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 for binary polynomial field curves.
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  *   Sheueling Chang-Shantz <sheueling.chang@sun.com>,
24  *   Stephen Fung <fungstep@hotmail.com>, and
25  *   Douglas Stebila <douglas@stebila.ca>, Sun Microsystems Laboratories.
26  *
27  * Alternatively, the contents of this file may be used under the terms of
28  * either the GNU General Public License Version 2 or later (the "GPL"), or
29  * the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
30  * in which case the provisions of the GPL or the LGPL are applicable instead
31  * of those above. If you wish to allow use of your version of this file only
32  * under the terms of either the GPL or the LGPL, and not to allow others to
33  * use your version of this file under the terms of the MPL, indicate your
34  * decision by deleting the provisions above and replace them with the notice
35  * and other provisions required by the GPL or the LGPL. If you do not delete
36  * the provisions above, a recipient may use your version of this file under
37  * the terms of any one of the MPL, the GPL or the LGPL.
38  *
39  * ***** END LICENSE BLOCK ***** */
40 /*
41  * Copyright 2007 Sun Microsystems, Inc.  All rights reserved.
42  * Use is subject to license terms.
43  *
44  * Sun elects to use this software under the MPL license.
45  */
46 
47 #pragma ident	"%Z%%M%	%I%	%E% SMI"
48 
49 #include "ec2.h"
50 #include "mplogic.h"
51 #include "mp_gf2m.h"
52 #ifndef _KERNEL
53 #include <stdlib.h>
54 #endif
55 
56 /* Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery
57  * projective coordinates. Uses algorithm Mdouble in appendix of Lopez, J.
58  * and Dahab, R.  "Fast multiplication on elliptic curves over GF(2^m)
59  * without precomputation". modified to not require precomputation of
60  * c=b^{2^{m-1}}. */
61 static mp_err
gf2m_Mdouble(mp_int * x,mp_int * z,const ECGroup * group,int kmflag)62 gf2m_Mdouble(mp_int *x, mp_int *z, const ECGroup *group, int kmflag)
63 {
64 	mp_err res = MP_OKAY;
65 	mp_int t1;
66 
67 	MP_DIGITS(&t1) = 0;
68 	MP_CHECKOK(mp_init(&t1, kmflag));
69 
70 	MP_CHECKOK(group->meth->field_sqr(x, x, group->meth));
71 	MP_CHECKOK(group->meth->field_sqr(z, &t1, group->meth));
72 	MP_CHECKOK(group->meth->field_mul(x, &t1, z, group->meth));
73 	MP_CHECKOK(group->meth->field_sqr(x, x, group->meth));
74 	MP_CHECKOK(group->meth->field_sqr(&t1, &t1, group->meth));
75 	MP_CHECKOK(group->meth->
76 			   field_mul(&group->curveb, &t1, &t1, group->meth));
77 	MP_CHECKOK(group->meth->field_add(x, &t1, x, group->meth));
78 
79   CLEANUP:
80 	mp_clear(&t1);
81 	return res;
82 }
83 
84 /* Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in
85  * Montgomery projective coordinates. Uses algorithm Madd in appendix of
86  * Lopex, J. and Dahab, R.  "Fast multiplication on elliptic curves over
87  * GF(2^m) without precomputation". */
88 static mp_err
gf2m_Madd(const mp_int * x,mp_int * x1,mp_int * z1,mp_int * x2,mp_int * z2,const ECGroup * group,int kmflag)89 gf2m_Madd(const mp_int *x, mp_int *x1, mp_int *z1, mp_int *x2, mp_int *z2,
90 		  const ECGroup *group, int kmflag)
91 {
92 	mp_err res = MP_OKAY;
93 	mp_int t1, t2;
94 
