1 /* *********************************************************************
2 *
3 * Sun elects to have this file available under and governed by the
4 * Mozilla Public License Version 1.1 ("MPL") (see
5 * http://www.mozilla.org/MPL/ for full license text). For the avoidance
6 * of doubt and subject to the following, Sun also elects to allow
7 * licensees to use this file under the MPL, the GNU General Public
8 * License version 2 only or the Lesser General Public License version
9 * 2.1 only. Any references to the "GNU General Public License version 2
10 * or later" or "GPL" in the following shall be construed to mean the
11 * GNU General Public License version 2 only. Any references to the "GNU
12 * Lesser General Public License version 2.1 or later" or "LGPL" in the
13 * following shall be construed to mean the GNU Lesser General Public
14 * License version 2.1 only. However, the following notice accompanied
15 * the original version of this file:
16 *
17 * Version: MPL 1.1/GPL 2.0/LGPL 2.1
18 *
19 * The contents of this file are subject to the Mozilla Public License Version
20 * 1.1 (the "License"); you may not use this file except in compliance with
21 * the License. You may obtain a copy of the License at
22 * http://www.mozilla.org/MPL/
23 *
24 * Software distributed under the License is distributed on an "AS IS" basis,
25 * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
26 * for the specific language governing rights and limitations under the
27 * License.
28 *
29 * The Original Code is the elliptic curve math library.
30 *
31 * The Initial Developer of the Original Code is
32 * Sun Microsystems, Inc.
33 * Portions created by the Initial Developer are Copyright (C) 2003
34 * the Initial Developer. All Rights Reserved.
35 *
36 * Contributor(s):
37 * Douglas Stebila <douglas@stebila.ca>, Sun Microsystems Laboratories
38 *
39 * Alternatively, the contents of this file may be used under the terms of
40 * either the GNU General Public License Version 2 or later (the "GPL"), or
41 * the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
42 * in which case the provisions of the GPL or the LGPL are applicable instead
43 * of those above. If you wish to allow use of your version of this file only
44 * under the terms of either the GPL or the LGPL, and not to allow others to
45 * use your version of this file under the terms of the MPL, indicate your
46 * decision by deleting the provisions above and replace them with the notice
47 * and other provisions required by the GPL or the LGPL. If you do not delete
48 * the provisions above, a recipient may use your version of this file under
49 * the terms of any one of the MPL, the GPL or the LGPL.
50 *
51 *********************************************************************** */
52 /*
53 * Copyright (c) 2007, Oracle and/or its affiliates. All rights reserved.
54 * Use is subject to license terms.
55 */
56
57 /* Uses Montgomery reduction for field arithmetic. See mpi/mpmontg.c for
58 * code implementation. */
59
60 #include "mpi.h"
61 #include "mplogic.h"
62 #include "mpi-priv.h"
63 #include "ecl-priv.h"
64 #include "ecp.h"
65 #ifndef _KERNEL
66 #include <stdlib.h>
67 #include <stdio.h>
68 #endif
69
70 /* Construct a generic GFMethod for arithmetic over prime fields with
71 * irreducible irr. */
72 GFMethod *
73 GFMethod_consGFp_mont(const mp_int *irr)
74 {
75 mp_err res = MP_OKAY;
76 int i;
77 GFMethod *meth = NULL;
78 mp_mont_modulus *mmm;
79
80 meth = GFMethod_consGFp(irr);
81 if (meth == NULL)
82 return NULL;
83
84 #ifdef _KERNEL
85 mmm = (mp_mont_modulus *) kmem_alloc(sizeof(mp_mont_modulus),
86 FLAG(irr));
87 #else
