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 #pragma ident "%Z%%M% %I% %E% SMI"
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 /* Checks if point P(px, py) is at infinity. Uses affine coordinates. */
55 mp_err
ec_GF2m_pt_is_inf_aff(const mp_int * px,const mp_int * py)56 ec_GF2m_pt_is_inf_aff(const mp_int *px, const mp_int *py)
57 {
58
59 if ((mp_cmp_z(px) == 0) && (mp_cmp_z(py) == 0)) {
60 return MP_YES;
61 } else {
62 return MP_NO;
63 }
64
65 }
66
67 /* Sets P(px, py) to be the point at infinity. Uses affine coordinates. */
68 mp_err
ec_GF2m_pt_set_inf_aff(mp_int * px,mp_int * py)69 ec_GF2m_pt_set_inf_aff(mp_int *px, mp_int *py)
70 {
71 mp_zero(px);
72 mp_zero(py);
73 return MP_OKAY;
74 }
75
76 /* Computes R = P + Q based on IEEE P1363 A.10.2. Elliptic curve points P,
77 * Q, and R can all be identical. Uses affine coordinates. */
78 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)79 ec_GF2m_pt_add_aff(const mp_int *px, const mp_int *py, const mp_int *qx,
80 const mp_int *qy, mp_int *rx, mp_int *ry,
81 const ECGroup *group)
82 {
83 mp_err res = MP_OKAY;
84 mp_int lambda, tempx, tempy;
85
86 MP_DIGITS(&lambda) = 0;
87 MP_DIGITS(&tempx) = 0;
88 MP_DIGITS(&tempy) = 0;
89 MP_CHECKOK(mp_init(&lambda, FLAG(px)));
90 MP_CHECKOK(mp_init(&tempx, FLAG(px)));
91 MP_CHECKOK(mp_init(&tempy, FLAG(px)));
92 /* if P = inf, then R = Q */
93 if (ec_GF2m_pt_is_inf_aff(px, py) == 0) {
94 MP_CHECKOK(mp_copy(qx, rx));
95 MP_CHECKOK(mp_copy(qy, ry));
96 res = MP_OKAY;
97 goto CLEANUP;
98 }
99 /* if Q = inf, then R = P */
100 if (ec_GF2m_pt_is_inf_aff(qx, qy) == 0) {
101 MP_CHECKOK(mp_copy(px, rx));
102 MP_CHECKOK(mp_copy(py, ry));
103 res = MP_OKAY;
104 goto CLEANUP;
105 }
106 /* if px != qx, then lambda = (py+qy) / (px+qx), tempx = a + lambda^2
107 * + lambda + px + qx */
108 if (mp_cmp(px, qx) != 0) {
109 MP_CHECKOK(group->meth->field_add(py, qy, &tempy, group->meth));
110 MP_CHECKOK(group->meth->field_add(px, qx, &tempx, group->meth));
111 MP_CHECKOK(group->meth->
112 field_div(&tempy, &tempx, &lambda, group->meth));
113 MP_CHECKOK(group->meth->field_sqr(&lambda, &tempx, group->meth));
114 MP_CHECKOK(group->meth->
115 field_add(&tempx, &lambda, &tempx, group->meth));
116 MP_CHECKOK(group->meth->
117 field_add(&tempx, &group->curvea, &tempx, group->meth));
118 MP_CHECKOK(group->meth->
119 field_add(&tempx, px, &tempx, group->meth));
120 MP_CHECKOK(group->meth->
121 field_add(&tempx, qx, &tempx, group->meth));
122 } else {
123 /* if py != qy or qx = 0, then R = inf */
124 if (((mp_cmp(py, qy) != 0)) || (mp_cmp_z(qx) == 0)) {
125 mp_zero(rx);
126 mp_zero(ry);
127 res = MP_OKAY;
128 goto CLEANUP;
129 }
130 /* lambda = qx + qy / qx */
131 MP_CHECKOK(group->meth->field_div(qy, qx, &lambda, group->meth));
132 MP_CHECKOK(group->meth->
133 field_add(&lambda, qx, &lambda, group->meth));
134 /* tempx = a + lambda^2 + lambda */
135 MP_CHECKOK(group->meth->field_sqr(&lambda, &tempx, group->meth));
136 MP_CHECKOK(group->meth->
137 field_add(&tempx, &lambda, &tempx, group->meth));
138 MP_CHECKOK(group->meth->
139 field_add(&tempx, &group->curvea, &tempx, group->meth));
140 }
141 /* ry = (qx + tempx) * lambda + tempx + qy */
142 MP_CHECKOK(group->meth->field_add(qx, &tempx, &tempy, group->meth));
143 MP_CHECKOK(group->meth->
144 field_mul(&tempy, &lambda, &tempy, group->meth));
145 MP_CHECKOK(group->meth->
146 field_add(&tempy, &tempx, &tempy, group->meth));
