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 prime 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 * Bodo Moeller <moeller@cdc.informatik.tu-darmstadt.de>,
27 * Nils Larsch <nla@trustcenter.de>, and
28 * Lenka Fibikova <fibikova@exp-math.uni-essen.de>, the OpenSSL Project
29 *
30 * Alternatively, the contents of this file may be used under the terms of
31 * either the GNU General Public License Version 2 or later (the "GPL"), or
32 * the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
33 * in which case the provisions of the GPL or the LGPL are applicable instead
34 * of those above. If you wish to allow use of your version of this file only
35 * under the terms of either the GPL or the LGPL, and not to allow others to
36 * use your version of this file under the terms of the MPL, indicate your
37 * decision by deleting the provisions above and replace them with the notice
38 * and other provisions required by the GPL or the LGPL. If you do not delete
39 * the provisions above, a recipient may use your version of this file under
40 * the terms of any one of the MPL, the GPL or the LGPL.
41 *
42 * ***** END LICENSE BLOCK ***** */
43 /*
44 * Copyright 2007 Sun Microsystems, Inc. All rights reserved.
45 * Use is subject to license terms.
46 *
47 * Sun elects to use this software under the MPL license.
48 */
49
50 #include "ecp.h"
51 #include "mplogic.h"
52 #ifndef _KERNEL
53 #include <stdlib.h>
54 #endif
55
56 /* Checks if point P(px, py) is at infinity. Uses affine coordinates. */
57 mp_err
ec_GFp_pt_is_inf_aff(const mp_int * px,const mp_int * py)58 ec_GFp_pt_is_inf_aff(const mp_int *px, const mp_int *py)
59 {
60
61 if ((mp_cmp_z(px) == 0) && (mp_cmp_z(py) == 0)) {
62 return MP_YES;
63 } else {
64 return MP_NO;
65 }
66
67 }
68
69 /* Sets P(px, py) to be the point at infinity. Uses affine coordinates. */
70 mp_err
ec_GFp_pt_set_inf_aff(mp_int * px,mp_int * py)71 ec_GFp_pt_set_inf_aff(mp_int *px, mp_int *py)
72 {
73 mp_zero(px);
74 mp_zero(py);
75 return MP_OKAY;
76 }
77
78 /* Computes R = P + Q based on IEEE P1363 A.10.1. Elliptic curve points P,
79 * Q, and R can all be identical. Uses affine coordinates. Assumes input
80 * is already field-encoded using field_enc, and returns output that is
81 * still field-encoded. */
82 mp_err
ec_GFp_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)83 ec_GFp_pt_add_aff(const mp_int *px, const mp_int *py, const mp_int *qx,
84 const mp_int *qy, mp_int *rx, mp_int *ry,
85 const ECGroup *group)
86 {
87 mp_err res = MP_OKAY;
88 mp_int lambda, temp, tempx, tempy;
89
90 MP_DIGITS(&lambda) = 0;
91 MP_DIGITS(&temp) = 0;
92 MP_DIGITS(&tempx) = 0;
93 MP_DIGITS(&tempy) = 0;
94 MP_CHECKOK(mp_init(&lambda, FLAG(px)));
95 MP_CHECKOK(mp_init(&temp, FLAG(px)));
96 MP_CHECKOK(mp_init(&tempx, FLAG(px)));
97 MP_CHECKOK(mp_init(&tempy, FLAG(px)));
98 /* if P = inf, then R = Q */
99 if (ec_GFp_pt_is_inf_aff(px, py) == 0) {
100 MP_CHECKOK(mp_copy(qx, rx));
101 MP_CHECKOK(mp_copy(qy, ry));
102 res = MP_OKAY;
