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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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|
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return ((num_digits - 1) * 64 + i); |
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} |
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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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|
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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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|
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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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|
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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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|
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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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|
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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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|
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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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|
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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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|
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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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|
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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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|
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/* Computes result = left - right, returning borrow. Can modify in place. */ |
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u64 vli_sub(u64 *result, const u64 *left, const u64 *right, |
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unsigned int ndigits) |
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{ |
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u64 borrow = 0; |
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int i; |
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for (i = 0; i < ndigits; i++) { |
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u64 diff; |
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diff = left[i] - right[i] - borrow; |
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if (diff != left[i]) |
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borrow = (diff > left[i]); |
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result[i] = diff; |
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} |
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return borrow; |
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} |
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EXPORT_SYMBOL(vli_sub); |
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/* Computes result = left - right, returning borrow. Can modify in place. */ |
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static u64 vli_usub(u64 *result, const u64 *left, u64 right, |
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unsigned int ndigits) |
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{ |
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u64 borrow = right; |
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int i; |
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for (i = 0; i < ndigits; i++) { |
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u64 diff; |
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diff = left[i] - borrow; |
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if (diff != left[i]) |
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borrow = (diff > left[i]); |
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result[i] = diff; |
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} |
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return borrow; |
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} |
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static uint128_t mul_64_64(u64 left, u64 right) |
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{ |
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uint128_t result; |
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#if defined(CONFIG_ARCH_SUPPORTS_INT128) |
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unsigned __int128 m = (unsigned __int128)left * right; |
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result.m_low = m; |
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result.m_high = m >> 64; |
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#else |
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u64 a0 = left & 0xffffffffull; |
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u64 a1 = left >> 32; |
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u64 b0 = right & 0xffffffffull; |
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u64 b1 = right >> 32; |
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u64 m0 = a0 * b0; |
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u64 m1 = a0 * b1; |
