1 /* *********************************************************************
2 *
3 * Sun elects to have this file available under and governed by the
4 * Mozilla Public License Version 1.1 ("MPL") (see
5 * http://www.mozilla.org/MPL/ for full license text). For the avoidance
6 * of doubt and subject to the following, Sun also elects to allow
7 * licensees to use this file under the MPL, the GNU General Public
8 * License version 2 only or the Lesser General Public License version
9 * 2.1 only. Any references to the "GNU General Public License version 2
10 * or later" or "GPL" in the following shall be construed to mean the
11 * GNU General Public License version 2 only. Any references to the "GNU
12 * Lesser General Public License version 2.1 or later" or "LGPL" in the
13 * following shall be construed to mean the GNU Lesser General Public
14 * License version 2.1 only. However, the following notice accompanied
15 * the original version of this file:
16 *
17 * Version: MPL 1.1/GPL 2.0/LGPL 2.1
18 *
19 * The contents of this file are subject to the Mozilla Public License Version
20 * 1.1 (the "License"); you may not use this file except in compliance with
21 * the License. You may obtain a copy of the License at
22 * http://www.mozilla.org/MPL/
23 *
24 * Software distributed under the License is distributed on an "AS IS" basis,
25 * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
26 * for the specific language governing rights and limitations under the
27 * License.
28 *
29 * The Original Code is the elliptic curve math library for prime field curves.
30 *
31 * The Initial Developer of the Original Code is
32 * Sun Microsystems, Inc.
33 * Portions created by the Initial Developer are Copyright (C) 2003
34 * the Initial Developer. All Rights Reserved.
35 *
36 * Contributor(s):
37 * Sheueling Chang-Shantz <sheueling.chang@sun.com>,
38 * Stephen Fung <fungstep@hotmail.com>, and
39 * Douglas Stebila <douglas@stebila.ca>, Sun Microsystems Laboratories.
40 * Bodo Moeller <moeller@cdc.informatik.tu-darmstadt.de>,
41 * Nils Larsch <nla@trustcenter.de>, and
42 * Lenka Fibikova <fibikova@exp-math.uni-essen.de>, the OpenSSL Project
43 *
44 * Alternatively, the contents of this file may be used under the terms of
45 * either the GNU General Public License Version 2 or later (the "GPL"), or
46 * the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
47 * in which case the provisions of the GPL or the LGPL are applicable instead
48 * of those above. If you wish to allow use of your version of this file only
49 * under the terms of either the GPL or the LGPL, and not to allow others to
50 * use your version of this file under the terms of the MPL, indicate your
51 * decision by deleting the provisions above and replace them with the notice
52 * and other provisions required by the GPL or the LGPL. If you do not delete
53 * the provisions above, a recipient may use your version of this file under
54 * the terms of any one of the MPL, the GPL or the LGPL.
55 *
56 *********************************************************************** */
57 /*
58 * Copyright (c) 2007, 2011, Oracle and/or its affiliates. All rights reserved.
59 * Use is subject to license terms.
60 */
61
62 #include "ecp.h"
63 #include "mplogic.h"
64 #ifndef _KERNEL
65 #include <stdlib.h>
66 #endif
67
