1 /*
2 * Copyright (c) 2007, 2011, Oracle and/or its affiliates. All rights reserved.
3 * Use is subject to license terms.
4 *
5 * This library is free software; you can redistribute it and/or
6 * modify it under the terms of the GNU Lesser General Public
7 * License as published by the Free Software Foundation; either
8 * version 2.1 of the License, or (at your option) any later version.
9 *
10 * This library is distributed in the hope that it will be useful,
11 * but WITHOUT ANY WARRANTY; without even the implied warranty of
12 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 * Lesser General Public License for more details.
14 *
15 * You should have received a copy of the GNU Lesser General Public License
16 * along with this library; if not, write to the Free Software Foundation,
17 * Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
18 *
19 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
20 * or visit www.oracle.com if you need additional information or have any
21 * questions.
22 */
23
24 /* *********************************************************************
25 *
26 * The Original Code is the elliptic curve math library.
27 *
28 * The Initial Developer of the Original Code is
29 * Sun Microsystems, Inc.
30 * Portions created by the Initial Developer are Copyright (C) 2003
31 * the Initial Developer. All Rights Reserved.
32 *
33 * Contributor(s):
34 * Douglas Stebila <douglas@stebila.ca>, Sun Microsystems Laboratories
35 *
36 *********************************************************************** */
37
38 /* Uses Montgomery reduction for field arithmetic. See mpi/mpmontg.c for
39 * code implementation. */
40
41 #include "mpi.h"
42 #include "mplogic.h"
43 #include "mpi-priv.h"
44 #include "ecl-priv.h"
45 #include "ecp.h"
46 #ifndef _KERNEL
47 #include <stdlib.h>
48 #include <stdio.h>
49 #endif
50
51 /* Construct a generic GFMethod for arithmetic over prime fields with
52 * irreducible irr. */
53 GFMethod *
GFMethod_consGFp_mont(const mp_int * irr)54 GFMethod_consGFp_mont(const mp_int *irr)
55 {
56 mp_err res = MP_OKAY;
57 int i;
58 GFMethod *meth = NULL;
59 mp_mont_modulus *mmm;
60
61 meth = GFMethod_consGFp(irr);
62 if (meth == NULL)
63 return NULL;
64
65 #ifdef _KERNEL
66 mmm = (mp_mont_modulus *) kmem_alloc(sizeof(mp_mont_modulus),
67 FLAG(irr));
68 #else
69 mmm = (mp_mont_modulus *) malloc(sizeof(mp_mont_modulus));
70 #endif
71 if (mmm == NULL) {
72 res = MP_MEM;
73 goto CLEANUP;
74 }
75
76 meth->field_mul = &ec_GFp_mul_mont;
77 meth->field_sqr = &ec_GFp_sqr_mont;
78 meth->field_div = &ec_GFp_div_mont;
79 meth->field_enc = &ec_GFp_enc_mont;
80 meth->field_dec = &ec_GFp_dec_mont;
81 meth->extra1 = mmm;
82 meth->extra2 = NULL;
83 meth->extra_free = &ec_GFp_extra_free_mont;
84
85 mmm->N = meth->irr;
86 i = mpl_significant_bits(&meth->irr);
87 i += MP_DIGIT_BIT - 1;
88 mmm->b = i - i % MP_DIGIT_BIT;
89 mmm->n0prime = 0 - s_mp_invmod_radix(MP_DIGIT(&meth->irr, 0));
90
91 CLEANUP:
92 if (res != MP_OKAY) {
93 GFMethod_free(meth);
94 return NULL;
95 }
96 return meth;
97 }
98
99 /* Wrapper functions for generic prime field arithmetic. */
100
101 /* Field multiplication using Montgomery reduction. */
102 mp_err
