DXR is a code search and navigation tool aimed at making sense of large projects. It supports full-text and regex searches as well as structural queries.

Mercurial (fddffdeab170)

VCS Links

Line Code
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137
/* This Source Code Form is subject to the terms of the Mozilla Public
 * License, v. 2.0. If a copy of the MPL was not distributed with this
 * file, You can obtain one at http://mozilla.org/MPL/2.0/. */

#include "ecp.h"
#include "mpi.h"
#include "mplogic.h"
#include "mpi-priv.h"

#define ECP521_DIGITS ECL_CURVE_DIGITS(521)

/* Fast modular reduction for p521 = 2^521 - 1.  a can be r. Uses
 * algorithm 2.31 from Hankerson, Menezes, Vanstone. Guide to 
 * Elliptic Curve Cryptography. */
static mp_err
ec_GFp_nistp521_mod(const mp_int *a, mp_int *r, const GFMethod *meth)
{
	mp_err res = MP_OKAY;
	int a_bits = mpl_significant_bits(a);
	unsigned int i;

	/* m1, m2 are statically-allocated mp_int of exactly the size we need */
	mp_int m1;

	mp_digit s1[ECP521_DIGITS] = { 0 };

	MP_SIGN(&m1) = MP_ZPOS;
	MP_ALLOC(&m1) = ECP521_DIGITS;
	MP_USED(&m1) = ECP521_DIGITS;
	MP_DIGITS(&m1) = s1;

	if (a_bits < 521) {
		if (a==r) return MP_OKAY;
		return mp_copy(a, r);
	}
	/* for polynomials larger than twice the field size or polynomials 
	 * not using all words, use regular reduction */
	if (a_bits > (521*2)) {
		MP_CHECKOK(mp_mod(a, &meth->irr, r));
	} else {
#define FIRST_DIGIT (ECP521_DIGITS-1)
		for (i = FIRST_DIGIT; i < MP_USED(a)-1; i++) {
			s1[i-FIRST_DIGIT] = (MP_DIGIT(a, i) >> 9) 
				| (MP_DIGIT(a, 1+i) << (MP_DIGIT_BIT-9));
		}
		s1[i-FIRST_DIGIT] = MP_DIGIT(a, i) >> 9;

		if ( a != r ) {
			MP_CHECKOK(s_mp_pad(r,ECP521_DIGITS));
			for (i = 0; i < ECP521_DIGITS; i++) {
				MP_DIGIT(r,i) = MP_DIGIT(a, i);
			}
		}
		MP_USED(r) = ECP521_DIGITS;
		MP_DIGIT(r,FIRST_DIGIT) &=  0x1FF;

		MP_CHECKOK(s_mp_add(r, &m1));
		if (MP_DIGIT(r, FIRST_DIGIT) & 0x200) {
			MP_CHECKOK(s_mp_add_d(r,1));
			MP_DIGIT(r,FIRST_DIGIT) &=  0x1FF;
		} else if (s_mp_cmp(r, &meth->irr) == 0) {
			mp_zero(r);
		}
		s_mp_clamp(r);
	}

  CLEANUP:
	return res;
}

/* Compute the square of polynomial a, reduce modulo p521. Store the
 * result in r.  r could be a.  Uses optimized modular reduction for p521. 
 */
static mp_err
ec_GFp_nistp521_sqr(const mp_int *a, mp_int *r, const GFMethod *meth)
{
	mp_err res = MP_OKAY;

	MP_CHECKOK(mp_sqr(a, r));
	MP_CHECKOK(ec_GFp_nistp521_mod(r, r, meth));
  CLEANUP:
	return res;
}

/* Compute the product of two polynomials a and b, reduce modulo p521.
 * Store the result in r.  r could be a or b; a could be b.  Uses
 * optimized modular reduction for p521. */
static mp_err
ec_GFp_nistp521_mul(const mp_int *a, const mp_int *b, mp_int *r,
					const GFMethod *meth)
{
	mp_err res = MP_OKAY;

	MP_CHECKOK(mp_mul(a, b, r));
	MP_CHECKOK(ec_GFp_nistp521_mod(r, r, meth));
  CLEANUP:
	return res;
}

/* Divides two field elements. If a is NULL, then returns the inverse of
 * b. */
static mp_err
ec_GFp_nistp521_div(const mp_int *a, const mp_int *b, mp_int *r,
		   const GFMethod *meth)
{
	mp_err res = MP_OKAY;
	mp_int t;

	/* If a is NULL, then return the inverse of b, otherwise return a/b. */
	if (a == NULL) {
		return mp_invmod(b, &meth->irr, r);
	} else {
		/* MPI doesn't support divmod, so we implement it using invmod and 
		 * mulmod. */
		MP_CHECKOK(mp_init(&t));
		MP_CHECKOK(mp_invmod(b, &meth->irr, &t));
		MP_CHECKOK(mp_mul(a, &t, r));
		MP_CHECKOK(ec_GFp_nistp521_mod(r, r, meth));
	  CLEANUP:
		mp_clear(&t);
		return res;
	}
}

/* Wire in fast field arithmetic and precomputation of base point for
 * named curves. */
mp_err
ec_group_set_gfp521(ECGroup *group, ECCurveName name)
{
	if (name == ECCurve_NIST_P521) {
		group->meth->field_mod = &ec_GFp_nistp521_mod;
		group->meth->field_mul = &ec_GFp_nistp521_mul;
		group->meth->field_sqr = &ec_GFp_nistp521_sqr;
		group->meth->field_div = &ec_GFp_nistp521_div;
	}
	return MP_OKAY;
}