68 /* Checks if point P(px, py) is at infinity. Uses affine coordinates. */
69 mp_err
70 ec_GFp_pt_is_inf_aff(const mp_int *px, const mp_int *py)
71 {
72
73 if ((mp_cmp_z(px) == 0) && (mp_cmp_z(py) == 0)) {
74 return MP_YES;
75 } else {
76 return MP_NO;
77 }
78
79 }
80
81 /* Sets P(px, py) to be the point at infinity. Uses affine coordinates. */
82 mp_err
83 ec_GFp_pt_set_inf_aff(mp_int *px, mp_int *py)
84 {
85 mp_zero(px);
86 mp_zero(py);
87 return MP_OKAY;
88 }
89
90 /* Computes R = P + Q based on IEEE P1363 A.10.1. Elliptic curve points P,
91 * Q, and R can all be identical. Uses affine coordinates. Assumes input
92 * is already field-encoded using field_enc, and returns output that is
93 * still field-encoded. */
94 mp_err
95 ec_GFp_pt_add_aff(const mp_int *px, const mp_int *py, const mp_int *qx,
96 const mp_int *qy, mp_int *rx, mp_int *ry,
97 const ECGroup *group)
98 {
99 mp_err res = MP_OKAY;
100 mp_int lambda, temp, tempx, tempy;
101
102 MP_DIGITS(&lambda) = 0;
103 MP_DIGITS(&temp) = 0;
104 MP_DIGITS(&tempx) = 0;
105 MP_DIGITS(&tempy) = 0;
106 MP_CHECKOK(mp_init(&lambda, FLAG(px)));
107 MP_CHECKOK(mp_init(&temp, FLAG(px)));
108 MP_CHECKOK(mp_init(&tempx, FLAG(px)));
109 MP_CHECKOK(mp_init(&tempy, FLAG(px)));
110 /* if P = inf, then R = Q */
111 if (ec_GFp_pt_is_inf_aff(px, py) == 0) {
112 MP_CHECKOK(mp_copy(qx, rx));
113 MP_CHECKOK(mp_copy(qy, ry));
114 res = MP_OKAY;
115 goto CLEANUP;
116 }
117 /* if Q = inf, then R = P */
118 if (ec_GFp_pt_is_inf_aff(qx, qy) == 0) {
119 MP_CHECKOK(mp_copy(px, rx));
120 MP_CHECKOK(mp_copy(py, ry));
121 res = MP_OKAY;
122 goto CLEANUP;
123 }
124 /* if px != qx, then lambda = (py-qy) / (px-qx) */
125 if (mp_cmp(px, qx) != 0) {
126 MP_CHECKOK(group->meth->field_sub(py, qy, &tempy, group->meth));
127 MP_CHECKOK(group->meth->field_sub(px, qx, &tempx, group->meth));
128 MP_CHECKOK(group->meth->
129 field_div(&tempy, &tempx, &lambda, group->meth));
130 } else {
131 /* if py != qy or qy = 0, then R = inf */
132 if (((mp_cmp(py, qy) != 0)) || (mp_cmp_z(qy) == 0)) {
133 mp_zero(rx);
134 mp_zero(ry);
135 res = MP_OKAY;
136 goto CLEANUP;
137 }
138 /* lambda = (3qx^2+a) / (2qy) */
139 MP_CHECKOK(group->meth->field_sqr(qx, &tempx, group->meth));
140 MP_CHECKOK(mp_set_int(&temp, 3));
141 if (group->meth->field_enc) {
142 MP_CHECKOK(group->meth->field_enc(&temp, &temp, group->meth));
143 }
144 MP_CHECKOK(group->meth->
145 field_mul(&tempx, &temp, &tempx, group->meth));
146 MP_CHECKOK(group->meth->
147 field_add(&tempx, &group->curvea, &tempx, group->meth));
148 MP_CHECKOK(mp_set_int(&temp, 2));
149 if (group->meth->field_enc) {
150 MP_CHECKOK(group->meth->field_enc(&temp, &temp, group->meth));
151 }
152 MP_CHECKOK(group->meth->field_mul(qy, &temp, &tempy, group->meth));
153 MP_CHECKOK(group->meth->
154 field_div(&tempx, &tempy, &lambda, group->meth));
155 }
156 /* rx = lambda^2 - px - qx */
157 MP_CHECKOK(group->meth->field_sqr(&lambda, &tempx, group->meth));
158 MP_CHECKOK(group->meth->field_sub(&tempx, px, &tempx, group->meth));
159 MP_CHECKOK(group->meth->field_sub(&tempx, qx, &tempx, group->meth));
160 /* ry = (x1-x2) * lambda - y1 */
161 MP_CHECKOK(group->meth->field_sub(qx, &tempx, &tempy, group->meth));
162 MP_CHECKOK(group->meth->
163 field_mul(&tempy, &lambda, &tempy, group->meth));
164 MP_CHECKOK(group->meth->field_sub(&tempy, qy, &tempy, group->meth));
