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 #pragma ident "%Z%%M% %I% %E% SMI"
51
52 #include "ecp.h"
53 #include "mplogic.h"
54 #ifndef _KERNEL
55 #include <stdlib.h>
56 #endif
57
58 /* Checks if point P(px, py) is at infinity. Uses affine coordinates. */
59 mp_err
ec_GFp_pt_is_inf_aff(const mp_int * px,const mp_int * py)60 ec_GFp_pt_is_inf_aff(const mp_int *px, const mp_int *py)
61 {
62
63 if ((mp_cmp_z(px) == 0) && (mp_cmp_z(py) == 0)) {
64 return MP_YES;
65 } else {
66 return MP_NO;
67 }
68
69 }
70
71 /* Sets P(px, py) to be the point at infinity. Uses affine coordinates. */
72 mp_err
ec_GFp_pt_set_inf_aff(mp_int * px,mp_int * py)73 ec_GFp_pt_set_inf_aff(mp_int *px, mp_int *py)
74 {
75 mp_zero(px);
76 mp_zero(py);
77 return MP_OKAY;
78 }
79
80 /* Computes R = P + Q based on IEEE P1363 A.10.1. Elliptic curve points P,
81 * Q, and R can all be identical. Uses affine coordinates. Assumes input
82 * is already field-encoded using field_enc, and returns output that is
83 * still field-encoded. */
84 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)85 ec_GFp_pt_add_aff(const mp_int *px, const mp_int *py, const mp_int *qx,
86 const mp_int *qy, mp_int *rx, mp_int *ry,
87 const ECGroup *group)
88 {
89 mp_err res = MP_OKAY;
90 mp_int lambda, temp, tempx, tempy;
91
92 MP_DIGITS(&lambda) = 0;
93 MP_DIGITS(&temp) = 0;
94 MP_DIGITS(&tempx) = 0;
95 MP_DIGITS(&tempy) = 0;
96 MP_CHECKOK(mp_init(&lambda, FLAG(px)));
97 MP_CHECKOK(mp_init(&temp, FLAG(px)));
98 MP_CHECKOK(mp_init(&tempx, FLAG(px)));
99 MP_CHECKOK(mp_init(&tempy, FLAG(px)));
100 /* if P = inf, then R = Q */
101 if (ec_GFp_pt_is_inf_aff(px, py) == 0) {
102 MP_CHECKOK(mp_copy(qx, rx));
103 MP_CHECKOK(mp_copy(qy, ry));
104 res = MP_OKAY;
105 goto CLEANUP;
106 }
107 /* if Q = inf, then R = P */
108 if (ec_GFp_pt_is_inf_aff(qx, qy) == 0) {
109 MP_CHECKOK(mp_copy(px, rx));
110 MP_CHECKOK(mp_copy(py, ry));
111 res = MP_OKAY;
112 goto CLEANUP;
113 }
114 /* if px != qx, then lambda = (py-qy) / (px-qx) */
115 if (mp_cmp(px, qx) != 0) {
116 MP_CHECKOK(group->meth->field_sub(py, qy, &tempy, group->meth));
117 MP_CHECKOK(group->meth->field_sub(px, qx, &tempx, group->meth));
118 MP_CHECKOK(group->meth->
119 field_div(&tempy, &tempx, &lambda, group->meth));
120 } else {
121 /* if py != qy or qy = 0, then R = inf */
122 if (((mp_cmp(py, qy) != 0)) || (mp_cmp_z(qy) == 0)) {
123 mp_zero(rx);
124 mp_zero(ry);
125 res = MP_OKAY;
126 goto CLEANUP;
127 }
128 /* lambda = (3qx^2+a) / (2qy) */
129 MP_CHECKOK(group->meth->field_sqr(qx, &tempx, group->meth));
130 MP_CHECKOK(mp_set_int(&temp, 3));
131 if (group->meth->field_enc) {
132 MP_CHECKOK(group->meth->field_enc(&temp, &temp, group->meth));
133 }
134 MP_CHECKOK(group->meth->
135 field_mul(&tempx, &temp, &tempx, group->meth));
136 MP_CHECKOK(group->meth->
137 field_add(&tempx, &group->curvea, &tempx, group->meth));
138 MP_CHECKOK(mp_set_int(&temp, 2));
139 if (group->meth->field_enc) {
140 MP_CHECKOK(group->meth->field_enc(&temp, &temp, group->meth));
141 }
142 MP_CHECKOK(group->meth->field_mul(qy, &temp, &tempy, group->meth));
143 MP_CHECKOK(group->meth->
144 field_div(&tempx, &tempy, &lambda, group->meth));
145 }
146 /* rx = lambda^2 - px - qx */
147 MP_CHECKOK(group->meth->field_sqr(&lambda, &tempx, group->meth));
148 MP_CHECKOK(group->meth->field_sub(&tempx, px, &tempx, group->meth));
149 MP_CHECKOK(group->meth->field_sub(&tempx, qx, &tempx, group->meth));
150 /* ry = (x1-x2) * lambda - y1 */
151 MP_CHECKOK(group->meth->field_sub(qx, &tempx, &tempy, group->meth));
152 MP_CHECKOK(group->meth->