103 goto CLEANUP;
104 }
105 /* if Q = inf, then R = P */
106 if (ec_GFp_pt_is_inf_aff(qx, qy) == 0) {
107 MP_CHECKOK(mp_copy(px, rx));
108 MP_CHECKOK(mp_copy(py, ry));
109 res = MP_OKAY;
110 goto CLEANUP;
111 }
112 /* if px != qx, then lambda = (py-qy) / (px-qx) */
113 if (mp_cmp(px, qx) != 0) {
114 MP_CHECKOK(group->meth->field_sub(py, qy, &tempy, group->meth));
115 MP_CHECKOK(group->meth->field_sub(px, qx, &tempx, group->meth));
116 MP_CHECKOK(group->meth->
117 field_div(&tempy, &tempx, &lambda, group->meth));
118 } else {
119 /* if py != qy or qy = 0, then R = inf */
120 if (((mp_cmp(py, qy) != 0)) || (mp_cmp_z(qy) == 0)) {
121 mp_zero(rx);
122 mp_zero(ry);
123 res = MP_OKAY;
124 goto CLEANUP;
125 }
126 /* lambda = (3qx^2+a) / (2qy) */
127 MP_CHECKOK(group->meth->field_sqr(qx, &tempx, group->meth));
128 MP_CHECKOK(mp_set_int(&temp, 3));
129 if (group->meth->field_enc) {
130 MP_CHECKOK(group->meth->field_enc(&temp, &temp, group->meth));
131 }
132 MP_CHECKOK(group->meth->
133 field_mul(&tempx, &temp, &tempx, group->meth));
134 MP_CHECKOK(group->meth->
135 field_add(&tempx, &group->curvea, &tempx, group->meth));
136 MP_CHECKOK(mp_set_int(&temp, 2));
137 if (group->meth->field_enc) {
138 MP_CHECKOK(group->meth->field_enc(&temp, &temp, group->meth));
139 }
140 MP_CHECKOK(group->meth->field_mul(qy, &temp, &tempy, group->meth));
141 MP_CHECKOK(group->meth->
142 field_div(&tempx, &tempy, &lambda, group->meth));
143 }
144 /* rx = lambda^2 - px - qx */
145 MP_CHECKOK(group->meth->field_sqr(&lambda, &tempx, group->meth));
146 MP_CHECKOK(group->meth->field_sub(&tempx, px, &tempx, group->meth));
147 MP_CHECKOK(group->meth->field_sub(&tempx, qx, &tempx, group->meth));
148 /* ry = (x1-x2) * lambda - y1 */
149 MP_CHECKOK(group->meth->field_sub(qx, &tempx, &tempy, group->meth));
150 MP_CHECKOK(group->meth->
151 field_mul(&tempy, &lambda, &tempy, group->meth));
152 MP_CHECKOK(group->meth->field_sub(&tempy, qy, &tempy, group->meth));
153 MP_CHECKOK(mp_copy(&tempx, rx));
154 MP_CHECKOK(mp_copy(&tempy, ry));
155
156 CLEANUP:
157 mp_clear(&lambda);
158 mp_clear(&temp);
159 mp_clear(&tempx);
160 mp_clear(&tempy);
161 return res;
162 }
163
164 /* Computes R = P - Q. Elliptic curve points P, Q, and R can all be
165 * identical. Uses affine coordinates. Assumes input is already
166 * field-encoded using field_enc, and returns output that is still
167 * field-encoded. */
168 mp_err
ec_GFp_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)169 ec_GFp_pt_sub_aff(const mp_int *px, const mp_int *py, const mp_int *qx,
170 const mp_int *qy, mp_int *rx, mp_int *ry,
171 const ECGroup *group)
172 {
173 mp_err res = MP_OKAY;
174 mp_int nqy;
175
176 MP_DIGITS(&nqy) = 0;
177 MP_CHECKOK(mp_init(&nqy, FLAG(px)));
178 /* nqy = -qy */
179 MP_CHECKOK(group->meth->field_neg(qy, &nqy, group->meth));
180 res = group->point_add(px, py, qx, &nqy, rx, ry, group);
181 CLEANUP:
182 mp_clear(&nqy);
183 return res;
184 }
185
186 /* Computes R = 2P. Elliptic curve points P and R can be identical. Uses