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u64 m2 = a1 * b0; |
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u64 m3 = a1 * b1; |
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m2 += (m0 >> 32); |
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m2 += m1; |
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|
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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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|
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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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|
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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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|
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result[ndigits * 2 - 1] = r01.m_low; |
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} |
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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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|
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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; |
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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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|
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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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|
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for (i = min; i <= k && i <= k - i; i++) { |
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uint128_t product; |
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|
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product = mul_64_64(left[i], left[k - i]); |
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|
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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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|
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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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|
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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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|
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result[ndigits * 2 - 1] = r01.m_low; |
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} |
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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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|
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carry = vli_add(result, left, right, ndigits); |
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|
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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. |
|
* Since -x % d == d - x, we can get the correct result from |
|
* result + mod (with overflow). |
|
*/ |
|
if (borrow) |
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vli_add(result, result, mod, ndigits); |
|
} |
|
|
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/* |
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* Computes result = product % mod |
|
* for special form moduli: p = 2^k-c, for small c (note the minus sign) |
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* |
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* References: |
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* R. Crandall, C. Pomerance. Prime Numbers: A Computational Perspective. |
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* 9 Fast Algorithms for Large-Integer Arithmetic. 9.2.3 Moduli of special form |
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* Algorithm 9.2.13 (Fast mod operation for special-form moduli). |
|
*/ |
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static void vli_mmod_special(u64 *result, const u64 *product, |
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const u64 *mod, unsigned int ndigits) |
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{ |
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u64 c = -mod[0]; |
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u64 t[ECC_MAX_DIGITS * 2]; |
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u64 r[ECC_MAX_DIGITS * 2]; |
|
|
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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); |
|
} |
|
|
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/* |
|
* 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, |
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const u64 *mod, unsigned int ndigits) |
|
{ |
|
u64 c2 = mod[0] * 2; |
|
u64 q[ECC_MAX_DIGITS]; |
|
u64 r[ECC_MAX_DIGITS * 2]; |
|
u64 m[ECC_MAX_DIGITS * 2]; /* expanded mod */ |
|
int carry; /* last bit that doesn't fit into q */ |
|
int i; |
|
|
|
vli_set(m, mod, ndigits); |
|
vli_clear(m + ndigits, ndigits); |
|
|
|
vli_set(r, product, ndigits); |
|
/* q and carry are top bits */ |
|
vli_set(q, product + ndigits, ndigits); |
|
vli_clear(r + ndigits, ndigits); |
|
carry = vli_is_negative(r, ndigits); |
|
if (carry) |
|
r[ndigits - 1] &= (1ull << 63) - 1; |
|
for (i = 1; carry || !vli_is_zero(q, ndigits); i++) { |
|
u64 qc[ECC_MAX_DIGITS * 2]; |
