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 * 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 #include "ec2.h"
46 #include "mplogic.h"
47 #include "mp_gf2m.h"
48 #ifndef _KERNEL
49 #include <stdlib.h>
50 #endif
51
52 /* Checks if point P(px, py) is at infinity. Uses affine coordinates. */
53 mp_err
ec_GF2m_pt_is_inf_aff(const mp_int * px,const mp_int * py)54 ec_GF2m_pt_is_inf_aff(const mp_int *px, const mp_int *py)
55 {
56
57 if ((mp_cmp_z(px) == 0) && (mp_cmp_z(py) == 0)) {
58 return MP_YES;
59 } else {
60 return MP_NO;
61 }
62
63 }
64
65 /* Sets P(px, py) to be the point at infinity. Uses affine coordinates. */
66 mp_err
ec_GF2m_pt_set_inf_aff(mp_int * px,mp_int * py)67 ec_GF2m_pt_set_inf_aff(mp_int *px, mp_int *py)
68 {
69 mp_zero(px);
70 mp_zero(py);
71 return MP_OKAY;
72 }
73
74 /* Computes R = P + Q based on IEEE P1363 A.10.2. Elliptic curve points P,
75 * Q, and R can all be identical. Uses affine coordinates. */
76 mp_err
ec_GF2m_pt_add_aff(const mp_int * px,const mp_int * py,const mp_int * qx,const mp_int * qy,mp_int * rx,mp_int * ry,const ECGroup * group)77 ec_GF2m_pt_add_aff(const mp_int *px, const mp_int *py, const mp_int *qx,
78 const mp_int *qy, mp_int *rx, mp_int *ry,
79 const ECGroup *group)
80 {
81 mp_err res = MP_OKAY;
82 mp_int lambda, tempx, tempy;
83
84 MP_DIGITS(&lambda) = 0;
85 MP_DIGITS(&tempx) = 0;
86 MP_DIGITS(&tempy) = 0;
87 MP_CHECKOK(mp_init(&lambda, FLAG(px)));
88 MP_CHECKOK(mp_init(&tempx, FLAG(px)));
89 MP_CHECKOK(mp_init(&tempy, FLAG(px)));
90 /* if P = inf, then R = Q */
91 if (ec_GF2m_pt_is_inf_aff(px, py) == 0) {
92 MP_CHECKOK(mp_copy(qx, rx));
93 MP_CHECKOK(mp_copy(qy, ry));
94 res = MP_OKAY;
95 goto CLEANUP;
96 }
97 /* if Q = inf, then R = P */
98 if (ec_GF2m_pt_is_inf_aff(qx, qy) == 0) {
99 MP_CHECKOK(mp_copy(px, rx));
100 MP_CHECKOK(mp_copy(py, ry));
101 res = MP_OKAY;
102 goto CLEANUP;
103 }
104 /* if px != qx, then lambda = (py+qy) / (px+qx), tempx = a + lambda^2
105 * + lambda + px + qx */
106 if (mp_cmp(px, qx) != 0) {
107 MP_CHECKOK(group->meth->field_add(py, qy, &tempy, group->meth));
108 MP_CHECKOK(group->meth->field_add(px, qx, &tempx, group->meth));
109 MP_CHECKOK(group->meth->
110 field_div(&tempy, &tempx, &lambda, group->meth));
111 MP_CHECKOK(group->meth->field_sqr(&lambda, &tempx, group->meth));
112 MP_CHECKOK(group->meth->
113 field_add(&tempx, &lambda, &tempx, group->meth));
114 MP_CHECKOK(group->meth->
115 field_add(&tempx, &group->curvea, &tempx, group->meth));
116 MP_CHECKOK(group->meth->
117 field_add(&tempx, px, &tempx, group->meth));
118 MP_CHECKOK(group->meth->
119 field_add(&tempx, qx, &tempx, group->meth));
120 } else {