153 field_mul(&tempy, &lambda, &tempy, group->meth));
154 MP_CHECKOK(group->meth->field_sub(&tempy, qy, &tempy, group->meth));
155 MP_CHECKOK(mp_copy(&tempx, rx));
156 MP_CHECKOK(mp_copy(&tempy, ry));
157
158 CLEANUP:
159 mp_clear(&lambda);
160 mp_clear(&temp);
161 mp_clear(&tempx);
162 mp_clear(&tempy);
163 return res;
164 }
165
166 /* Computes R = P - Q. Elliptic curve points P, Q, and R can all be
167 * identical. Uses affine coordinates. Assumes input is already
168 * field-encoded using field_enc, and returns output that is still
169 * field-encoded. */
170 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)171 ec_GFp_pt_sub_aff(const mp_int *px, const mp_int *py, const mp_int *qx,
172 const mp_int *qy, mp_int *rx, mp_int *ry,
173 const ECGroup *group)
174 {
175 mp_err res = MP_OKAY;
176 mp_int nqy;
177
178 MP_DIGITS(&nqy) = 0;
179 MP_CHECKOK(mp_init(&nqy, FLAG(px)));
180 /* nqy = -qy */
181 MP_CHECKOK(group->meth->field_neg(qy, &nqy, group->meth));
182 res = group->point_add(px, py, qx, &nqy, rx, ry, group);
183 CLEANUP:
184 mp_clear(&nqy);
185 return res;
186 }
187
188 /* Computes R = 2P. Elliptic curve points P and R can be identical. Uses
189 * affine coordinates. Assumes input is already field-encoded using
190 * field_enc, and returns output that is still field-encoded. */
191 mp_err
ec_GFp_pt_dbl_aff(const mp_int * px,const mp_int * py,mp_int * rx,mp_int * ry,const ECGroup * group)192 ec_GFp_pt_dbl_aff(const mp_int *px, const mp_int *py, mp_int *rx,
193 mp_int *ry, const ECGroup *group)
194 {
195 return ec_GFp_pt_add_aff(px, py, px, py, rx, ry, group);
196 }
197
198 /* by default, this routine is unused and thus doesn't need to be compiled */
199 #ifdef ECL_ENABLE_GFP_PT_MUL_AFF
200 /* Computes R = nP based on IEEE P1363 A.10.3. Elliptic curve points P and
201 * R can be identical. Uses affine coordinates. Assumes input is already
202 * field-encoded using field_enc, and returns output that is still
203 * field-encoded. */
204 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)205 ec_GFp_pt_mul_aff(const mp_int *n, const mp_int *px, const mp_int *py,
206 mp_int *rx, mp_int *ry, const ECGroup *group)
207 {
208 mp_err res = MP_OKAY;
209 mp_int k, k3, qx, qy, sx, sy;
210 int b1, b3, i, l;
211
212 MP_DIGITS(&k) = 0;
213 MP_DIGITS(&k3) = 0;
214 MP_DIGITS(&qx) = 0;
215 MP_DIGITS(&qy) = 0;
216 MP_DIGITS(&sx) = 0;
217 MP_DIGITS(&sy) = 0;
218 MP_CHECKOK(mp_init(&k));
219 MP_CHECKOK(mp_init(&k3));
220 MP_CHECKOK(mp_init(&qx));
221 MP_CHECKOK(mp_init(&qy));
222 MP_CHECKOK(mp_init(&sx));
223 MP_CHECKOK(mp_init(&sy));
224
225 /* if n = 0 then r = inf */
226 if (mp_cmp_z(n) == 0) {
227 mp_zero(rx);
228 mp_zero(ry);
229 res = MP_OKAY;
230 goto CLEANUP;
231 }
232 /* Q = P, k = n */
233 MP_CHECKOK(mp_copy(px, &qx));
234 MP_CHECKOK(mp_copy(py, &qy));
235 MP_CHECKOK(mp_copy(n, &k));
236 /* if n < 0 then Q = -Q, k = -k */
237 if (mp_cmp_z(n) < 0) {
238 MP_CHECKOK(group->meth->field_neg(&qy, &qy, group->meth));
239 MP_CHECKOK(mp_neg(&k, &k));
240 }
241 #ifdef ECL_DEBUG /* basic double and add method */
242 l = mpl_significant_bits(&k) - 1;
243 MP_CHECKOK(mp_copy(&qx, &sx));
244 MP_CHECKOK(mp_copy(&qy, &sy));
245 for (i = l - 1; i >= 0; i--) {
246 /* S = 2S */
247 MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group));
248 /* if k_i = 1, then S = S + Q */
249 if (mpl_get_bit(&k, i) != 0) {
250 MP_CHECKOK(group->
251 point_add(&sx, &sy, &qx, &qy, &sx, &sy, group));
252 }
253 }
254 #else /* double and add/subtract method from
255 * standard */
256 /* k3 = 3 * k */