88 mmm = (mp_mont_modulus *) malloc(sizeof(mp_mont_modulus));
89 #endif
90 if (mmm == NULL) {
91 res = MP_MEM;
92 goto CLEANUP;
93 }
94
95 meth->field_mul = &ec_GFp_mul_mont;
96 meth->field_sqr = &ec_GFp_sqr_mont;
97 meth->field_div = &ec_GFp_div_mont;
98 meth->field_enc = &ec_GFp_enc_mont;
99 meth->field_dec = &ec_GFp_dec_mont;
100 meth->extra1 = mmm;
101 meth->extra2 = NULL;
102 meth->extra_free = &ec_GFp_extra_free_mont;
103
104 mmm->N = meth->irr;
105 i = mpl_significant_bits(&meth->irr);
106 i += MP_DIGIT_BIT - 1;
107 mmm->b = i - i % MP_DIGIT_BIT;
108 mmm->n0prime = 0 - s_mp_invmod_radix(MP_DIGIT(&meth->irr, 0));
109
110 CLEANUP:
111 if (res != MP_OKAY) {
112 GFMethod_free(meth);
113 return NULL;
114 }
115 return meth;
116 }
117
118 /* Wrapper functions for generic prime field arithmetic. */
119
120 /* Field multiplication using Montgomery reduction. */
121 mp_err
122 ec_GFp_mul_mont(const mp_int *a, const mp_int *b, mp_int *r,
123 const GFMethod *meth)
124 {
125 mp_err res = MP_OKAY;
126
127 #ifdef MP_MONT_USE_MP_MUL
128 /* if MP_MONT_USE_MP_MUL is defined, then the function s_mp_mul_mont
129 * is not implemented and we have to use mp_mul and s_mp_redc directly
130 */
131 MP_CHECKOK(mp_mul(a, b, r));
132 MP_CHECKOK(s_mp_redc(r, (mp_mont_modulus *) meth->extra1));
133 #else
134 mp_int s;
135
136 MP_DIGITS(&s) = 0;
137 /* s_mp_mul_mont doesn't allow source and destination to be the same */
138 if ((a == r) || (b == r)) {
139 MP_CHECKOK(mp_init(&s, FLAG(a)));
140 MP_CHECKOK(s_mp_mul_mont
141 (a, b, &s, (mp_mont_modulus *) meth->extra1));
142 MP_CHECKOK(mp_copy(&s, r));
143 mp_clear(&s);
144 } else {
145 return s_mp_mul_mont(a, b, r, (mp_mont_modulus *) meth->extra1);
146 }
147 #endif
148 CLEANUP:
149 return res;
150 }
151
152 /* Field squaring using Montgomery reduction. */
153 mp_err
154 ec_GFp_sqr_mont(const mp_int *a, mp_int *r, const GFMethod *meth)
155 {
156 return ec_GFp_mul_mont(a, a, r, meth);
157 }
158
159 /* Field division using Montgomery reduction. */
160 mp_err
161 ec_GFp_div_mont(const mp_int *a, const mp_int *b, mp_int *r,
162 const GFMethod *meth)
163 {
164 mp_err res = MP_OKAY;
165
166 /* if A=aZ represents a encoded in montgomery coordinates with Z and #
167 * and \ respectively represent multiplication and division in
168 * montgomery coordinates, then A\B = (a/b)Z = (A/B)Z and Binv =
169 * (1/b)Z = (1/B)(Z^2) where B # Binv = Z */
170 MP_CHECKOK(ec_GFp_div(a, b, r, meth));
171 MP_CHECKOK(ec_GFp_enc_mont(r, r, meth));
172 if (a == NULL) {
173 MP_CHECKOK(ec_GFp_enc_mont(r, r, meth));
174 }
175 CLEANUP:
176 return res;
177 }
178
179 /* Encode a field element in Montgomery form. See s_mp_to_mont in
180 * mpi/mpmontg.c */
181 mp_err
182 ec_GFp_enc_mont(const mp_int *a, mp_int *r, const GFMethod *meth)
183 {
184 mp_mont_modulus *mmm;
185 mp_err res = MP_OKAY;
186
187 mmm = (mp_mont_modulus *) meth->extra1;
188 MP_CHECKOK(mpl_lsh(a, r, mmm->b));
189 MP_CHECKOK(mp_mod(r, &mmm->N, r));
190 CLEANUP:
191 return res;
192 }
193
194 /* Decode a field element from Montgomery form. */
195 mp_err
196 ec_GFp_dec_mont(const mp_int *a, mp_int *r, const GFMethod *meth)
197 {
198 mp_err res = MP_OKAY;
199
200 if (a != r) {
201 MP_CHECKOK(mp_copy(a, r));
202 }
203 MP_CHECKOK(s_mp_redc(r, (mp_mont_modulus *) meth->extra1));
204 CLEANUP:
205 return res;
206 }
207
208 /* Free the memory allocated to the extra fields of Montgomery GFMethod
209 * object. */
210 void
211 ec_GFp_extra_free_mont(GFMethod *meth)
212 {
213 if (meth->extra1 != NULL) {
214 #ifdef _KERNEL
215 kmem_free(meth->extra1, sizeof(mp_mont_modulus));
216 #else
217 free(meth->extra1);
218 #endif
219 meth->extra1 = NULL;
220 }
221 }