ec_GFp_mul_mont(const mp_int * a,const mp_int * b,mp_int * r,const GFMethod * meth)103 ec_GFp_mul_mont(const mp_int *a, const mp_int *b, mp_int *r,
104 const GFMethod *meth)
105 {
106 mp_err res = MP_OKAY;
107
108 #ifdef MP_MONT_USE_MP_MUL
109 /* if MP_MONT_USE_MP_MUL is defined, then the function s_mp_mul_mont
110 * is not implemented and we have to use mp_mul and s_mp_redc directly
111 */
112 MP_CHECKOK(mp_mul(a, b, r));
113 MP_CHECKOK(s_mp_redc(r, (mp_mont_modulus *) meth->extra1));
114 #else
115 mp_int s;
116
117 MP_DIGITS(&s) = 0;
118 /* s_mp_mul_mont doesn't allow source and destination to be the same */
119 if ((a == r) || (b == r)) {
120 MP_CHECKOK(mp_init(&s, FLAG(a)));
121 MP_CHECKOK(s_mp_mul_mont
122 (a, b, &s, (mp_mont_modulus *) meth->extra1));
123 MP_CHECKOK(mp_copy(&s, r));
124 mp_clear(&s);
125 } else {
126 return s_mp_mul_mont(a, b, r, (mp_mont_modulus *) meth->extra1);
127 }
128 #endif
129 CLEANUP:
130 return res;
131 }
132
133 /* Field squaring using Montgomery reduction. */
134 mp_err
ec_GFp_sqr_mont(const mp_int * a,mp_int * r,const GFMethod * meth)135 ec_GFp_sqr_mont(const mp_int *a, mp_int *r, const GFMethod *meth)
136 {
137 return ec_GFp_mul_mont(a, a, r, meth);
138 }
139
140 /* Field division using Montgomery reduction. */
141 mp_err
ec_GFp_div_mont(const mp_int * a,const mp_int * b,mp_int * r,const GFMethod * meth)142 ec_GFp_div_mont(const mp_int *a, const mp_int *b, mp_int *r,
143 const GFMethod *meth)
144 {
145 mp_err res = MP_OKAY;
146
147 /* if A=aZ represents a encoded in montgomery coordinates with Z and #
148 * and \ respectively represent multiplication and division in
149 * montgomery coordinates, then A\B = (a/b)Z = (A/B)Z and Binv =
150 * (1/b)Z = (1/B)(Z^2) where B # Binv = Z */
151 MP_CHECKOK(ec_GFp_div(a, b, r, meth));
152 MP_CHECKOK(ec_GFp_enc_mont(r, r, meth));
153 if (a == NULL) {
154 MP_CHECKOK(ec_GFp_enc_mont(r, r, meth));
155 }
156 CLEANUP:
157 return res;
158 }
159
160 /* Encode a field element in Montgomery form. See s_mp_to_mont in
161 * mpi/mpmontg.c */
162 mp_err
ec_GFp_enc_mont(const mp_int * a,mp_int * r,const GFMethod * meth)163 ec_GFp_enc_mont(const mp_int *a, mp_int *r, const GFMethod *meth)
164 {
165 mp_mont_modulus *mmm;
166 mp_err res = MP_OKAY;
167
168 mmm = (mp_mont_modulus *) meth->extra1;
169 MP_CHECKOK(mpl_lsh(a, r, mmm->b));
170 MP_CHECKOK(mp_mod(r, &mmm->N, r));
171 CLEANUP:
172 return res;
173 }
174
175 /* Decode a field element from Montgomery form. */
176 mp_err
ec_GFp_dec_mont(const mp_int * a,mp_int * r,const GFMethod * meth)177 ec_GFp_dec_mont(const mp_int *a, mp_int *r, const GFMethod *meth)
178 {
179 mp_err res = MP_OKAY;
180
181 if (a != r) {
182 MP_CHECKOK(mp_copy(a, r));
183 }
184 MP_CHECKOK(s_mp_redc(r, (mp_mont_modulus *) meth->extra1));
185 CLEANUP:
186 return res;
187 }
188
189 /* Free the memory allocated to the extra fields of Montgomery GFMethod
190 * object. */
191 void
ec_GFp_extra_free_mont(GFMethod * meth)192 ec_GFp_extra_free_mont(GFMethod *meth)
193 {
194 if (meth->extra1 != NULL) {
195 #ifdef _KERNEL
196 kmem_free(meth->extra1, sizeof(mp_mont_modulus));
197 #else
198 free(meth->extra1);
199 #endif
200 meth->extra1 = NULL;
201 }
202 }
203