187 * affine coordinates. Assumes input is already field-encoded using
188 * field_enc, and returns output that is still field-encoded. */
189 mp_err
ec_GFp_pt_dbl_aff(const mp_int * px,const mp_int * py,mp_int * rx,mp_int * ry,const ECGroup * group)190 ec_GFp_pt_dbl_aff(const mp_int *px, const mp_int *py, mp_int *rx,
191 mp_int *ry, const ECGroup *group)
192 {
193 return ec_GFp_pt_add_aff(px, py, px, py, rx, ry, group);
194 }
195
196 /* by default, this routine is unused and thus doesn't need to be compiled */
197 #ifdef ECL_ENABLE_GFP_PT_MUL_AFF
198 /* Computes R = nP based on IEEE P1363 A.10.3. Elliptic curve points P and
199 * R can be identical. Uses affine coordinates. Assumes input is already
200 * field-encoded using field_enc, and returns output that is still
201 * field-encoded. */
202 mp_err
ec_GFp_pt_mul_aff(const mp_int * n,const mp_int * px,const mp_int * py,mp_int * rx,mp_int * ry,const ECGroup * group)203 ec_GFp_pt_mul_aff(const mp_int *n, const mp_int *px, const mp_int *py,
204 mp_int *rx, mp_int *ry, const ECGroup *group)
205 {
206 mp_err res = MP_OKAY;
207 mp_int k, k3, qx, qy, sx, sy;
208 int b1, b3, i, l;
209
210 MP_DIGITS(&k) = 0;
211 MP_DIGITS(&k3) = 0;
212 MP_DIGITS(&qx) = 0;
213 MP_DIGITS(&qy) = 0;
214 MP_DIGITS(&sx) = 0;
215 MP_DIGITS(&sy) = 0;
216 MP_CHECKOK(mp_init(&k));
217 MP_CHECKOK(mp_init(&k3));
218 MP_CHECKOK(mp_init(&qx));
219 MP_CHECKOK(mp_init(&qy));
220 MP_CHECKOK(mp_init(&sx));
221 MP_CHECKOK(mp_init(&sy));
222
223 /* if n = 0 then r = inf */
224 if (mp_cmp_z(n) == 0) {
225 mp_zero(rx);
226 mp_zero(ry);
227 res = MP_OKAY;
228 goto CLEANUP;
229 }
230 /* Q = P, k = n */
231 MP_CHECKOK(mp_copy(px, &qx));
232 MP_CHECKOK(mp_copy(py, &qy));
233 MP_CHECKOK(mp_copy(n, &k));
234 /* if n < 0 then Q = -Q, k = -k */
235 if (mp_cmp_z(n) < 0) {
236 MP_CHECKOK(group->meth->field_neg(&qy, &qy, group->meth));
237 MP_CHECKOK(mp_neg(&k, &k));
238 }
239 #ifdef ECL_DEBUG /* basic double and add method */
240 l = mpl_significant_bits(&k) - 1;
241 MP_CHECKOK(mp_copy(&qx, &sx));
242 MP_CHECKOK(mp_copy(&qy, &sy));
243 for (i = l - 1; i >= 0; i--) {
244 /* S = 2S */
245 MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group));
246 /* if k_i = 1, then S = S + Q */
247 if (mpl_get_bit(&k, i) != 0) {
248 MP_CHECKOK(group->
249 point_add(&sx, &sy, &qx, &qy, &sx, &sy, group));
250 }
251 }
252 #else /* double and add/subtract method from
253 * standard */
254 /* k3 = 3 * k */
255 MP_CHECKOK(mp_set_int(&k3, 3));
256 MP_CHECKOK(mp_mul(&k, &k3, &k3));
257 /* S = Q */
258 MP_CHECKOK(mp_copy(&qx, &sx));
259 MP_CHECKOK(mp_copy(&qy, &sy));
260 /* l = index of high order bit in binary representation of 3*k */
261 l = mpl_significant_bits(&k3) - 1;
262 /* for i = l-1 downto 1 */
263 for (i = l - 1; i >= 1; i--) {
264 /* S = 2S */
265 MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group));
266 b3 = MP_GET_BIT(&k3, i);
267 b1 = MP_GET_BIT(&k, i);
268 /* if k3_i = 1 and k_i = 0, then S = S + Q */
269 if ((b3 == 1) && (b1 == 0)) {