165 MP_CHECKOK(mp_copy(&tempx, rx));
166 MP_CHECKOK(mp_copy(&tempy, ry));
167
168 CLEANUP:
169 mp_clear(&lambda);
170 mp_clear(&temp);
171 mp_clear(&tempx);
172 mp_clear(&tempy);
173 return res;
174 }
175
176 /* Computes R = P - Q. Elliptic curve points P, Q, and R can all be
177 * identical. Uses affine coordinates. Assumes input is already
178 * field-encoded using field_enc, and returns output that is still
179 * field-encoded. */
180 mp_err
181 ec_GFp_pt_sub_aff(const mp_int *px, const mp_int *py, const mp_int *qx,
182 const mp_int *qy, mp_int *rx, mp_int *ry,
183 const ECGroup *group)
184 {
185 mp_err res = MP_OKAY;
186 mp_int nqy;
187
188 MP_DIGITS(&nqy) = 0;
189 MP_CHECKOK(mp_init(&nqy, FLAG(px)));
190 /* nqy = -qy */
191 MP_CHECKOK(group->meth->field_neg(qy, &nqy, group->meth));
192 res = group->point_add(px, py, qx, &nqy, rx, ry, group);
193 CLEANUP:
194 mp_clear(&nqy);
195 return res;
196 }
197
198 /* Computes R = 2P. Elliptic curve points P and R can be identical. Uses
199 * affine coordinates. Assumes input is already field-encoded using
200 * field_enc, and returns output that is still field-encoded. */
201 mp_err
202 ec_GFp_pt_dbl_aff(const mp_int *px, const mp_int *py, mp_int *rx,
203 mp_int *ry, const ECGroup *group)
204 {
205 return ec_GFp_pt_add_aff(px, py, px, py, rx, ry, group);
206 }
207
208 /* by default, this routine is unused and thus doesn't need to be compiled */
209 #ifdef ECL_ENABLE_GFP_PT_MUL_AFF
210 /* Computes R = nP based on IEEE P1363 A.10.3. Elliptic curve points P and
211 * R can be identical. Uses affine coordinates. Assumes input is already
212 * field-encoded using field_enc, and returns output that is still
213 * field-encoded. */
214 mp_err
215 ec_GFp_pt_mul_aff(const mp_int *n, const mp_int *px, const mp_int *py,
216 mp_int *rx, mp_int *ry, const ECGroup *group)
217 {
218 mp_err res = MP_OKAY;
219 mp_int k, k3, qx, qy, sx, sy;
220 int b1, b3, i, l;
221
222 MP_DIGITS(&k) = 0;
223 MP_DIGITS(&k3) = 0;
224 MP_DIGITS(&qx) = 0;
225 MP_DIGITS(&qy) = 0;
226 MP_DIGITS(&sx) = 0;
227 MP_DIGITS(&sy) = 0;
228 MP_CHECKOK(mp_init(&k));
229 MP_CHECKOK(mp_init(&k3));
230 MP_CHECKOK(mp_init(&qx));
231 MP_CHECKOK(mp_init(&qy));
232 MP_CHECKOK(mp_init(&sx));
233 MP_CHECKOK(mp_init(&sy));
234
235 /* if n = 0 then r = inf */
236 if (mp_cmp_z(n) == 0) {
237 mp_zero(rx);
238 mp_zero(ry);
239 res = MP_OKAY;
240 goto CLEANUP;
241 }
242 /* Q = P, k = n */
243 MP_CHECKOK(mp_copy(px, &qx));
244 MP_CHECKOK(mp_copy(py, &qy));
245 MP_CHECKOK(mp_copy(n, &k));
246 /* if n < 0 then Q = -Q, k = -k */
247 if (mp_cmp_z(n) < 0) {
248 MP_CHECKOK(group->meth->field_neg(&qy, &qy, group->meth));
249 MP_CHECKOK(mp_neg(&k, &k));
250 }
251 #ifdef ECL_DEBUG /* basic double and add method */
252 l = mpl_significant_bits(&k) - 1;
253 MP_CHECKOK(mp_copy(&qx, &sx));
254 MP_CHECKOK(mp_copy(&qy, &sy));
255 for (i = l - 1; i >= 0; i--) {
256 /* S = 2S */
257 MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group));
258 /* if k_i = 1, then S = S + Q */
259 if (mpl_get_bit(&k, i) != 0) {
260 MP_CHECKOK(group->
261 point_add(&sx, &sy, &qx, &qy, &sx, &sy, group));
262 }
263 }
264 #else /* double and add/subtract method from
265 * standard */
266 /* k3 = 3 * k */
267 MP_CHECKOK(mp_set_int(&k3, 3));
268 MP_CHECKOK(mp_mul(&k, &k3, &k3));
269 /* S = Q */
270 MP_CHECKOK(mp_copy(&qx, &sx));