|
|
|
vli_umult(qc, q, c2, ndigits); |
|
if (carry) |
|
vli_uadd(qc, qc, mod[0], ndigits * 2); |
|
vli_set(q, qc + ndigits, ndigits); |
|
vli_clear(qc + ndigits, ndigits); |
|
carry = vli_is_negative(qc, ndigits); |
|
if (carry) |
|
qc[ndigits - 1] &= (1ull << 63) - 1; |
|
if (i & 1) |
|
vli_sub(r, r, qc, ndigits * 2); |
|
else |
|
vli_add(r, r, qc, ndigits * 2); |
|
} |
|
while (vli_is_negative(r, ndigits * 2)) |
|
vli_add(r, r, m, ndigits * 2); |
|
while (vli_cmp(r, m, ndigits * 2) >= 0) |
|
vli_sub(r, r, m, ndigits * 2); |
|
|
|
vli_set(result, r, ndigits); |
|
} |
|
|
|
/* |
|
* Computes result = product % mod, where product is 2N words long. |
|
* Reference: Ken MacKay's micro-ecc. |
|
* Currently only designed to work for curve_p or curve_n. |
|
*/ |
|
static void vli_mmod_slow(u64 *result, u64 *product, const u64 *mod, |
|
unsigned int ndigits) |
|
{ |
|
u64 mod_m[2 * ECC_MAX_DIGITS]; |
|
u64 tmp[2 * ECC_MAX_DIGITS]; |
|
u64 *v[2] = { tmp, product }; |
|
u64 carry = 0; |
|
unsigned int i; |
|
/* Shift mod so its highest set bit is at the maximum position. */ |
|
int shift = (ndigits * 2 * 64) - vli_num_bits(mod, ndigits); |
|
int word_shift = shift / 64; |
|
int bit_shift = shift % 64; |
|
|
|
vli_clear(mod_m, word_shift); |
|
if (bit_shift > 0) { |
|
for (i = 0; i < ndigits; ++i) { |
|
mod_m[word_shift + i] = (mod[i] << bit_shift) | carry; |
|
carry = mod[i] >> (64 - bit_shift); |
|
} |
|
} else |
|
vli_set(mod_m + word_shift, mod, ndigits); |
|
|
|
for (i = 1; shift >= 0; --shift) { |
|
u64 borrow = 0; |
|
unsigned int j; |
|
|
|
for (j = 0; j < ndigits * 2; ++j) { |
|
u64 diff = v[i][j] - mod_m[j] - borrow; |
|
|
|
if (diff != v[i][j]) |
|
borrow = (diff > v[i][j]); |
|
v[1 - i][j] = diff; |
|
} |
|
i = !(i ^ borrow); /* Swap the index if there was no borrow */ |
|
vli_rshift1(mod_m, ndigits); |
|
mod_m[ndigits - 1] |= mod_m[ndigits] << (64 - 1); |
|
vli_rshift1(mod_m + ndigits, ndigits); |
|
} |
|
vli_set(result, v[i], ndigits); |
|
} |
|
|
|
/* Computes result = product % mod using Barrett's reduction with precomputed |
|
* value mu appended to the mod after ndigits, mu = (2^{2w} / mod) and have |
|
* length ndigits + 1, where mu * (2^w - 1) should not overflow ndigits |
|
* boundary. |
|
* |
|
* Reference: |
|
* R. Brent, P. Zimmermann. Modern Computer Arithmetic. 2010. |
|
* 2.4.1 Barrett's algorithm. Algorithm 2.5. |
|
*/ |
|
static void vli_mmod_barrett(u64 *result, u64 *product, const u64 *mod, |
|
unsigned int ndigits) |
|
{ |
|
u64 q[ECC_MAX_DIGITS * 2]; |
|
u64 r[ECC_MAX_DIGITS * 2]; |
|
const u64 *mu = mod + ndigits; |
|
|
|
vli_mult(q, product + ndigits, mu, ndigits); |
|
if (mu[ndigits]) |
|
vli_add(q + ndigits, q + ndigits, product + ndigits, ndigits); |
|
vli_mult(r, mod, q + ndigits, ndigits); |
|
vli_sub(r, product, r, ndigits * 2); |
|
while (!vli_is_zero(r + ndigits, ndigits) || |
|
vli_cmp(r, mod, ndigits) != -1) { |
|
u64 carry; |
|
|
|
carry = vli_sub(r, r, mod, ndigits); |
|
vli_usub(r + ndigits, r + ndigits, carry, ndigits); |
|
} |
|
vli_set(result, r, ndigits); |
|
} |
|
|
|
/* Computes p_result = p_product % curve_p. |
|
* See algorithm 5 and 6 from |
|
* http://www.isys.uni-klu.ac.at/PDF/2001-0126-MT.pdf |
|
*/ |
|
static void vli_mmod_fast_192(u64 *result, const u64 *product, |
|
const u64 *curve_prime, u64 *tmp) |
|
{ |
|
const unsigned int ndigits = 3; |
|
int carry; |
|
|
|
vli_set(result, product, ndigits); |
|
|
|
vli_set(tmp, &product[3], ndigits); |
|
carry = vli_add(result, result, tmp, ndigits); |
|
|
|
tmp[0] = 0; |
|
tmp[1] = product[3]; |
|
tmp[2] = product[4]; |
|
carry += vli_add(result, result, tmp, ndigits); |
|
|
|
tmp[0] = tmp[1] = product[5]; |
|
tmp[2] = 0; |
|
carry += vli_add(result, result, tmp, ndigits); |
|
|
|
while (carry || vli_cmp(curve_prime, result, ndigits) != 1) |
|
carry -= vli_sub(result, result, curve_prime, ndigits); |
|
} |
|
|
|
/* Computes result = product % curve_prime |
|
* from http://www.nsa.gov/ia/_files/nist-routines.pdf |
|
*/ |
|
static void vli_mmod_fast_256(u64 *result, const u64 *product, |
|
const u64 *curve_prime, u64 *tmp) |
|
{ |
|
int carry; |
|
const unsigned int ndigits = 4; |
|
|
|
/* t */ |
|
vli_set(result, product, ndigits); |
|
|
|
/* s1 */ |
|
tmp[0] = 0; |
|
tmp[1] = product[5] & 0xffffffff00000000ull; |
|
tmp[2] = product[6]; |
|
tmp[3] = product[7]; |
|
carry = vli_lshift(tmp, tmp, 1, ndigits); |
|
carry += vli_add(result, result, tmp, ndigits); |
|
|
|
/* s2 */ |
|
tmp[1] = product[6] << 32; |
|
tmp[2] = (product[6] >> 32) | (product[7] << 32); |
|
tmp[3] = product[7] >> 32; |
|
carry += vli_lshift(tmp, tmp, 1, ndigits); |
|
carry += vli_add(result, result, tmp, ndigits); |
|
|
|
/* s3 */ |
|
tmp[0] = product[4]; |
|
tmp[1] = product[5] & 0xffffffff; |
|
tmp[2] = 0; |
|
tmp[3] = product[7]; |
|
carry += vli_add(result, result, tmp, ndigits); |
|
|
|
/* s4 */ |
|
tmp[0] = (product[4] >> 32) | (product[5] << 32); |
|
tmp[1] = (product[5] >> 32) | (product[6] & 0xffffffff00000000ull); |
|
tmp[2] = product[7]; |
|
tmp[3] = (product[6] >> 32) | (product[4] << 32); |
|
carry += vli_add(result, result, tmp, ndigits); |
|
|
|
/* d1 */ |
|
tmp[0] = (product[5] >> 32) | (product[6] << 32); |
|
tmp[1] = (product[6] >> 32); |
|
tmp[2] = 0; |
|
tmp[3] = (product[4] & 0xffffffff) | (product[5] << 32); |
|
carry -= vli_sub(result, result, tmp, ndigits); |
|
|
|
/* d2 */ |
|
tmp[0] = product[6]; |
|
tmp[1] = product[7]; |
|