270 MP_CHECKOK(group->
271 point_add(&sx, &sy, &qx, &qy, &sx, &sy, group));
272 /* if k3_i = 0 and k_i = 1, then S = S - Q */
273 } else if ((b3 == 0) && (b1 == 1)) {
274 MP_CHECKOK(group->
275 point_sub(&sx, &sy, &qx, &qy, &sx, &sy, group));
276 }
277 }
278 #endif
279 /* output S */
280 MP_CHECKOK(mp_copy(&sx, rx));
281 MP_CHECKOK(mp_copy(&sy, ry));
282
283 CLEANUP:
284 mp_clear(&k);
285 mp_clear(&k3);
286 mp_clear(&qx);
287 mp_clear(&qy);
288 mp_clear(&sx);
289 mp_clear(&sy);
290 return res;
291 }
292 #endif
293
294 /* Validates a point on a GFp curve. */
295 mp_err
ec_GFp_validate_point(const mp_int * px,const mp_int * py,const ECGroup * group)296 ec_GFp_validate_point(const mp_int *px, const mp_int *py, const ECGroup *group)
297 {
298 mp_err res = MP_NO;
299 mp_int accl, accr, tmp, pxt, pyt;
300
301 MP_DIGITS(&accl) = 0;
302 MP_DIGITS(&accr) = 0;
303 MP_DIGITS(&tmp) = 0;
304 MP_DIGITS(&pxt) = 0;
305 MP_DIGITS(&pyt) = 0;
306 MP_CHECKOK(mp_init(&accl, FLAG(px)));
307 MP_CHECKOK(mp_init(&accr, FLAG(px)));
308 MP_CHECKOK(mp_init(&tmp, FLAG(px)));
309 MP_CHECKOK(mp_init(&pxt, FLAG(px)));
310 MP_CHECKOK(mp_init(&pyt, FLAG(px)));
311
312 /* 1: Verify that publicValue is not the point at infinity */
313 if (ec_GFp_pt_is_inf_aff(px, py) == MP_YES) {
314 res = MP_NO;
315 goto CLEANUP;
316 }
317 /* 2: Verify that the coordinates of publicValue are elements
318 * of the field.
319 */
320 if ((MP_SIGN(px) == MP_NEG) || (mp_cmp(px, &group->meth->irr) >= 0) ||
321 (MP_SIGN(py) == MP_NEG) || (mp_cmp(py, &group->meth->irr) >= 0)) {
322 res = MP_NO;
323 goto CLEANUP;
324 }
325 /* 3: Verify that publicValue is on the curve. */
326 if (group->meth->field_enc) {
327 group->meth->field_enc(px, &pxt, group->meth);
328 group->meth->field_enc(py, &pyt, group->meth);
329 } else {
330 mp_copy(px, &pxt);
331 mp_copy(py, &pyt);
332 }
333 /* left-hand side: y^2 */
334 MP_CHECKOK( group->meth->field_sqr(&pyt, &accl, group->meth) );
335 /* right-hand side: x^3 + a*x + b */
336 MP_CHECKOK( group->meth->field_sqr(&pxt, &tmp, group->meth) );
337 MP_CHECKOK( group->meth->field_mul(&pxt, &tmp, &accr, group->meth) );
338 MP_CHECKOK( group->meth->field_mul(&group->curvea, &pxt, &tmp, group->meth) );
339 MP_CHECKOK( group->meth->field_add(&tmp, &accr, &accr, group->meth) );
340 MP_CHECKOK( group->meth->field_add(&accr, &group->curveb, &accr, group->meth) );
341 /* check LHS - RHS == 0 */
342 MP_CHECKOK( group->meth->field_sub(&accl, &accr, &accr, group->meth) );
343 if (mp_cmp_z(&accr) != 0) {
344 res = MP_NO;
345 goto CLEANUP;
346 }
347 /* 4: Verify that the order of the curve times the publicValue
348 * is the point at infinity.
349 */
350 MP_CHECKOK( ECPoint_mul(group, &group->order, px, py, &pxt, &pyt) );
351 if (ec_GFp_pt_is_inf_aff(&pxt, &pyt) != MP_YES) {
352 res = MP_NO;
353 goto CLEANUP;
354 }
355
356 res = MP_YES;
357
358 CLEANUP:
359 mp_clear(&accl);
360 mp_clear(&accr);
361 mp_clear(&tmp);
362 mp_clear(&pxt);
363 mp_clear(&pyt);
364 return res;
365 }
366