271 MP_CHECKOK(mp_copy(&qy, &sy));
272 /* l = index of high order bit in binary representation of 3*k */
273 l = mpl_significant_bits(&k3) - 1;
274 /* for i = l-1 downto 1 */
275 for (i = l - 1; i >= 1; i--) {
276 /* S = 2S */
277 MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group));
278 b3 = MP_GET_BIT(&k3, i);
279 b1 = MP_GET_BIT(&k, i);
280 /* if k3_i = 1 and k_i = 0, then S = S + Q */
281 if ((b3 == 1) && (b1 == 0)) {
282 MP_CHECKOK(group->
283 point_add(&sx, &sy, &qx, &qy, &sx, &sy, group));
284 /* if k3_i = 0 and k_i = 1, then S = S - Q */
285 } else if ((b3 == 0) && (b1 == 1)) {
286 MP_CHECKOK(group->
287 point_sub(&sx, &sy, &qx, &qy, &sx, &sy, group));
288 }
289 }
290 #endif
291 /* output S */
292 MP_CHECKOK(mp_copy(&sx, rx));
293 MP_CHECKOK(mp_copy(&sy, ry));
294
295 CLEANUP:
296 mp_clear(&k);
297 mp_clear(&k3);
298 mp_clear(&qx);
299 mp_clear(&qy);
300 mp_clear(&sx);
301 mp_clear(&sy);
302 return res;
303 }
304 #endif
305
306 /* Validates a point on a GFp curve. */
307 mp_err
308 ec_GFp_validate_point(const mp_int *px, const mp_int *py, const ECGroup *group)
309 {
310 mp_err res = MP_NO;
311 mp_int accl, accr, tmp, pxt, pyt;
312
313 MP_DIGITS(&accl) = 0;
314 MP_DIGITS(&accr) = 0;
315 MP_DIGITS(&tmp) = 0;
316 MP_DIGITS(&pxt) = 0;
317 MP_DIGITS(&pyt) = 0;
318 MP_CHECKOK(mp_init(&accl, FLAG(px)));
319 MP_CHECKOK(mp_init(&accr, FLAG(px)));
320 MP_CHECKOK(mp_init(&tmp, FLAG(px)));
321 MP_CHECKOK(mp_init(&pxt, FLAG(px)));
322 MP_CHECKOK(mp_init(&pyt, FLAG(px)));
323
324 /* 1: Verify that publicValue is not the point at infinity */
325 if (ec_GFp_pt_is_inf_aff(px, py) == MP_YES) {
326 res = MP_NO;
327 goto CLEANUP;
328 }
329 /* 2: Verify that the coordinates of publicValue are elements
330 * of the field.
331 */
332 if ((MP_SIGN(px) == MP_NEG) || (mp_cmp(px, &group->meth->irr) >= 0) ||
333 (MP_SIGN(py) == MP_NEG) || (mp_cmp(py, &group->meth->irr) >= 0)) {
334 res = MP_NO;
335 goto CLEANUP;
336 }
337 /* 3: Verify that publicValue is on the curve. */
338 if (group->meth->field_enc) {
339 group->meth->field_enc(px, &pxt, group->meth);
340 group->meth->field_enc(py, &pyt, group->meth);
341 } else {
342 mp_copy(px, &pxt);
343 mp_copy(py, &pyt);
344 }
345 /* left-hand side: y^2 */
346 MP_CHECKOK( group->meth->field_sqr(&pyt, &accl, group->meth) );
347 /* right-hand side: x^3 + a*x + b */
348 MP_CHECKOK( group->meth->field_sqr(&pxt, &tmp, group->meth) );
349 MP_CHECKOK( group->meth->field_mul(&pxt, &tmp, &accr, group->meth) );
350 MP_CHECKOK( group->meth->field_mul(&group->curvea, &pxt, &tmp, group->meth) );
351 MP_CHECKOK( group->meth->field_add(&tmp, &accr, &accr, group->meth) );
352 MP_CHECKOK( group->meth->field_add(&accr, &group->curveb, &accr, group->meth) );
353 /* check LHS - RHS == 0 */
354 MP_CHECKOK( group->meth->field_sub(&accl, &accr, &accr, group->meth) );
355 if (mp_cmp_z(&accr) != 0) {
356 res = MP_NO;
357 goto CLEANUP;
358 }
359 /* 4: Verify that the order of the curve times the publicValue
360 * is the point at infinity.
361 */
362 MP_CHECKOK( ECPoint_mul(group, &group->order, px, py, &pxt, &pyt) );
363 if (ec_GFp_pt_is_inf_aff(&pxt, &pyt) != MP_YES) {
364 res = MP_NO;
365 goto CLEANUP;
366 }
367
368 res = MP_YES;
369
370 CLEANUP:
371 mp_clear(&accl);
372 mp_clear(&accr);
373 mp_clear(&tmp);
374 mp_clear(&pxt);
375 mp_clear(&pyt);
376 return res;
377 }