xref: /illumos-gate/usr/src/common/crypto/ecc/ec2_mont.c (revision c40a6cd785e883b3f052b122c332e21174fc1871)
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 #include "ec2.h"
48 #include "mplogic.h"
49 #include "mp_gf2m.h"
50 #ifndef _KERNEL
51 #include <stdlib.h>
52 #endif
53 
54 /* Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery
55  * projective coordinates. Uses algorithm Mdouble in appendix of Lopez, J.
56  * and Dahab, R.  "Fast multiplication on elliptic curves over GF(2^m)
57  * without precomputation". modified to not require precomputation of
58  * c=b^{2^{m-1}}. */
59 static mp_err
gf2m_Mdouble(mp_int * x,mp_int * z,const ECGroup * group,int kmflag)60 gf2m_Mdouble(mp_int *x, mp_int *z, const ECGroup *group, int kmflag)
61 {
62 	mp_err res = MP_OKAY;
63 	mp_int t1;
64 
65 	MP_DIGITS(&t1) = 0;
66 	MP_CHECKOK(mp_init(&t1, kmflag));
67 
68 	MP_CHECKOK(group->meth->field_sqr(x, x, group->meth));
69 	MP_CHECKOK(group->meth->field_sqr(z, &t1, group->meth));
70 	MP_CHECKOK(group->meth->field_mul(x, &t1, z, group->meth));
71 	MP_CHECKOK(group->meth->field_sqr(x, x, group->meth));
72 	MP_CHECKOK(group->meth->field_sqr(&t1, &t1, group->meth));
73 	MP_CHECKOK(group->meth->
74 			   field_mul(&group->curveb, &t1, &t1, group->meth));
75 	MP_CHECKOK(group->meth->field_add(x, &t1, x, group->meth));
76 
77   CLEANUP:
78 	mp_clear(&t1);
79 	return res;
80 }
81 
82 /* Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in
83  * Montgomery projective coordinates. Uses algorithm Madd in appendix of
84  * Lopex, J. and Dahab, R.  "Fast multiplication on elliptic curves over
85  * GF(2^m) without precomputation". */
86 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)87 gf2m_Madd(const mp_int *x, mp_int *x1, mp_int *z1, mp_int *x2, mp_int *z2,
88 		  const ECGroup *group, int kmflag)
89 {
90 	mp_err res = MP_OKAY;
91 	mp_int t1, t2;
92 
93 	MP_DIGITS(&t1) = 0;
94 	MP_DIGITS(&t2) = 0;
95 	MP_CHECKOK(mp_init(&t1, kmflag));
96 	MP_CHECKOK(mp_init(&t2, kmflag));
97 
98 	MP_CHECKOK(mp_copy(x, &t1));
99 	MP_CHECKOK(group->meth->field_mul(x1, z2, x1, group->meth));
100 	MP_CHECKOK(group->meth->field_mul(z1, x2, z1, group->meth));
101 	MP_CHECKOK(group->meth->field_mul(x1, z1, &t2, group->meth));
102 	MP_CHECKOK(group->meth->field_add(z1, x1, z1, group->meth));
103 	MP_CHECKOK(group->meth->field_sqr(z1, z1, group->meth));
104 	MP_CHECKOK(group->meth->field_mul(z1, &t1, x1, group->meth));
105 	MP_CHECKOK(group->meth->field_add(x1, &t2, x1, group->meth));
106 
107   CLEANUP:
108 	mp_clear(&t1);
109 	mp_clear(&t2);
110 	return res;
111 }
112 
113 /* Compute the x, y affine coordinates from the point (x1, z1) (x2, z2)
114  * using Montgomery point multiplication algorithm Mxy() in appendix of