147 MP_CHECKOK(group->meth->field_add(&tempy, qy, ry, group->meth));
148 /* rx = tempx */
149 MP_CHECKOK(mp_copy(&tempx, rx));
150
151 CLEANUP:
152 mp_clear(&lambda);
153 mp_clear(&tempx);
154 mp_clear(&tempy);
155 return res;
156 }
157
158 /* Computes R = P - Q. Elliptic curve points P, Q, and R can all be
159 * identical. Uses affine coordinates. */
160 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)161 ec_GF2m_pt_sub_aff(const mp_int *px, const mp_int *py, const mp_int *qx,
162 const mp_int *qy, mp_int *rx, mp_int *ry,
163 const ECGroup *group)
164 {
165 mp_err res = MP_OKAY;
166 mp_int nqy;
167
168 MP_DIGITS(&nqy) = 0;
169 MP_CHECKOK(mp_init(&nqy, FLAG(px)));
170 /* nqy = qx+qy */
171 MP_CHECKOK(group->meth->field_add(qx, qy, &nqy, group->meth));
172 MP_CHECKOK(group->point_add(px, py, qx, &nqy, rx, ry, group));
173 CLEANUP:
174 mp_clear(&nqy);
175 return res;
176 }
177
178 /* Computes R = 2P. Elliptic curve points P and R can be identical. Uses
179 * affine coordinates. */
180 mp_err
ec_GF2m_pt_dbl_aff(const mp_int * px,const mp_int * py,mp_int * rx,mp_int * ry,const ECGroup * group)181 ec_GF2m_pt_dbl_aff(const mp_int *px, const mp_int *py, mp_int *rx,
182 mp_int *ry, const ECGroup *group)
183 {
184 return group->point_add(px, py, px, py, rx, ry, group);
185 }
186
187 /* by default, this routine is unused and thus doesn't need to be compiled */
188 #ifdef ECL_ENABLE_GF2M_PT_MUL_AFF
189 /* Computes R = nP based on IEEE P1363 A.10.3. Elliptic curve points P and
190 * R can be identical. Uses affine coordinates. */
191 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)192 ec_GF2m_pt_mul_aff(const mp_int *n, const mp_int *px, const mp_int *py,
193 mp_int *rx, mp_int *ry, const ECGroup *group)
194 {
195 mp_err res = MP_OKAY;
196 mp_int k, k3, qx, qy, sx, sy;
197 int b1, b3, i, l;
198
199 MP_DIGITS(&k) = 0;
200 MP_DIGITS(&k3) = 0;
201 MP_DIGITS(&qx) = 0;
202 MP_DIGITS(&qy) = 0;
203 MP_DIGITS(&sx) = 0;
204 MP_DIGITS(&sy) = 0;
205 MP_CHECKOK(mp_init(&k));
206 MP_CHECKOK(mp_init(&k3));
207 MP_CHECKOK(mp_init(&qx));
208 MP_CHECKOK(mp_init(&qy));
209 MP_CHECKOK(mp_init(&sx));
210 MP_CHECKOK(mp_init(&sy));
211
212 /* if n = 0 then r = inf */
213 if (mp_cmp_z(n) == 0) {
214 mp_zero(rx);
215 mp_zero(ry);
216 res = MP_OKAY;
217 goto CLEANUP;
218 }
219 /* Q = P, k = n */
220 MP_CHECKOK(mp_copy(px, &qx));
221 MP_CHECKOK(mp_copy(py, &qy));
222 MP_CHECKOK(mp_copy(n, &k));
223 /* if n < 0 then Q = -Q, k = -k */
224 if (mp_cmp_z(n) < 0) {
225 MP_CHECKOK(group->meth->field_add(&qx, &qy, &qy, group->meth));
226 MP_CHECKOK(mp_neg(&k, &k));
227 }
228 #ifdef ECL_DEBUG /* basic double and add method */
229 l = mpl_significant_bits(&k) - 1;
230 MP_CHECKOK(mp_copy(&qx, &sx));
231 MP_CHECKOK(mp_copy(&qy, &sy));
232 for (i = l - 1; i >= 0; i--) {
233 /* S = 2S */
234 MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group));
235 /* if k_i = 1, then S = S + Q */
236 if (mpl_get_bit(&k, i) != 0) {
237 MP_CHECKOK(group->
238 point_add(&sx, &sy, &qx, &qy, &sx, &sy, group));
239 }
240 }
241 #else /* double and add/subtract method from
242 * standard */
243 /* k3 = 3 * k */
244 MP_CHECKOK(mp_set_int(&k3, 3));
245 MP_CHECKOK(mp_mul(&k, &k3, &k3));
246 /* S = Q */
247 MP_CHECKOK(mp_copy(&qx, &sx));
248 MP_CHECKOK(mp_copy(&qy, &sy));
249 /* l = index of high order bit in binary representation of 3*k */
250 l = mpl_significant_bits(&k3) - 1;
251 /* for i = l-1 downto 1 */