121 /* if py != qy or qx = 0, then R = inf */
122 if (((mp_cmp(py, qy) != 0)) || (mp_cmp_z(qx) == 0)) {
123 mp_zero(rx);
124 mp_zero(ry);
125 res = MP_OKAY;
126 goto CLEANUP;
127 }
128 /* lambda = qx + qy / qx */
129 MP_CHECKOK(group->meth->field_div(qy, qx, &lambda, group->meth));
130 MP_CHECKOK(group->meth->
131 field_add(&lambda, qx, &lambda, group->meth));
132 /* tempx = a + lambda^2 + lambda */
133 MP_CHECKOK(group->meth->field_sqr(&lambda, &tempx, group->meth));
134 MP_CHECKOK(group->meth->
135 field_add(&tempx, &lambda, &tempx, group->meth));
136 MP_CHECKOK(group->meth->
137 field_add(&tempx, &group->curvea, &tempx, group->meth));
138 }
139 /* ry = (qx + tempx) * lambda + tempx + qy */
140 MP_CHECKOK(group->meth->field_add(qx, &tempx, &tempy, group->meth));
141 MP_CHECKOK(group->meth->
142 field_mul(&tempy, &lambda, &tempy, group->meth));
143 MP_CHECKOK(group->meth->
144 field_add(&tempy, &tempx, &tempy, group->meth));
145 MP_CHECKOK(group->meth->field_add(&tempy, qy, ry, group->meth));
146 /* rx = tempx */
147 MP_CHECKOK(mp_copy(&tempx, rx));
148
149 CLEANUP:
150 mp_clear(&lambda);
151 mp_clear(&tempx);
152 mp_clear(&tempy);
153 return res;
154 }
155
156 /* Computes R = P - Q. Elliptic curve points P, Q, and R can all be
157 * identical. Uses affine coordinates. */
158 mp_err
ec_GF2m_pt_sub_aff(const mp_int * px,const mp_int * py,const mp_int * qx,const mp_int * qy,mp_int * rx,mp_int * ry,const ECGroup * group)159 ec_GF2m_pt_sub_aff(const mp_int *px, const mp_int *py, const mp_int *qx,
160 const mp_int *qy, mp_int *rx, mp_int *ry,
161 const ECGroup *group)
162 {
163 mp_err res = MP_OKAY;
164 mp_int nqy;
165
166 MP_DIGITS(&nqy) = 0;
167 MP_CHECKOK(mp_init(&nqy, FLAG(px)));
168 /* nqy = qx+qy */
169 MP_CHECKOK(group->meth->field_add(qx, qy, &nqy, group->meth));
170 MP_CHECKOK(group->point_add(px, py, qx, &nqy, rx, ry, group));
171 CLEANUP:
172 mp_clear(&nqy);
173 return res;
174 }
175
176 /* Computes R = 2P. Elliptic curve points P and R can be identical. Uses
177 * affine coordinates. */
178 mp_err
ec_GF2m_pt_dbl_aff(const mp_int * px,const mp_int * py,mp_int * rx,mp_int * ry,const ECGroup * group)179 ec_GF2m_pt_dbl_aff(const mp_int *px, const mp_int *py, mp_int *rx,
180 mp_int *ry, const ECGroup *group)
181 {
182 return group->point_add(px, py, px, py, rx, ry, group);
183 }
184
185 /* by default, this routine is unused and thus doesn't need to be compiled */
186 #ifdef ECL_ENABLE_GF2M_PT_MUL_AFF
187 /* Computes R = nP based on IEEE P1363 A.10.3. Elliptic curve points P and
188 * R can be identical. Uses affine coordinates. */
189 mp_err
