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