95 	MP_DIGITS(&t1) = 0;
96 	MP_DIGITS(&t2) = 0;
97 	MP_CHECKOK(mp_init(&t1, kmflag));
98 	MP_CHECKOK(mp_init(&t2, kmflag));
99 
100 	MP_CHECKOK(mp_copy(x, &t1));
101 	MP_CHECKOK(group->meth->field_mul(x1, z2, x1, group->meth));
102 	MP_CHECKOK(group->meth->field_mul(z1, x2, z1, group->meth));
103 	MP_CHECKOK(group->meth->field_mul(x1, z1, &t2, group->meth));
104 	MP_CHECKOK(group->meth->field_add(z1, x1, z1, group->meth));
105 	MP_CHECKOK(group->meth->field_sqr(z1, z1, group->meth));
106 	MP_CHECKOK(group->meth->field_mul(z1, &t1, x1, group->meth));
107 	MP_CHECKOK(group->meth->field_add(x1, &t2, x1, group->meth));
108 
109   CLEANUP:
110 	mp_clear(&t1);
111 	mp_clear(&t2);
112 	return res;
113 }
114 
115 /* Compute the x, y affine coordinates from the point (x1, z1) (x2, z2)
116  * using Montgomery point multiplication algorithm Mxy() in appendix of
117  * Lopex, J. and Dahab, R.  "Fast multiplication on elliptic curves over
118  * GF(2^m) without precomputation". Returns: 0 on error 1 if return value
119  * should be the point at infinity 2 otherwise */
120 static int
gf2m_Mxy(const mp_int * x,const mp_int * y,mp_int * x1,mp_int * z1,mp_int * x2,mp_int * z2,const ECGroup * group)121 gf2m_Mxy(const mp_int *x, const mp_int *y, mp_int *x1, mp_int *z1,
122 		 mp_int *x2, mp_int *z2, const ECGroup *group)
123 {
124 	mp_err res = MP_OKAY;
125 	int ret = 0;
126 	mp_int t3, t4, t5;
127 
128 	MP_DIGITS(&t3) = 0;
129 	MP_DIGITS(&t4) = 0;
130 	MP_DIGITS(&t5) = 0;
131 	MP_CHECKOK(mp_init(&t3, FLAG(x2)));
132 	MP_CHECKOK(mp_init(&t4, FLAG(x2)));
133 	MP_CHECKOK(mp_init(&t5, FLAG(x2)));
134 
135 	if (mp_cmp_z(z1) == 0) {
136 		mp_zero(x2);
137 		mp_zero(z2);
138 		ret = 1;
139 		goto CLEANUP;
140 	}
141 
142 	if (mp_cmp_z(z2) == 0) {
143 		MP_CHECKOK(mp_copy(x, x2));
144 		MP_CHECKOK(group->meth->field_add(x, y, z2, group->meth));
145 		ret = 2;
146 		goto CLEANUP;
147 	}
148 
149 	MP_CHECKOK(mp_set_int(&t5, 1));
150 	if (group->meth->field_enc) {
151 		MP_CHECKOK(group->meth->field_enc(&t5, &t5, group->meth));
152 	}
153 
154 	MP_CHECKOK(group->meth->field_mul(z1, z2, &t3, group->meth));
155 
156 	MP_CHECKOK(group->meth->field_mul(z1, x, z1, group->meth));
157 	MP_CHECKOK(group->meth->field_add(z1, x1, z1, group->meth));
158 	MP_CHECKOK(group->meth->field_mul(z2, x, z2, group->meth));
159 	MP_CHECKOK(group->meth->field_mul(z2, x1, x1, group->meth));
160 	MP_CHECKOK(group->meth->field_add(z2, x2, z2, group->meth));
161 
162 	MP_CHECKOK(group->meth->field_mul(z2, z1, z2, group->meth));
163 	MP_CHECKOK(group->meth->field_sqr(x, &t4, group->meth));
164 	MP_CHECKOK(group->meth->field_add(&t4, y, &t4, group->meth));
165 	MP_CHECKOK(group->meth->field_mul(&t4, &t3, &t4, group->meth));
166 	MP_CHECKOK(group->meth->field_add(&t4, z2, &t4, group->meth));
167 
168 	MP_CHECKOK(group->meth->field_mul(&t3, x, &t3, group->meth));
169 	MP_CHECKOK(group->meth->field_div(&t5, &t3, &t3, group->meth));
170 	MP_CHECKOK(group->meth->field_mul(&t3, &t4, &t4, group->meth));
171 	MP_CHECKOK(group->meth->field_mul(x1, &t3, x2, group->meth));
172 	MP_CHECKOK(group->meth->field_add(x2, x, z2, group->meth));
173 
174 	MP_CHECKOK(group->meth->field_mul(z2, &t4, z2, group->meth));
175 	MP_CHECKOK(group->meth->field_add(z2, y, z2, group->meth));