ec_GF2m_pt_mul_aff(const mp_int * n,const mp_int * px,const mp_int * py,mp_int * rx,mp_int * ry,const ECGroup * group)190 ec_GF2m_pt_mul_aff(const mp_int *n, const mp_int *px, const mp_int *py,
191 mp_int *rx, mp_int *ry, const ECGroup *group)
192 {
193 mp_err res = MP_OKAY;
194 mp_int k, k3, qx, qy, sx, sy;
195 int b1, b3, i, l;
196
197 MP_DIGITS(&k) = 0;
198 MP_DIGITS(&k3) = 0;
199 MP_DIGITS(&qx) = 0;
200 MP_DIGITS(&qy) = 0;
201 MP_DIGITS(&sx) = 0;
202 MP_DIGITS(&sy) = 0;
203 MP_CHECKOK(mp_init(&k));
204 MP_CHECKOK(mp_init(&k3));
205 MP_CHECKOK(mp_init(&qx));
206 MP_CHECKOK(mp_init(&qy));
207 MP_CHECKOK(mp_init(&sx));
208 MP_CHECKOK(mp_init(&sy));
209
210 /* if n = 0 then r = inf */
211 if (mp_cmp_z(n) == 0) {
212 mp_zero(rx);
213 mp_zero(ry);
214 res = MP_OKAY;
215 goto CLEANUP;
216 }
217 /* Q = P, k = n */
218 MP_CHECKOK(mp_copy(px, &qx));
219 MP_CHECKOK(mp_copy(py, &qy));
220 MP_CHECKOK(mp_copy(n, &k));
221 /* if n < 0 then Q = -Q, k = -k */
222 if (mp_cmp_z(n) < 0) {
223 MP_CHECKOK(group->meth->field_add(&qx, &qy, &qy, group->meth));
224 MP_CHECKOK(mp_neg(&k, &k));
225 }
226 #ifdef ECL_DEBUG /* basic double and add method */
227 l = mpl_significant_bits(&k) - 1;
228 MP_CHECKOK(mp_copy(&qx, &sx));
229 MP_CHECKOK(mp_copy(&qy, &sy));
230 for (i = l - 1; i >= 0; i--) {
231 /* S = 2S */
232 MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group));
233 /* if k_i = 1, then S = S + Q */
234 if (mpl_get_bit(&k, i) != 0) {
235 MP_CHECKOK(group->
236 point_add(&sx, &sy, &qx, &qy, &sx, &sy, group));
237 }
238 }
239 #else /* double and add/subtract method from
240 * standard */
241 /* k3 = 3 * k */
242 MP_CHECKOK(mp_set_int(&k3, 3));
243 MP_CHECKOK(mp_mul(&k, &k3, &k3));
244 /* S = Q */
245 MP_CHECKOK(mp_copy(&qx, &sx));
246 MP_CHECKOK(mp_copy(&qy, &sy));
247 /* l = index of high order bit in binary representation of 3*k */
248 l = mpl_significant_bits(&k3) - 1;
249 /* for i = l-1 downto 1 */
250 for (i = l - 1; i >= 1; i--) {
251 /* S = 2S */
252 MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group));
253 b3 = MP_GET_BIT(&k3, i);
254 b1 = MP_GET_BIT(&k, i);
255 /* if k3_i = 1 and k_i = 0, then S = S + Q */
256 if ((b3 == 1) && (b1 == 0)) {
257 MP_CHECKOK(group->
258 point_add(&sx, &sy, &qx, &qy, &sx, &sy, group));
259 /* if k3_i = 0 and k_i = 1, then S = S - Q */
260 } else if ((b3 == 0) && (b1 == 1)) {
261 MP_CHECKOK(group->
262 point_sub(&sx, &sy, &qx, &qy, &sx, &sy, group));
263 }
264 }
265 #endif
266 /* output S */
267 MP_CHECKOK(mp_copy(&sx, rx));
268 MP_CHECKOK(mp_copy(&sy, ry));
269
270 CLEANUP:
271 mp_clear(&k);
272 mp_clear(&k3);
273 mp_clear(&qx);
274 mp_clear(&qy);
275 mp_clear(&sx);
276 mp_clear(&sy);
277 return res;
278 }