257 MP_CHECKOK(mp_set_int(&k3, 3));
258 MP_CHECKOK(mp_mul(&k, &k3, &k3));
259 /* S = Q */
260 MP_CHECKOK(mp_copy(&qx, &sx));
261 MP_CHECKOK(mp_copy(&qy, &sy));
262 /* l = index of high order bit in binary representation of 3*k */
263 l = mpl_significant_bits(&k3) - 1;
264 /* for i = l-1 downto 1 */
265 for (i = l - 1; i >= 1; i--) {
266 /* S = 2S */
267 MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group));
268 b3 = MP_GET_BIT(&k3, i);
269 b1 = MP_GET_BIT(&k, i);
270 /* if k3_i = 1 and k_i = 0, then S = S + Q */
271 if ((b3 == 1) && (b1 == 0)) {
272 MP_CHECKOK(group->
273 point_add(&sx, &sy, &qx, &qy, &sx, &sy, group));
274 /* if k3_i = 0 and k_i = 1, then S = S - Q */
275 } else if ((b3 == 0) && (b1 == 1)) {
276 MP_CHECKOK(group->
277 point_sub(&sx, &sy, &qx, &qy, &sx, &sy, group));
278 }
279 }
280 #endif
281 /* output S */
282 MP_CHECKOK(mp_copy(&sx, rx));
283 MP_CHECKOK(mp_copy(&sy, ry));
284
285 CLEANUP:
286 mp_clear(&k);
287 mp_clear(&k3);
288 mp_clear(&qx);
289 mp_clear(&qy);
290 mp_clear(&sx);
291 mp_clear(&sy);
292 return res;
293 }
294 #endif
295
296 /* Validates a point on a GFp curve. */
297 mp_err
ec_GFp_validate_point(const mp_int * px,const mp_int * py,const ECGroup * group)298 ec_GFp_validate_point(const mp_int *px, const mp_int *py, const ECGroup *group)
299 {
300 mp_err res = MP_NO;
301 mp_int accl, accr, tmp, pxt, pyt;
302
303 MP_DIGITS(&accl) = 0;
304 MP_DIGITS(&accr) = 0;
305 MP_DIGITS(&tmp) = 0;
306 MP_DIGITS(&pxt) = 0;
307 MP_DIGITS(&pyt) = 0;
308 MP_CHECKOK(mp_init(&accl, FLAG(px)));
309 MP_CHECKOK(mp_init(&accr, FLAG(px)));
310 MP_CHECKOK(mp_init(&tmp, FLAG(px)));
311 MP_CHECKOK(mp_init(&pxt, FLAG(px)));
312 MP_CHECKOK(mp_init(&pyt, FLAG(px)));
313
314 /* 1: Verify that publicValue is not the point at infinity */
315 if (ec_GFp_pt_is_inf_aff(px, py) == MP_YES) {
316 res = MP_NO;
317 goto CLEANUP;
318 }
319 /* 2: Verify that the coordinates of publicValue are elements
320 * of the field.
321 */
322 if ((MP_SIGN(px) == MP_NEG) || (mp_cmp(px, &group->meth->irr) >= 0) ||
323 (MP_SIGN(py) == MP_NEG) || (mp_cmp(py, &group->meth->irr) >= 0)) {
324 res = MP_NO;
325 goto CLEANUP;
326 }
327 /* 3: Verify that publicValue is on the curve. */
328 if (group->meth->field_enc) {
329 group->meth->field_enc(px, &pxt, group->meth);
330 group->meth->field_enc(py, &pyt, group->meth);
331 } else {
332 mp_copy(px, &pxt);
333 mp_copy(py, &pyt);
334 }
335 /* left-hand side: y^2 */
336 MP_CHECKOK( group->meth->field_sqr(&pyt, &accl, group->meth) );
337 /* right-hand side: x^3 + a*x + b */
338 MP_CHECKOK( group->meth->field_sqr(&pxt, &tmp, group->meth) );
339 MP_CHECKOK( group->meth->field_mul(&pxt, &tmp, &accr, group->meth) );
340 MP_CHECKOK( group->meth->field_mul(&group->curvea, &pxt, &tmp, group->meth) );
341 MP_CHECKOK( group->meth->field_add(&tmp, &accr, &accr, group->meth) );
342 MP_CHECKOK( group->meth->field_add(&accr, &group->curveb, &accr, group->meth) );
343 /* check LHS - RHS == 0 */
344 MP_CHECKOK( group->meth->field_sub(&accl, &accr, &accr, group->meth) );
345 if (mp_cmp_z(&accr) != 0) {
346 res = MP_NO;
347 goto CLEANUP;
348 }
349 /* 4: Verify that the order of the curve times the publicValue
350 * is the point at infinity.
351 */
352 MP_CHECKOK( ECPoint_mul(group, &group->order, px, py, &pxt, &pyt) );
353 if (ec_GFp_pt_is_inf_aff(&pxt, &pyt) != MP_YES) {
354 res = MP_NO;
355 goto CLEANUP;
356 }
357
358 res = MP_YES;
359
360 CLEANUP:
361 mp_clear(&accl);
362 mp_clear(&accr);
363 mp_clear(&tmp);
364 mp_clear(&pxt);
365 mp_clear(&pyt);
366 return res;
367 }
368