252 for (i = l - 1; i >= 1; i--) {
253 /* S = 2S */
254 MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group));
255 b3 = MP_GET_BIT(&k3, i);
256 b1 = MP_GET_BIT(&k, i);
257 /* if k3_i = 1 and k_i = 0, then S = S + Q */
258 if ((b3 == 1) && (b1 == 0)) {
259 MP_CHECKOK(group->
260 point_add(&sx, &sy, &qx, &qy, &sx, &sy, group));
261 /* if k3_i = 0 and k_i = 1, then S = S - Q */
262 } else if ((b3 == 0) && (b1 == 1)) {
263 MP_CHECKOK(group->
264 point_sub(&sx, &sy, &qx, &qy, &sx, &sy, group));
265 }
266 }
267 #endif
268 /* output S */
269 MP_CHECKOK(mp_copy(&sx, rx));
270 MP_CHECKOK(mp_copy(&sy, ry));
271
272 CLEANUP:
273 mp_clear(&k);
274 mp_clear(&k3);
275 mp_clear(&qx);
276 mp_clear(&qy);
277 mp_clear(&sx);
278 mp_clear(&sy);
279 return res;
280 }
281 #endif
282
283 /* Validates a point on a GF2m curve. */
284 mp_err
ec_GF2m_validate_point(const mp_int * px,const mp_int * py,const ECGroup * group)285 ec_GF2m_validate_point(const mp_int *px, const mp_int *py, const ECGroup *group)
286 {
287 mp_err res = MP_NO;
288 mp_int accl, accr, tmp, pxt, pyt;
289
290 MP_DIGITS(&accl) = 0;
291 MP_DIGITS(&accr) = 0;
292 MP_DIGITS(&tmp) = 0;
293 MP_DIGITS(&pxt) = 0;
294 MP_DIGITS(&pyt) = 0;
295 MP_CHECKOK(mp_init(&accl, FLAG(px)));
296 MP_CHECKOK(mp_init(&accr, FLAG(px)));
297 MP_CHECKOK(mp_init(&tmp, FLAG(px)));
298 MP_CHECKOK(mp_init(&pxt, FLAG(px)));
299 MP_CHECKOK(mp_init(&pyt, FLAG(px)));
300
301 /* 1: Verify that publicValue is not the point at infinity */
302 if (ec_GF2m_pt_is_inf_aff(px, py) == MP_YES) {
303 res = MP_NO;
304 goto CLEANUP;
305 }
306 /* 2: Verify that the coordinates of publicValue are elements
307 * of the field.
308 */
309 if ((MP_SIGN(px) == MP_NEG) || (mp_cmp(px, &group->meth->irr) >= 0) ||
310 (MP_SIGN(py) == MP_NEG) || (mp_cmp(py, &group->meth->irr) >= 0)) {
311 res = MP_NO;
312 goto CLEANUP;
313 }
314 /* 3: Verify that publicValue is on the curve. */
315 if (group->meth->field_enc) {
316 group->meth->field_enc(px, &pxt, group->meth);
317 group->meth->field_enc(py, &pyt, group->meth);
318 } else {
319 mp_copy(px, &pxt);
320 mp_copy(py, &pyt);
321 }
322 /* left-hand side: y^2 + x*y */
323 MP_CHECKOK( group->meth->field_sqr(&pyt, &accl, group->meth) );
324 MP_CHECKOK( group->meth->field_mul(&pxt, &pyt, &tmp, group->meth) );
325 MP_CHECKOK( group->meth->field_add(&accl, &tmp, &accl, group->meth) );
326 /* right-hand side: x^3 + a*x^2 + b */
327 MP_CHECKOK( group->meth->field_sqr(&pxt, &tmp, group->meth) );
328 MP_CHECKOK( group->meth->field_mul(&pxt, &tmp, &accr, group->meth) );
329 MP_CHECKOK( group->meth->field_mul(&group->curvea, &tmp, &tmp, group->meth) );
330 MP_CHECKOK( group->meth->field_add(&tmp, &accr, &accr, group->meth) );
331 MP_CHECKOK( group->meth->field_add(&accr, &group->curveb, &accr, group->meth) );
332 /* check LHS - RHS == 0 */
333 MP_CHECKOK( group->meth->field_add(&accl, &accr, &accr, group->meth) );
334 if (mp_cmp_z(&accr) != 0) {
335 res = MP_NO;
336 goto CLEANUP;
337 }
338 /* 4: Verify that the order of the curve times the publicValue
339 * is the point at infinity.
340 */
341 MP_CHECKOK( ECPoint_mul(group, &group->order, px, py, &pxt, &pyt) );
342 if (ec_GF2m_pt_is_inf_aff(&pxt, &pyt) != MP_YES) {
343 res = MP_NO;
344 goto CLEANUP;
345 }
346
347 res = MP_YES;
348
349 CLEANUP:
350 mp_clear(&accl);
351 mp_clear(&accr);
352 mp_clear(&tmp);
353 mp_clear(&pxt);
354 mp_clear(&pyt);
355 return res;
356 }
357