tmp[2] = 0; |
|
tmp[3] = (product[4] >> 32) | (product[5] & 0xffffffff00000000ull); |
|
carry -= vli_sub(result, result, tmp, ndigits); |
|
|
|
/* d3 */ |
|
tmp[0] = (product[6] >> 32) | (product[7] << 32); |
|
tmp[1] = (product[7] >> 32) | (product[4] << 32); |
|
tmp[2] = (product[4] >> 32) | (product[5] << 32); |
|
tmp[3] = (product[6] << 32); |
|
carry -= vli_sub(result, result, tmp, ndigits); |
|
|
|
/* d4 */ |
|
tmp[0] = product[7]; |
|
tmp[1] = product[4] & 0xffffffff00000000ull; |
|
tmp[2] = product[5]; |
|
tmp[3] = product[6] & 0xffffffff00000000ull; |
|
carry -= vli_sub(result, result, tmp, ndigits); |
|
|
|
if (carry < 0) { |
|
do { |
|
carry += vli_add(result, result, curve_prime, ndigits); |
|
} while (carry < 0); |
|
} else { |
|
while (carry || vli_cmp(curve_prime, result, ndigits) != 1) |
|
carry -= vli_sub(result, result, curve_prime, ndigits); |
|
} |
|
} |
|
|
|
#define SL32OR32(x32, y32) (((u64)x32 << 32) | y32) |
|
#define AND64H(x64) (x64 & 0xffFFffFF00000000ull) |
|
#define AND64L(x64) (x64 & 0x00000000ffFFffFFull) |
|
|
|
/* Computes result = product % curve_prime |
|
* from "Mathematical routines for the NIST prime elliptic curves" |
|
*/ |
|
static void vli_mmod_fast_384(u64 *result, const u64 *product, |
|
const u64 *curve_prime, u64 *tmp) |
|
{ |
|
int carry; |
|
const unsigned int ndigits = 6; |
|
|
|
/* t */ |
|
vli_set(result, product, ndigits); |
|
|
|
/* s1 */ |
|
tmp[0] = 0; // 0 || 0 |
|
tmp[1] = 0; // 0 || 0 |
|
tmp[2] = SL32OR32(product[11], (product[10]>>32)); //a22||a21 |
|
tmp[3] = product[11]>>32; // 0 ||a23 |
|
tmp[4] = 0; // 0 || 0 |
|
tmp[5] = 0; // 0 || 0 |
|
carry = vli_lshift(tmp, tmp, 1, ndigits); |
|
carry += vli_add(result, result, tmp, ndigits); |
|
|
|
/* s2 */ |
|
tmp[0] = product[6]; //a13||a12 |
|
tmp[1] = product[7]; //a15||a14 |
|
tmp[2] = product[8]; //a17||a16 |
|
tmp[3] = product[9]; //a19||a18 |
|
tmp[4] = product[10]; //a21||a20 |
|
tmp[5] = product[11]; //a23||a22 |
|
carry += vli_add(result, result, tmp, ndigits); |
|
|
|
/* s3 */ |
|
tmp[0] = SL32OR32(product[11], (product[10]>>32)); //a22||a21 |
|
tmp[1] = SL32OR32(product[6], (product[11]>>32)); //a12||a23 |
|
tmp[2] = SL32OR32(product[7], (product[6])>>32); //a14||a13 |
|
tmp[3] = SL32OR32(product[8], (product[7]>>32)); //a16||a15 |
|
tmp[4] = SL32OR32(product[9], (product[8]>>32)); //a18||a17 |
|
tmp[5] = SL32OR32(product[10], (product[9]>>32)); //a20||a19 |
|
carry += vli_add(result, result, tmp, ndigits); |
|
|
|
/* s4 */ |
|
tmp[0] = AND64H(product[11]); //a23|| 0 |
|
tmp[1] = (product[10]<<32); //a20|| 0 |
|
tmp[2] = product[6]; //a13||a12 |
|
tmp[3] = product[7]; //a15||a14 |
|
tmp[4] = product[8]; //a17||a16 |
|
tmp[5] = product[9]; //a19||a18 |
|
carry += vli_add(result, result, tmp, ndigits); |
|
|
|
/* s5 */ |
|
tmp[0] = 0; // 0|| 0 |
|
tmp[1] = 0; // 0|| 0 |
|
tmp[2] = product[10]; //a21||a20 |
|
tmp[3] = product[11]; //a23||a22 |
|
tmp[4] = 0; // 0|| 0 |
|
tmp[5] = 0; // 0|| 0 |
|
carry += vli_add(result, result, tmp, ndigits); |
|
|
|
/* s6 */ |
|
tmp[0] = AND64L(product[10]); // 0 ||a20 |
|
tmp[1] = AND64H(product[10]); //a21|| 0 |
|
tmp[2] = product[11]; //a23||a22 |
|
tmp[3] = 0; // 0 || 0 |
|
tmp[4] = 0; // 0 || 0 |
|
tmp[5] = 0; // 0 || 0 |
|
carry += vli_add(result, result, tmp, ndigits); |
|
|
|
/* d1 */ |
|
tmp[0] = SL32OR32(product[6], (product[11]>>32)); //a12||a23 |
|
tmp[1] = SL32OR32(product[7], (product[6]>>32)); //a14||a13 |
|
tmp[2] = SL32OR32(product[8], (product[7]>>32)); //a16||a15 |
|
tmp[3] = SL32OR32(product[9], (product[8]>>32)); //a18||a17 |
|
tmp[4] = SL32OR32(product[10], (product[9]>>32)); //a20||a19 |
|
tmp[5] = SL32OR32(product[11], (product[10]>>32)); //a22||a21 |
|
carry -= vli_sub(result, result, tmp, ndigits); |
|
|
|
/* d2 */ |
|
tmp[0] = (product[10]<<32); //a20|| 0 |
|
tmp[1] = SL32OR32(product[11], (product[10]>>32)); //a22||a21 |
|
tmp[2] = (product[11]>>32); // 0 ||a23 |
|
tmp[3] = 0; // 0 || 0 |
|
tmp[4] = 0; // 0 || 0 |
|
tmp[5] = 0; // 0 || 0 |
|
carry -= vli_sub(result, result, tmp, ndigits); |
|
|
|
/* d3 */ |
|
tmp[0] = 0; // 0 || 0 |
|
tmp[1] = AND64H(product[11]); //a23|| 0 |
|
tmp[2] = product[11]>>32; // 0 ||a23 |
|
tmp[3] = 0; // 0 || 0 |
|
tmp[4] = 0; // 0 || 0 |
|
tmp[5] = 0; // 0 || 0 |
|
carry -= vli_sub(result, result, tmp, ndigits); |
|
|
|
if (carry < 0) { |
|
do { |
|
carry += vli_add(result, result, curve_prime, ndigits); |
|
} while (carry < 0); |
|
} else { |
|
while (carry || vli_cmp(curve_prime, result, ndigits) != 1) |
|
carry -= vli_sub(result, result, curve_prime, ndigits); |
|
} |
|
|
|
} |
|
|
|
#undef SL32OR32 |
|
#undef AND64H |
|
#undef AND64L |
|
|
|
/* Computes result = product % curve_prime for different curve_primes. |
|
* |
|
* Note that curve_primes are distinguished just by heuristic check and |
|
* not by complete conformance check. |
|
*/ |
|
static bool vli_mmod_fast(u64 *result, u64 *product, |
|
const struct ecc_curve *curve) |
|
{ |
|
u64 tmp[2 * ECC_MAX_DIGITS]; |
|
const u64 *curve_prime = curve->p; |
|
const unsigned int ndigits = curve->g.ndigits; |
|
|
|
/* All NIST curves have name prefix 'nist_' */ |
|
if (strncmp(curve->name, "nist_", 5) != 0) { |
|
/* Try to handle Pseudo-Marsenne primes. */ |
|
if (curve_prime[ndigits - 1] == -1ull) { |
|
vli_mmod_special(result, product, curve_prime, |
|
ndigits); |
|
return true; |
|
} else if (curve_prime[ndigits - 1] == 1ull << 63 && |
|
curve_prime[ndigits - 2] == 0) { |
|