279 #endif
280
281 /* Validates a point on a GF2m curve. */
282 mp_err
ec_GF2m_validate_point(const mp_int * px,const mp_int * py,const ECGroup * group)283 ec_GF2m_validate_point(const mp_int *px, const mp_int *py, const ECGroup *group)
284 {
285 mp_err res = MP_NO;
286 mp_int accl, accr, tmp, pxt, pyt;
287
288 MP_DIGITS(&accl) = 0;
289 MP_DIGITS(&accr) = 0;
290 MP_DIGITS(&tmp) = 0;
291 MP_DIGITS(&pxt) = 0;
292 MP_DIGITS(&pyt) = 0;
293 MP_CHECKOK(mp_init(&accl, FLAG(px)));
294 MP_CHECKOK(mp_init(&accr, FLAG(px)));
295 MP_CHECKOK(mp_init(&tmp, FLAG(px)));
296 MP_CHECKOK(mp_init(&pxt, FLAG(px)));
297 MP_CHECKOK(mp_init(&pyt, FLAG(px)));
298
299 /* 1: Verify that publicValue is not the point at infinity */
300 if (ec_GF2m_pt_is_inf_aff(px, py) == MP_YES) {
301 res = MP_NO;
302 goto CLEANUP;
303 }
304 /* 2: Verify that the coordinates of publicValue are elements
305 * of the field.
306 */
307 if ((MP_SIGN(px) == MP_NEG) || (mp_cmp(px, &group->meth->irr) >= 0) ||
308 (MP_SIGN(py) == MP_NEG) || (mp_cmp(py, &group->meth->irr) >= 0)) {
309 res = MP_NO;
310 goto CLEANUP;
311 }
312 /* 3: Verify that publicValue is on the curve. */
313 if (group->meth->field_enc) {
314 group->meth->field_enc(px, &pxt, group->meth);
315 group->meth->field_enc(py, &pyt, group->meth);
316 } else {
317 mp_copy(px, &pxt);
318 mp_copy(py, &pyt);
319 }
320 /* left-hand side: y^2 + x*y */
321 MP_CHECKOK( group->meth->field_sqr(&pyt, &accl, group->meth) );
322 MP_CHECKOK( group->meth->field_mul(&pxt, &pyt, &tmp, group->meth) );
323 MP_CHECKOK( group->meth->field_add(&accl, &tmp, &accl, group->meth) );
324 /* right-hand side: x^3 + a*x^2 + b */
325 MP_CHECKOK( group->meth->field_sqr(&pxt, &tmp, group->meth) );
326 MP_CHECKOK( group->meth->field_mul(&pxt, &tmp, &accr, group->meth) );
327 MP_CHECKOK( group->meth->field_mul(&group->curvea, &tmp, &tmp, group->meth) );
328 MP_CHECKOK( group->meth->field_add(&tmp, &accr, &accr, group->meth) );
329 MP_CHECKOK( group->meth->field_add(&accr, &group->curveb, &accr, group->meth) );
330 /* check LHS - RHS == 0 */
331 MP_CHECKOK( group->meth->field_add(&accl, &accr, &accr, group->meth) );
332 if (mp_cmp_z(&accr) != 0) {
333 res = MP_NO;
334 goto CLEANUP;
335 }
336 /* 4: Verify that the order of the curve times the publicValue
337 * is the point at infinity.
338 */
339 MP_CHECKOK( ECPoint_mul(group, &group->order, px, py, &pxt, &pyt) );
340 if (ec_GF2m_pt_is_inf_aff(&pxt, &pyt) != MP_YES) {
341 res = MP_NO;
342 goto CLEANUP;
343 }
344
345 res = MP_YES;
346
347 CLEANUP:
348 mp_clear(&accl);
349 mp_clear(&accr);
350 mp_clear(&tmp);
351 mp_clear(&pxt);
352 mp_clear(&pyt);
353 return res;
354 }
355