115  * Lopex, J. and Dahab, R.  "Fast multiplication on elliptic curves over
116  * GF(2^m) without precomputation". Returns: 0 on error 1 if return value
117  * should be the point at infinity 2 otherwise */
118 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)119 gf2m_Mxy(const mp_int *x, const mp_int *y, mp_int *x1, mp_int *z1,
120 		 mp_int *x2, mp_int *z2, const ECGroup *group)
121 {
122 	mp_err res = MP_OKAY;
123 	int ret = 0;
124 	mp_int t3, t4, t5;
125 
126 	MP_DIGITS(&t3) = 0;
127 	MP_DIGITS(&t4) = 0;
128 	MP_DIGITS(&t5) = 0;
129 	MP_CHECKOK(mp_init(&t3, FLAG(x2)));
130 	MP_CHECKOK(mp_init(&t4, FLAG(x2)));
131 	MP_CHECKOK(mp_init(&t5, FLAG(x2)));
132 
133 	if (mp_cmp_z(z1) == 0) {
134 		mp_zero(x2);
135 		mp_zero(z2);
136 		ret = 1;
137 		goto CLEANUP;
138 	}
139 
140 	if (mp_cmp_z(z2) == 0) {
141 		MP_CHECKOK(mp_copy(x, x2));
142 		MP_CHECKOK(group->meth->field_add(x, y, z2, group->meth));
143 		ret = 2;
144 		goto CLEANUP;
145 	}
146 
147 	MP_CHECKOK(mp_set_int(&t5, 1));
148 	if (group->meth->field_enc) {
149 		MP_CHECKOK(group->meth->field_enc(&t5, &t5, group->meth));
150 	}
151 
152 	MP_CHECKOK(group->meth->field_mul(z1, z2, &t3, group->meth));
153 
154 	MP_CHECKOK(group->meth->field_mul(z1, x, z1, group->meth));
155 	MP_CHECKOK(group->meth->field_add(z1, x1, z1, group->meth));
156 	MP_CHECKOK(group->meth->field_mul(z2, x, z2, group->meth));
157 	MP_CHECKOK(group->meth->field_mul(z2, x1, x1, group->meth));
158 	MP_CHECKOK(group->meth->field_add(z2, x2, z2, group->meth));
159 
160 	MP_CHECKOK(group->meth->field_mul(z2, z1, z2, group->meth));
161 	MP_CHECKOK(group->meth->field_sqr(x, &t4, group->meth));
162 	MP_CHECKOK(group->meth->field_add(&t4, y, &t4, group->meth));
163 	MP_CHECKOK(group->meth->field_mul(&t4, &t3, &t4, group->meth));
164 	MP_CHECKOK(group->meth->field_add(&t4, z2, &t4, group->meth));
165 
166 	MP_CHECKOK(group->meth->field_mul(&t3, x, &t3, group->meth));
167 	MP_CHECKOK(group->meth->field_div(&t5, &t3, &t3, group->meth));
168 	MP_CHECKOK(group->meth->field_mul(&t3, &t4, &t4, group->meth));
169 	MP_CHECKOK(group->meth->field_mul(x1, &t3, x2, group->meth));
170 	MP_CHECKOK(group->meth->field_add(x2, x, z2, group->meth));
171 
172 	MP_CHECKOK(group->meth->field_mul(z2, &t4, z2, group->meth));
173 	MP_CHECKOK(group->meth->field_add(z2, y, z2, group->meth));
174 
175 	ret = 2;
176 
177   CLEANUP:
178 	mp_clear(&t3);
179 	mp_clear(&t4);
180 	mp_clear(&t5);
181 	if (res == MP_OKAY) {
182 		return ret;
183 	} else {
184 		return 0;
185 	}
186 }
187 
188 /* Computes R = nP based on algorithm 2P of Lopex, J. and Dahab, R.  "Fast
189  * multiplication on elliptic curves over GF(2^m) without
190  * precomputation". Elliptic curve points P and R can be identical. Uses