176 
177 	ret = 2;
178 
179   CLEANUP:
180 	mp_clear(&t3);
181 	mp_clear(&t4);
182 	mp_clear(&t5);
183 	if (res == MP_OKAY) {
184 		return ret;
185 	} else {
186 		return 0;
187 	}
188 }
189 
190 /* Computes R = nP based on algorithm 2P of Lopex, J. and Dahab, R.  "Fast
191  * multiplication on elliptic curves over GF(2^m) without
192  * precomputation". Elliptic curve points P and R can be identical. Uses
193  * Montgomery projective coordinates. */
194 mp_err
ec_GF2m_pt_mul_mont(const mp_int * n,const mp_int * px,const mp_int * py,mp_int * rx,mp_int * ry,const ECGroup * group)195 ec_GF2m_pt_mul_mont(const mp_int *n, const mp_int *px, const mp_int *py,
196 					mp_int *rx, mp_int *ry, const ECGroup *group)
197 {
198 	mp_err res = MP_OKAY;
199 	mp_int x1, x2, z1, z2;
200 	int i, j;
201 	mp_digit top_bit, mask;
202 
203 	MP_DIGITS(&x1) = 0;
204 	MP_DIGITS(&x2) = 0;
205 	MP_DIGITS(&z1) = 0;
206 	MP_DIGITS(&z2) = 0;
207 	MP_CHECKOK(mp_init(&x1, FLAG(n)));
208 	MP_CHECKOK(mp_init(&x2, FLAG(n)));
209 	MP_CHECKOK(mp_init(&z1, FLAG(n)));
210 	MP_CHECKOK(mp_init(&z2, FLAG(n)));
211 
212 	/* if result should be point at infinity */
213 	if ((mp_cmp_z(n) == 0) || (ec_GF2m_pt_is_inf_aff(px, py) == MP_YES)) {
214 		MP_CHECKOK(ec_GF2m_pt_set_inf_aff(rx, ry));
215 		goto CLEANUP;
216 	}
217 
218 	MP_CHECKOK(mp_copy(px, &x1));	/* x1 = px */
219 	MP_CHECKOK(mp_set_int(&z1, 1));	/* z1 = 1 */
220 	MP_CHECKOK(group->meth->field_sqr(&x1, &z2, group->meth));	/* z2 =
221 																 * x1^2 =
222 																 * px^2 */
223 	MP_CHECKOK(group->meth->field_sqr(&z2, &x2, group->meth));
224 	MP_CHECKOK(group->meth->field_add(&x2, &group->curveb, &x2, group->meth));	/* x2
225 																				 * =
226 																				 * px^4
227 																				 * +
228 																				 * b
229 																				 */
230 
231 	/* find top-most bit and go one past it */
232 	i = MP_USED(n) - 1;
233 	j = MP_DIGIT_BIT - 1;
234 	top_bit = 1;
235 	top_bit <<= MP_DIGIT_BIT - 1;
236 	mask = top_bit;
237 	while (!(MP_DIGITS(n)[i] & mask)) {
238 		mask >>= 1;
239 		j--;
240 	}
241 	mask >>= 1;
242 	j--;
243 
244 	/* if top most bit was at word break, go to next word */
245 	if (!mask) {
246 		i--;
247 		j = MP_DIGIT_BIT - 1;
248 		mask = top_bit;
249 	}
250 
251 	for (; i >= 0; i--) {
252 		for (; j >= 0; j--) {
253 			if (MP_DIGITS(n)[i] & mask) {
254 				MP_CHECKOK(gf2m_Madd(px, &x1, &z1, &x2, &z2, group, FLAG(n)));
255 				MP_CHECKOK(gf2m_Mdouble(&x2, &z2, group, FLAG(n)));
256 			} else {
257 				MP_CHECKOK(gf2m_Madd(px, &x2, &z2, &x1, &z1, group, FLAG(n)));
258 				MP_CHECKOK(gf2m_Mdouble(&x1, &z1, group, FLAG(n)));
259 			}
260 			mask >>= 1;
261 		}
262 		j = MP_DIGIT_BIT - 1;
263 		mask = top_bit;
264 	}
265 
266 	/* convert out of "projective" coordinates */
267 	i = gf2m_Mxy(px, py, &x1, &z1, &x2, &z2, group);
268 	if (i == 0) {
269 		res = MP_BADARG;
270 		goto CLEANUP;
271 	} else if (i == 1) {
272 		MP_CHECKOK(ec_GF2m_pt_set_inf_aff(rx, ry));
273 	} else {
274 		MP_CHECKOK(mp_copy(&x2, rx));
275 		MP_CHECKOK(mp_copy(&z2, ry));
276 	}
277 
278   CLEANUP:
279 	mp_clear(&x1);
280 	mp_clear(&x2);
281 	mp_clear(&z1);
282 	mp_clear(&z2);
283 	return res;
284 }
285