vli_mmod_special2(result, product, curve_prime, |
|
ndigits); |
|
return true; |
|
} |
|
vli_mmod_barrett(result, product, curve_prime, ndigits); |
|
return true; |
|
} |
|
|
|
switch (ndigits) { |
|
case 3: |
|
vli_mmod_fast_192(result, product, curve_prime, tmp); |
|
break; |
|
case 4: |
|
vli_mmod_fast_256(result, product, curve_prime, tmp); |
|
break; |
|
case 6: |
|
vli_mmod_fast_384(result, product, curve_prime, tmp); |
|
break; |
|
default: |
|
pr_err_ratelimited("ecc: unsupported digits size!\n"); |
|
return false; |
|
} |
|
|
|
return true; |
|
} |
|
|
|
/* Computes result = (left * right) % mod. |
|
* Assumes that mod is big enough curve order. |
|
*/ |
|
void vli_mod_mult_slow(u64 *result, const u64 *left, const u64 *right, |
|
const u64 *mod, unsigned int ndigits) |
|
{ |
|
u64 product[ECC_MAX_DIGITS * 2]; |
|
|
|
vli_mult(product, left, right, ndigits); |
|
vli_mmod_slow(result, product, mod, ndigits); |
|
} |
|
EXPORT_SYMBOL(vli_mod_mult_slow); |
|
|
|
/* Computes result = (left * right) % curve_prime. */ |
|
static void vli_mod_mult_fast(u64 *result, const u64 *left, const u64 *right, |
|
const struct ecc_curve *curve) |
|
{ |
|
u64 product[2 * ECC_MAX_DIGITS]; |
|
|
|
vli_mult(product, left, right, curve->g.ndigits); |
|
vli_mmod_fast(result, product, curve); |
|
} |
|
|
|
/* Computes result = left^2 % curve_prime. */ |
|
static void vli_mod_square_fast(u64 *result, const u64 *left, |
|
const struct ecc_curve *curve) |
|
{ |
|
u64 product[2 * ECC_MAX_DIGITS]; |
|
|
|
vli_square(product, left, curve->g.ndigits); |
|
vli_mmod_fast(result, product, curve); |
|
} |
|
|
|
#define EVEN(vli) (!(vli[0] & 1)) |
|
/* Computes result = (1 / p_input) % mod. All VLIs are the same size. |
|
* See "From Euclid's GCD to Montgomery Multiplication to the Great Divide" |
|
* https://labs.oracle.com/techrep/2001/smli_tr-2001-95.pdf |
|
*/ |
|
void vli_mod_inv(u64 *result, const u64 *input, const u64 *mod, |
|
unsigned int ndigits) |
|
{ |
|
u64 a[ECC_MAX_DIGITS], b[ECC_MAX_DIGITS]; |
|
u64 u[ECC_MAX_DIGITS], v[ECC_MAX_DIGITS]; |
|
u64 carry; |
|
int cmp_result; |
|
|
|
if (vli_is_zero(input, ndigits)) { |
|
vli_clear(result, ndigits); |
|
return; |
|
} |
|
|
|
vli_set(a, input, ndigits); |
|
vli_set(b, mod, ndigits); |
|
vli_clear(u, ndigits); |
|
u[0] = 1; |
|
vli_clear(v, ndigits); |
|
|
|
while ((cmp_result = vli_cmp(a, b, ndigits)) != 0) { |
|
carry = 0; |
|
|
|
if (EVEN(a)) { |
|
vli_rshift1(a, ndigits); |
|
|
|
if (!EVEN(u)) |
|
carry = vli_add(u, u, mod, ndigits); |
|
|
|
vli_rshift1(u, ndigits); |
|
if (carry) |
|
u[ndigits - 1] |= 0x8000000000000000ull; |
|
} else if (EVEN(b)) { |
|
vli_rshift1(b, ndigits); |
|
|
|
if (!EVEN(v)) |
|
carry = vli_add(v, v, mod, ndigits); |
|
|
|
vli_rshift1(v, ndigits); |
|
if (carry) |
|
v[ndigits - 1] |= 0x8000000000000000ull; |
|
} else if (cmp_result > 0) { |
|
vli_sub(a, a, b, ndigits); |
|
vli_rshift1(a, ndigits); |
|
|
|
if (vli_cmp(u, v, ndigits) < 0) |
|
vli_add(u, u, mod, ndigits); |
|
|
|
vli_sub(u, u, v, ndigits); |
|
if (!EVEN(u)) |
|
carry = vli_add(u, u, mod, ndigits); |
|
|
|
vli_rshift1(u, ndigits); |
|
if (carry) |
|
u[ndigits - 1] |= 0x8000000000000000ull; |
|
} else { |
|
vli_sub(b, b, a, ndigits); |
|
vli_rshift1(b, ndigits); |
|
|
|
if (vli_cmp(v, u, ndigits) < 0) |
|
vli_add(v, v, mod, ndigits); |
|
|
|
vli_sub(v, v, u, ndigits); |
|
if (!EVEN(v)) |
|
carry = vli_add(v, v, mod, ndigits); |
|
|
|
vli_rshift1(v, ndigits); |
|
if (carry) |
|
v[ndigits - 1] |= 0x8000000000000000ull; |
|
} |
|
} |
|
|
|
vli_set(result, u, ndigits); |
|
} |
|
EXPORT_SYMBOL(vli_mod_inv); |
|
|
|
/* ------ Point operations ------ */ |
|
|
|
/* Returns true if p_point is the point at infinity, false otherwise. */ |
|
static bool ecc_point_is_zero(const struct ecc_point *point) |
|
{ |
|
return (vli_is_zero(point->x, point->ndigits) && |
|
vli_is_zero(point->y, point->ndigits)); |
|
} |
|
|
|
/* Point multiplication algorithm using Montgomery's ladder with co-Z |
|
* coordinates. From https://eprint.iacr.org/2011/338.pdf |
|
*/ |
|
|
|
/* Double in place */ |
|
static void ecc_point_double_jacobian(u64 *x1, u64 *y1, u64 *z1, |
|
const struct ecc_curve *curve) |
|
{ |
|
/* t1 = x, t2 = y, t3 = z */ |
|
u64 t4[ECC_MAX_DIGITS]; |
|
u64 t5[ECC_MAX_DIGITS]; |
|
const u64 *curve_prime = curve->p; |
|
const unsigned int ndigits = curve->g.ndigits; |
|
|
|
if (vli_is_zero(z1, ndigits)) |
|
return; |
|
|
|
/* t4 = y1^2 */ |
|
vli_mod_square_fast(t4, y1, curve); |
|
/* t5 = x1*y1^2 = A */ |
|
vli_mod_mult_fast(t5, x1, t4, curve); |
|
/* t4 = y1^4 */ |
|
vli_mod_square_fast(t4, t4, curve); |
|
/* t2 = y1*z1 = z3 */ |
|
vli_mod_mult_fast(y1, y1, z1, curve); |
|
/* t3 = z1^2 */ |
|
vli_mod_square_fast(z1, z1, curve); |
|
|
|
/* t1 = x1 + z1^2 */ |
|
vli_mod_add(x1, x1, z1, curve_prime, ndigits); |
|
/* t3 = 2*z1^2 */ |
|
vli_mod_add(z1, z1, z1, curve_prime, ndigits); |
|
/* t3 = x1 - z1^2 */ |
|
vli_mod_sub(z1, x1, z1, curve_prime, ndigits); |
|
/* t1 = x1^2 - z1^4 */ |
|
vli_mod_mult_fast(x1, x1, z1, curve); |
|
|
|
/* t3 = 2*(x1^2 - z1^4) */ |
|
vli_mod_add(z1, x1, x1, curve_prime, ndigits); |
|
/* t1 = 3*(x1^2 - z1^4) */ |
|
vli_mod_add(x1, x1, z1, curve_prime, ndigits); |
|
if (vli_test_bit(x1, 0)) { |
|
u64 carry = vli_add(x1, x1, curve_prime, ndigits); |
|
|
|
vli_rshift1(x1, ndigits); |
|
x1[ndigits - 1] |= carry << 63; |
|
} else { |
|
vli_rshift1(x1, ndigits); |
|
} |
|
/* t1 = 3/2*(x1^2 - z1^4) = B */ |
|
|
|