191  * Montgomery projective coordinates. */
192 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)193 ec_GF2m_pt_mul_mont(const mp_int *n, const mp_int *px, const mp_int *py,
194 					mp_int *rx, mp_int *ry, const ECGroup *group)
195 {
196 	mp_err res = MP_OKAY;
197 	mp_int x1, x2, z1, z2;
198 	int i, j;
199 	mp_digit top_bit, mask;
200 
201 	MP_DIGITS(&x1) = 0;
202 	MP_DIGITS(&x2) = 0;
203 	MP_DIGITS(&z1) = 0;
204 	MP_DIGITS(&z2) = 0;
205 	MP_CHECKOK(mp_init(&x1, FLAG(n)));
206 	MP_CHECKOK(mp_init(&x2, FLAG(n)));
207 	MP_CHECKOK(mp_init(&z1, FLAG(n)));
208 	MP_CHECKOK(mp_init(&z2, FLAG(n)));
209 
210 	/* if result should be point at infinity */
211 	if ((mp_cmp_z(n) == 0) || (ec_GF2m_pt_is_inf_aff(px, py) == MP_YES)) {
212 		MP_CHECKOK(ec_GF2m_pt_set_inf_aff(rx, ry));
213 		goto CLEANUP;
214 	}
215 
216 	MP_CHECKOK(mp_copy(px, &x1));	/* x1 = px */
217 	MP_CHECKOK(mp_set_int(&z1, 1));	/* z1 = 1 */
218 	MP_CHECKOK(group->meth->field_sqr(&x1, &z2, group->meth));	/* z2 =
219 																 * x1^2 =
220 																 * px^2 */
221 	MP_CHECKOK(group->meth->field_sqr(&z2, &x2, group->meth));
222 	MP_CHECKOK(group->meth->field_add(&x2, &group->curveb, &x2, group->meth));	/* x2
223 																				 * =
224 																				 * px^4
225 																				 * +
226 																				 * b
227 																				 */
228 
229 	/* find top-most bit and go one past it */
230 	i = MP_USED(n) - 1;
231 	j = MP_DIGIT_BIT - 1;
232 	top_bit = 1;
233 	top_bit <<= MP_DIGIT_BIT - 1;
234 	mask = top_bit;
235 	while (!(MP_DIGITS(n)[i] & mask)) {
236 		mask >>= 1;
237 		j--;
238 	}
239 	mask >>= 1;
240 	j--;
241 
242 	/* if top most bit was at word break, go to next word */
243 	if (!mask) {
244 		i--;
245 		j = MP_DIGIT_BIT - 1;
246 		mask = top_bit;
247 	}
248 
249 	for (; i >= 0; i--) {
250 		for (; j >= 0; j--) {
251 			if (MP_DIGITS(n)[i] & mask) {
252 				MP_CHECKOK(gf2m_Madd(px, &x1, &z1, &x2, &z2, group, FLAG(n)));
253 				MP_CHECKOK(gf2m_Mdouble(&x2, &z2, group, FLAG(n)));
254 			} else {
255 				MP_CHECKOK(gf2m_Madd(px, &x2, &z2, &x1, &z1, group, FLAG(n)));
256 				MP_CHECKOK(gf2m_Mdouble(&x1, &z1, group, FLAG(n)));
257 			}
258 			mask >>= 1;
259 		}
260 		j = MP_DIGIT_BIT - 1;
261 		mask = top_bit;
262 	}
263 
264 	/* convert out of "projective" coordinates */
265 	i = gf2m_Mxy(px, py, &x1, &z1, &x2, &z2, group);
266 	if (i == 0) {
267 		res = MP_BADARG;
268 		goto CLEANUP;
269 	} else if (i == 1) {
270 		MP_CHECKOK(ec_GF2m_pt_set_inf_aff(rx, ry));
271 	} else {
272 		MP_CHECKOK(mp_copy(&x2, rx));
273 		MP_CHECKOK(mp_copy(&z2, ry));
274 	}
275 
276   CLEANUP:
277 	mp_clear(&x1);
278 	mp_clear(&x2);
279 	mp_clear(&z1);
280 	mp_clear(&z2);
281 	return res;
282 }
283