/* t3 = B^2 */ |
|
vli_mod_square_fast(z1, x1, curve); |
|
/* t3 = B^2 - A */ |
|
vli_mod_sub(z1, z1, t5, curve_prime, ndigits); |
|
/* t3 = B^2 - 2A = x3 */ |
|
vli_mod_sub(z1, z1, t5, curve_prime, ndigits); |
|
/* t5 = A - x3 */ |
|
vli_mod_sub(t5, t5, z1, curve_prime, ndigits); |
|
/* t1 = B * (A - x3) */ |
|
vli_mod_mult_fast(x1, x1, t5, curve); |
|
/* t4 = B * (A - x3) - y1^4 = y3 */ |
|
vli_mod_sub(t4, x1, t4, curve_prime, ndigits); |
|
|
|
vli_set(x1, z1, ndigits); |
|
vli_set(z1, y1, ndigits); |
|
vli_set(y1, t4, ndigits); |
|
} |
|
|
|
/* Modify (x1, y1) => (x1 * z^2, y1 * z^3) */ |
|
static void apply_z(u64 *x1, u64 *y1, u64 *z, const struct ecc_curve *curve) |
|
{ |
|
u64 t1[ECC_MAX_DIGITS]; |
|
|
|
vli_mod_square_fast(t1, z, curve); /* z^2 */ |
|
vli_mod_mult_fast(x1, x1, t1, curve); /* x1 * z^2 */ |
|
vli_mod_mult_fast(t1, t1, z, curve); /* z^3 */ |
|
vli_mod_mult_fast(y1, y1, t1, curve); /* y1 * z^3 */ |
|
} |
|
|
|
/* P = (x1, y1) => 2P, (x2, y2) => P' */ |
|
static void xycz_initial_double(u64 *x1, u64 *y1, u64 *x2, u64 *y2, |
|
u64 *p_initial_z, const struct ecc_curve *curve) |
|
{ |
|
u64 z[ECC_MAX_DIGITS]; |
|
const unsigned int ndigits = curve->g.ndigits; |
|
|
|
vli_set(x2, x1, ndigits); |
|
vli_set(y2, y1, ndigits); |
|
|
|
vli_clear(z, ndigits); |
|
z[0] = 1; |
|
|
|
if (p_initial_z) |
|
vli_set(z, p_initial_z, ndigits); |
|
|
|
apply_z(x1, y1, z, curve); |
|
|
|
ecc_point_double_jacobian(x1, y1, z, curve); |
|
|
|
apply_z(x2, y2, z, curve); |
|
} |
|
|
|
/* Input P = (x1, y1, Z), Q = (x2, y2, Z) |
|
* Output P' = (x1', y1', Z3), P + Q = (x3, y3, Z3) |
|
* or P => P', Q => P + Q |
|
*/ |
|
static void xycz_add(u64 *x1, u64 *y1, u64 *x2, u64 *y2, |
|
const struct ecc_curve *curve) |
|
{ |
|
/* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */ |
|
u64 t5[ECC_MAX_DIGITS]; |
|
const u64 *curve_prime = curve->p; |
|
const unsigned int ndigits = curve->g.ndigits; |
|
|
|
/* t5 = x2 - x1 */ |
|
vli_mod_sub(t5, x2, x1, curve_prime, ndigits); |
|
/* t5 = (x2 - x1)^2 = A */ |
|
vli_mod_square_fast(t5, t5, curve); |
|
/* t1 = x1*A = B */ |
|
vli_mod_mult_fast(x1, x1, t5, curve); |
|
/* t3 = x2*A = C */ |
|
vli_mod_mult_fast(x2, x2, t5, curve); |
|
/* t4 = y2 - y1 */ |
|
vli_mod_sub(y2, y2, y1, curve_prime, ndigits); |
|
/* t5 = (y2 - y1)^2 = D */ |
|
vli_mod_square_fast(t5, y2, curve); |
|
|
|
/* t5 = D - B */ |
|
vli_mod_sub(t5, t5, x1, curve_prime, ndigits); |
|
/* t5 = D - B - C = x3 */ |
|
vli_mod_sub(t5, t5, x2, curve_prime, ndigits); |
|
/* t3 = C - B */ |
|
vli_mod_sub(x2, x2, x1, curve_prime, ndigits); |
|
/* t2 = y1*(C - B) */ |
|
vli_mod_mult_fast(y1, y1, x2, curve); |
|
/* t3 = B - x3 */ |
|
vli_mod_sub(x2, x1, t5, curve_prime, ndigits); |
|
/* t4 = (y2 - y1)*(B - x3) */ |
|
vli_mod_mult_fast(y2, y2, x2, curve); |
|
/* t4 = y3 */ |
|
vli_mod_sub(y2, y2, y1, curve_prime, ndigits); |
|
|
|
vli_set(x2, t5, ndigits); |
|
} |
|
|
|
/* Input P = (x1, y1, Z), Q = (x2, y2, Z) |
|
* Output P + Q = (x3, y3, Z3), P - Q = (x3', y3', Z3) |
|
* or P => P - Q, Q => P + Q |
|
*/ |
|
static void xycz_add_c(u64 *x1, u64 *y1, u64 *x2, u64 *y2, |
|
const struct ecc_curve *curve) |
|
{ |
|
/* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */ |
|
u64 t5[ECC_MAX_DIGITS]; |
|
u64 t6[ECC_MAX_DIGITS]; |
|
u64 t7[ECC_MAX_DIGITS]; |
|
const u64 *curve_prime = curve->p; |
|
const unsigned int ndigits = curve->g.ndigits; |
|
|
|
/* t5 = x2 - x1 */ |
|
vli_mod_sub(t5, x2, x1, curve_prime, ndigits); |
|
/* t5 = (x2 - x1)^2 = A */ |
|
vli_mod_square_fast(t5, t5, curve); |
|
/* t1 = x1*A = B */ |
|
vli_mod_mult_fast(x1, x1, t5, curve); |
|
/* t3 = x2*A = C */ |
|
vli_mod_mult_fast(x2, x2, t5, curve); |
|
/* t4 = y2 + y1 */ |
|
vli_mod_add(t5, y2, y1, curve_prime, ndigits); |
|
/* t4 = y2 - y1 */ |
|
vli_mod_sub(y2, y2, y1, curve_prime, ndigits); |
|
|
|
/* t6 = C - B */ |
|
vli_mod_sub(t6, x2, x1, curve_prime, ndigits); |
|
/* t2 = y1 * (C - B) */ |
|
vli_mod_mult_fast(y1, y1, t6, curve); |
|
/* t6 = B + C */ |
|
vli_mod_add(t6, x1, x2, curve_prime, ndigits); |
|
/* t3 = (y2 - y1)^2 */ |
|
vli_mod_square_fast(x2, y2, curve); |
|
/* t3 = x3 */ |
|
vli_mod_sub(x2, x2, t6, curve_prime, ndigits); |
|
|
|
/* t7 = B - x3 */ |
|
vli_mod_sub(t7, x1, x2, curve_prime, ndigits); |
|
/* t4 = (y2 - y1)*(B - x3) */ |
|
vli_mod_mult_fast(y2, y2, t7, curve); |
|
/* t4 = y3 */ |
|
vli_mod_sub(y2, y2, y1, curve_prime, ndigits); |
|
|
|
/* t7 = (y2 + y1)^2 = F */ |
|
vli_mod_square_fast(t7, t5, curve); |
|
/* t7 = x3' */ |
|
vli_mod_sub(t7, t7, t6, curve_prime, ndigits); |
|
/* t6 = x3' - B */ |
|
vli_mod_sub(t6, t7, x1, curve_prime, ndigits); |
|
/* t6 = (y2 + y1)*(x3' - B) */ |
|
vli_mod_mult_fast(t6, t6, t5, curve); |
|
/* t2 = y3' */ |
|
vli_mod_sub(y1, t6, y1, curve_prime, ndigits); |
|
|
|
vli_set(x1, t7, ndigits); |
|
} |
|
|
|
static void ecc_point_mult(struct ecc_point *result, |
|
const struct ecc_point *point, const u64 *scalar, |
|
u64 *initial_z, const struct ecc_curve *curve, |
|
unsigned int ndigits) |
|
{ |
|
/* R0 and R1 */ |
|
u64 rx[2][ECC_MAX_DIGITS]; |
|
u64 ry[2][ECC_MAX_DIGITS]; |
|
u64 z[ECC_MAX_DIGITS]; |
|
u64 sk[2][ECC_MAX_DIGITS]; |
|
u64 *curve_prime = curve->p; |
|
int i, nb; |
|
int num_bits; |
|
int carry; |
|
|
|
carry = vli_add(sk[0], scalar, curve->n, ndigits); |
|
vli_add(sk[1], sk[0], curve->n, ndigits); |
|
scalar = sk[!carry]; |
|
num_bits = sizeof(u64) * ndigits * 8 + 1; |
|
|
|
vli_set(rx[1], point->x, ndigits); |
|
vli_set(ry[1], point->y, ndigits); |
|
|
|
xycz_initial_double(rx[1], ry[1], rx[0], ry[0], initial_z, curve); |
|
|
|
for (i = num_bits - 2; i > 0; i--) { |
|
nb = !vli_test_bit(scalar, i); |
|
xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb], curve); |
|
xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve); |
|
} |
|
|
|
nb = !vli_test_bit(scalar, 0); |
|
xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb], curve); |
|
|
|
/* Find final 1/Z value. */ |
|
/* X1 - X0 */ |
|
vli_mod_sub(z, rx[1], rx[0], curve_prime, ndigits); |
|
/* Yb * (X1 - X0) */ |
|
vli_mod_mult_fast(z, z, ry[1 - nb], curve); |
|
/* xP * Yb * (X1 - X0) */ |
|
vli_mod_mult_fast(z, z, point->x, curve); |
|
|
|
/* 1 / (xP * Yb * (X1 - X0)) */ |
|
vli_mod_inv(z, z, curve_prime, point->ndigits); |
|
|
|
/* yP / (xP * Yb * (X1 - X0)) */ |
|
vli_mod_mult_fast(z, z, point->y, curve); |
|
/* Xb * yP / (xP * Yb * (X1 - X0)) */ |
|
vli_mod_mult_fast(z, z, rx[1 - nb], curve); |
|
/* End 1/Z calculation */ |
|
|
|
xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve); |
|
|
|
apply_z(rx[0], ry[0], z, curve); |
|
|
|
vli_set(result->x, rx[0], ndigits); |
|
vli_set(result->y, ry[0], ndigits); |
|
} |
|
|
|
/* Computes R = P + Q mod p */ |
|
static void ecc_point_add(const struct ecc_point *result, |
|
const struct ecc_point *p, const struct ecc_point *q, |
|
const struct ecc_curve *curve) |
|
{ |
|
u64 z[ECC_MAX_DIGITS]; |
|
u64 px[ECC_MAX_DIGITS]; |
|
u64 py[ECC_MAX_DIGITS]; |
|
unsigned int ndigits = curve->g.ndigits; |
|
|
|
vli_set(result->x, q->x, ndigits); |
|
vli_set(result->y, q->y, ndigits); |
|
vli_mod_sub(z, result->x, p->x, curve->p, ndigits); |
|
vli_set(px, p->x, ndigits); |
|
vli_set(py, p->y, ndigits); |
|
xycz_add(px, py, result->x, result->y, curve); |
|
vli_mod_inv(z, z, curve->p, ndigits); |
|
apply_z(result->x, result->y, z, curve); |
|
} |
|
|
|
/* Computes R = u1P + u2Q mod p using Shamir's trick. |
|
* Based on: Kenneth MacKay's micro-ecc (2014). |
|
*/ |
|
void ecc_point_mult_shamir(const struct ecc_point *result, |
|
const u64 *u1, const struct ecc_point *p, |
|
const u64 *u2, const struct ecc_point *q, |
|
const struct ecc_curve *curve) |
|
{ |
|
u64 z[ECC_MAX_DIGITS]; |
|
u64 sump[2][ECC_MAX_DIGITS]; |
|
u64 *rx = result->x; |
|
u64 *ry = result->y; |
|
unsigned int ndigits = curve->g.ndigits; |
|
unsigned int num_bits; |
|
struct ecc_point sum = ECC_POINT_INIT(sump[0], sump[1], ndigits); |
|
const struct ecc_point *points[4]; |
|
const struct ecc_point *point; |
|
unsigned int idx; |
|
int i; |
|
|
|
ecc_point_add(&sum, p, q, curve); |
|
points[0] = NULL; |
|
points[1] = p; |
|
points[2] = q; |
|
points[3] = ∑ |
|
|
|
num_bits = max(vli_num_bits(u1, ndigits), vli_num_bits(u2, ndigits)); |
|
i = num_bits - 1; |
|
idx = (!!vli_test_bit(u1, i)) | ((!!vli_test_bit(u2, i)) << 1); |
|
point = points[idx]; |
|
|
|
vli_set(rx, point->x, ndigits); |
|
vli_set(ry, point->y, ndigits); |
|
vli_clear(z + 1, ndigits - 1); |
|
z[0] = 1; |
|
|
|
for (--i; i >= 0; i--) { |
|
ecc_point_double_jacobian(rx, ry, z, curve); |
|
idx = (!!vli_test_bit(u1, i)) | ((!!vli_test_bit(u2, i)) << 1); |
|
point = points[idx]; |
|
if (point) { |
|
u64 tx[ECC_MAX_DIGITS]; |
|
u64 ty[ECC_MAX_DIGITS]; |
|
u64 tz[ECC_MAX_DIGITS]; |
|
|
|
vli_set(tx, point->x, ndigits); |
|
vli_set(ty, point->y, ndigits); |
|
apply_z(tx, ty, z, curve); |
|
vli_mod_sub(tz, rx, tx, curve->p, ndigits); |
|
xycz_add(tx, ty, rx, ry, curve); |
|
vli_mod_mult_fast(z, z, tz, curve); |
|
} |
|
} |
|
vli_mod_inv(z, z, curve->p, ndigits); |
|
apply_z(rx, ry, z, curve); |
|
} |
|
EXPORT_SYMBOL(ecc_point_mult_shamir); |
|
|
|
static int __ecc_is_key_valid(const struct ecc_curve *curve, |
|
const u64 *private_key, unsigned int ndigits) |
|
{ |
|
u64 one[ECC_MAX_DIGITS] = { 1, }; |
|
u64 res[ECC_MAX_DIGITS]; |
|
|
|
if (!private_key) |
|
return -EINVAL; |
|
|
|
if (curve->g.ndigits != ndigits) |
|
return -EINVAL; |
|
|
|
/* Make sure the private key is in the range [2, n-3]. */ |
|
if (vli_cmp(one, private_key, ndigits) != -1) |
|
return -EINVAL; |
|
vli_sub(res, curve->n, one, ndigits); |
|
vli_sub(res, res, one, ndigits); |
|
if (vli_cmp(res, private_key, ndigits) != 1) |
|
return -EINVAL; |
|
|
|
return 0; |
|
} |
|
|
|
int ecc_is_key_valid(unsigned int curve_id, unsigned int ndigits, |
|
const u64 *private_key, unsigned int private_key_len) |
|
{ |
|
int nbytes; |
|
const struct ecc_curve *curve = ecc_get_curve(curve_id); |
|
|
|
nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT; |
|
|
|
if (private_key_len != nbytes) |
|
return -EINVAL; |
|
|
|
return __ecc_is_key_valid(curve, private_key, ndigits); |
|
} |
|
EXPORT_SYMBOL(ecc_is_key_valid); |
|
|
|
/* |
|
* ECC private keys are generated using the method of extra random bits, |
|
* equivalent to that described in FIPS 186-4, Appendix B.4.1. |
|
* |
|
* d = (c mod(n–1)) + 1 where c is a string of random bits, 64 bits longer |
|
* than requested |
|
* 0 <= c mod(n-1) <= n-2 and implies that |
|
* 1 <= d <= n-1 |
|
* |
|
* This method generates a private key uniformly distributed in the range |
|
* [1, n-1]. |
|
*/ |
|
int ecc_gen_privkey(unsigned int curve_id, unsigned int ndigits, u64 *privkey) |
|
{ |
|
const struct ecc_curve *curve = ecc_get_curve(curve_id); |
|
u64 priv[ECC_MAX_DIGITS]; |
|
unsigned int nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT; |
|
unsigned int nbits = vli_num_bits(curve->n, ndigits); |
|
int err; |
|
|
|
/* Check that N is included in Table 1 of FIPS 186-4, section 6.1.1 */ |
|
if (nbits < 160 || ndigits > ARRAY_SIZE(priv)) |
|
return -EINVAL; |
|
|
|
/* |
|
* FIPS 186-4 recommends that the private key should be obtained from a |
|
* RBG with a security strength equal to or greater than the security |
|
* strength associated with N. |
|
* |
|
* The maximum security strength identified by NIST SP800-57pt1r4 for |
|
* ECC is 256 (N >= 512). |
|
* |
|
* This condition is met by the default RNG because it selects a favored |
|
* DRBG with a security strength of 256. |
|
*/ |
|
if (crypto_get_default_rng()) |
|
return -EFAULT; |
|
|
|
err = crypto_rng_get_bytes(crypto_default_rng, (u8 *)priv, nbytes); |
|
crypto_put_default_rng(); |
|
if (err) |
|
return err; |
|
|
|
/* Make sure the private key is in the valid range. */ |
|
if (__ecc_is_key_valid(curve, priv, ndigits)) |
|
return -EINVAL; |
|
|
|
ecc_swap_digits(priv, privkey, ndigits); |
|
|
|
return 0; |
|
} |
|
EXPORT_SYMBOL(ecc_gen_privkey); |
|
|
|
int ecc_make_pub_key(unsigned int curve_id, unsigned int ndigits, |
|
const u64 *private_key, u64 *public_key) |
|
{ |
|
int ret = 0; |
|
struct ecc_point *pk; |
|
u64 priv[ECC_MAX_DIGITS]; |
|
const struct ecc_curve *curve = ecc_get_curve(curve_id); |
|
|
|
if (!private_key || !curve || ndigits > ARRAY_SIZE(priv)) { |
|
ret = -EINVAL; |
|
goto out; |
|
} |
|
|
|
ecc_swap_digits(private_key, priv, ndigits); |
|
|
|
pk = ecc_alloc_point(ndigits); |
|
if (!pk) { |
|
ret = -ENOMEM; |
|
goto out; |
|
} |
|
|
|
ecc_point_mult(pk, &curve->g, priv, NULL, curve, ndigits); |
|
|
|
/* SP800-56A rev 3 5.6.2.1.3 key check */ |
|
if (ecc_is_pubkey_valid_full(curve, pk)) { |
|
ret = -EAGAIN; |
|
goto err_free_point; |
|
} |
|
|
|
ecc_swap_digits(pk->x, public_key, ndigits); |
|
ecc_swap_digits(pk->y, &public_key[ndigits], ndigits); |
|
|
|
err_free_point: |
|
ecc_free_point(pk); |
|
out: |
|
return ret; |
|
} |
|
EXPORT_SYMBOL(ecc_make_pub_key); |
|
|
|
/* SP800-56A section 5.6.2.3.4 partial verification: ephemeral keys only */ |
|
int ecc_is_pubkey_valid_partial(const struct ecc_curve *curve, |
|
struct ecc_point *pk) |
|
{ |
|
u64 yy[ECC_MAX_DIGITS], xxx[ECC_MAX_DIGITS], w[ECC_MAX_DIGITS]; |
|
|
|
if (WARN_ON(pk->ndigits != curve->g.ndigits)) |
|
return -EINVAL; |
|
|
|
/* Check 1: Verify key is not the zero point. */ |
|
if (ecc_point_is_zero(pk)) |
|
return -EINVAL; |
|
|
|
/* Check 2: Verify key is in the range [1, p-1]. */ |
|
if (vli_cmp(curve->p, pk->x, pk->ndigits) != 1) |
|
return -EINVAL; |
|
if (vli_cmp(curve->p, pk->y, pk->ndigits) != 1) |
|
return -EINVAL; |
|
|
|
/* Check 3: Verify that y^2 == (x^3 + a·x + b) mod p */ |
|
vli_mod_square_fast(yy, pk->y, curve); /* y^2 */ |
|
vli_mod_square_fast(xxx, pk->x, curve); /* x^2 */ |
|
vli_mod_mult_fast(xxx, xxx, pk->x, curve); /* x^3 */ |
|
vli_mod_mult_fast(w, curve->a, pk->x, curve); /* a·x */ |
|
vli_mod_add(w, w, curve->b, curve->p, pk->ndigits); /* a·x + b */ |
|
vli_mod_add(w, w, xxx, curve->p, pk->ndigits); /* x^3 + a·x + b */ |
|
if (vli_cmp(yy, w, pk->ndigits) != 0) /* Equation */ |
|
return -EINVAL; |
|
|
|
return 0; |
|
} |
|
EXPORT_SYMBOL(ecc_is_pubkey_valid_partial); |
|
|
|
/* SP800-56A section 5.6.2.3.3 full verification */ |
|
int ecc_is_pubkey_valid_full(const struct ecc_curve *curve, |
|
struct ecc_point *pk) |
|
{ |
|
struct ecc_point *nQ; |
|
|
|
/* Checks 1 through 3 */ |
|
int ret = ecc_is_pubkey_valid_partial(curve, pk); |
|
|
|
if (ret) |
|
return ret; |
|
|
|
/* Check 4: Verify that nQ is the zero point. */ |
|
nQ = ecc_alloc_point(pk->ndigits); |
|
if (!nQ) |
|
return -ENOMEM; |
|
|
|
ecc_point_mult(nQ, pk, curve->n, NULL, curve, pk->ndigits); |
|
if (!ecc_point_is_zero(nQ)) |
|
ret = -EINVAL; |
|
|
|
ecc_free_point(nQ); |
|
|
|
return ret; |
|
} |
|
EXPORT_SYMBOL(ecc_is_pubkey_valid_full); |
|
|
|
int crypto_ecdh_shared_secret(unsigned int curve_id, unsigned int ndigits, |
|
const u64 *private_key, const u64 *public_key, |
|
u64 *secret) |
|
{ |
|
int ret = 0; |
|
struct ecc_point *product, *pk; |
|
u64 priv[ECC_MAX_DIGITS]; |
|
u64 rand_z[ECC_MAX_DIGITS]; |
|
unsigned int nbytes; |
|
const struct ecc_curve *curve = ecc_get_curve(curve_id); |
|
|
|
if (!private_key || !public_key || !curve || |
|
ndigits > ARRAY_SIZE(priv) || ndigits > ARRAY_SIZE(rand_z)) { |
|
ret = -EINVAL; |
|
goto out; |
|
} |
|
|
|
nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT; |
|
|
|
get_random_bytes(rand_z, nbytes); |
|
|
|
pk = ecc_alloc_point(ndigits); |
|
if (!pk) { |
|
ret = -ENOMEM; |
|
goto out; |
|
} |
|
|
|
ecc_swap_digits(public_key, pk->x, ndigits); |
|
ecc_swap_digits(&public_key[ndigits], pk->y, ndigits); |
|
ret = ecc_is_pubkey_valid_partial(curve, pk); |
|
if (ret) |
|
goto err_alloc_product; |
|
|
|
ecc_swap_digits(private_key, priv, ndigits); |
|
|
|
product = ecc_alloc_point(ndigits); |
|
if (!product) { |
|
ret = -ENOMEM; |
|
goto err_alloc_product; |
|
} |
|
|
|
ecc_point_mult(product, pk, priv, rand_z, curve, ndigits); |
|
|
|
if (ecc_point_is_zero(product)) { |
|
ret = -EFAULT; |
|
goto err_validity; |
|
} |
|
|
|
ecc_swap_digits(product->x, secret, ndigits); |
|
|
|
err_validity: |
|
memzero_explicit(priv, sizeof(priv)); |
|
memzero_explicit(rand_z, sizeof(rand_z)); |
|
ecc_free_point(product); |
|
err_alloc_product: |
|
ecc_free_point(pk); |
|
out: |
|
return ret; |
|
} |
|
EXPORT_SYMBOL(crypto_ecdh_shared_secret); |
|
|
|
MODULE_LICENSE("Dual BSD/GPL");
|
|
|