1*c40a6cd7SToomas Soome /*
2f9fbec18Smcpowers * ***** BEGIN LICENSE BLOCK *****
3f9fbec18Smcpowers * Version: MPL 1.1/GPL 2.0/LGPL 2.1
4f9fbec18Smcpowers *
5f9fbec18Smcpowers * The contents of this file are subject to the Mozilla Public License Version
6f9fbec18Smcpowers * 1.1 (the "License"); you may not use this file except in compliance with
7f9fbec18Smcpowers * the License. You may obtain a copy of the License at
8f9fbec18Smcpowers * http://www.mozilla.org/MPL/
9f9fbec18Smcpowers *
10f9fbec18Smcpowers * Software distributed under the License is distributed on an "AS IS" basis,
11f9fbec18Smcpowers * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
12f9fbec18Smcpowers * for the specific language governing rights and limitations under the
13f9fbec18Smcpowers * License.
14f9fbec18Smcpowers *
15f9fbec18Smcpowers * The Original Code is the elliptic curve math library for binary polynomial field curves.
16f9fbec18Smcpowers *
17f9fbec18Smcpowers * The Initial Developer of the Original Code is
18f9fbec18Smcpowers * Sun Microsystems, Inc.
19f9fbec18Smcpowers * Portions created by the Initial Developer are Copyright (C) 2003
20f9fbec18Smcpowers * the Initial Developer. All Rights Reserved.
21f9fbec18Smcpowers *
22f9fbec18Smcpowers * Contributor(s):
23f9fbec18Smcpowers * Douglas Stebila <douglas@stebila.ca>, Sun Microsystems Laboratories
24f9fbec18Smcpowers *
25f9fbec18Smcpowers * Alternatively, the contents of this file may be used under the terms of
26f9fbec18Smcpowers * either the GNU General Public License Version 2 or later (the "GPL"), or
27f9fbec18Smcpowers * the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
28f9fbec18Smcpowers * in which case the provisions of the GPL or the LGPL are applicable instead
29f9fbec18Smcpowers * of those above. If you wish to allow use of your version of this file only
30f9fbec18Smcpowers * under the terms of either the GPL or the LGPL, and not to allow others to
31f9fbec18Smcpowers * use your version of this file under the terms of the MPL, indicate your
32f9fbec18Smcpowers * decision by deleting the provisions above and replace them with the notice
33f9fbec18Smcpowers * and other provisions required by the GPL or the LGPL. If you do not delete
34f9fbec18Smcpowers * the provisions above, a recipient may use your version of this file under
35f9fbec18Smcpowers * the terms of any one of the MPL, the GPL or the LGPL.
36f9fbec18Smcpowers *
37f9fbec18Smcpowers * ***** END LICENSE BLOCK ***** */
38f9fbec18Smcpowers /*
39f9fbec18Smcpowers * Copyright 2007 Sun Microsystems, Inc. All rights reserved.
40f9fbec18Smcpowers * Use is subject to license terms.
41f9fbec18Smcpowers *
42f9fbec18Smcpowers * Sun elects to use this software under the MPL license.
43f9fbec18Smcpowers */
44f9fbec18Smcpowers
45f9fbec18Smcpowers #include "ec2.h"
46f9fbec18Smcpowers #include "mplogic.h"
47f9fbec18Smcpowers #include "mp_gf2m.h"
48f9fbec18Smcpowers #ifndef _KERNEL
49f9fbec18Smcpowers #include <stdlib.h>
50f9fbec18Smcpowers #endif
51f9fbec18Smcpowers
52f9fbec18Smcpowers /* Checks if point P(px, py) is at infinity. Uses affine coordinates. */
53f9fbec18Smcpowers mp_err
ec_GF2m_pt_is_inf_aff(const mp_int * px,const mp_int * py)54f9fbec18Smcpowers ec_GF2m_pt_is_inf_aff(const mp_int *px, const mp_int *py)
55f9fbec18Smcpowers {
56f9fbec18Smcpowers
57f9fbec18Smcpowers if ((mp_cmp_z(px) == 0) && (mp_cmp_z(py) == 0)) {
58f9fbec18Smcpowers return MP_YES;
59f9fbec18Smcpowers } else {
60f9fbec18Smcpowers return MP_NO;
61f9fbec18Smcpowers }
62f9fbec18Smcpowers
63f9fbec18Smcpowers }
64f9fbec18Smcpowers
65f9fbec18Smcpowers /* Sets P(px, py) to be the point at infinity. Uses affine coordinates. */
66f9fbec18Smcpowers mp_err
ec_GF2m_pt_set_inf_aff(mp_int * px,mp_int * py)67f9fbec18Smcpowers ec_GF2m_pt_set_inf_aff(mp_int *px, mp_int *py)
68f9fbec18Smcpowers {
69f9fbec18Smcpowers mp_zero(px);
70f9fbec18Smcpowers mp_zero(py);
71f9fbec18Smcpowers return MP_OKAY;
72f9fbec18Smcpowers }
73f9fbec18Smcpowers
74*c40a6cd7SToomas Soome /* Computes R = P + Q based on IEEE P1363 A.10.2. Elliptic curve points P,
75f9fbec18Smcpowers * Q, and R can all be identical. Uses affine coordinates. */
76f9fbec18Smcpowers 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)77f9fbec18Smcpowers ec_GF2m_pt_add_aff(const mp_int *px, const mp_int *py, const mp_int *qx,
78f9fbec18Smcpowers const mp_int *qy, mp_int *rx, mp_int *ry,
79f9fbec18Smcpowers const ECGroup *group)
80f9fbec18Smcpowers {
81f9fbec18Smcpowers mp_err res = MP_OKAY;
82f9fbec18Smcpowers mp_int lambda, tempx, tempy;
83f9fbec18Smcpowers
84f9fbec18Smcpowers MP_DIGITS(&lambda) = 0;
85f9fbec18Smcpowers MP_DIGITS(&tempx) = 0;
86f9fbec18Smcpowers MP_DIGITS(&tempy) = 0;
87f9fbec18Smcpowers MP_CHECKOK(mp_init(&lambda, FLAG(px)));
88f9fbec18Smcpowers MP_CHECKOK(mp_init(&tempx, FLAG(px)));
89f9fbec18Smcpowers MP_CHECKOK(mp_init(&tempy, FLAG(px)));
90f9fbec18Smcpowers /* if P = inf, then R = Q */
91f9fbec18Smcpowers if (ec_GF2m_pt_is_inf_aff(px, py) == 0) {
92f9fbec18Smcpowers MP_CHECKOK(mp_copy(qx, rx));
93f9fbec18Smcpowers MP_CHECKOK(mp_copy(qy, ry));
94f9fbec18Smcpowers res = MP_OKAY;
95f9fbec18Smcpowers goto CLEANUP;
96f9fbec18Smcpowers }
97f9fbec18Smcpowers /* if Q = inf, then R = P */
98f9fbec18Smcpowers if (ec_GF2m_pt_is_inf_aff(qx, qy) == 0) {
99f9fbec18Smcpowers MP_CHECKOK(mp_copy(px, rx));
100f9fbec18Smcpowers MP_CHECKOK(mp_copy(py, ry));
101f9fbec18Smcpowers res = MP_OKAY;
102f9fbec18Smcpowers goto CLEANUP;
103f9fbec18Smcpowers }
104f9fbec18Smcpowers /* if px != qx, then lambda = (py+qy) / (px+qx), tempx = a + lambda^2
105f9fbec18Smcpowers * + lambda + px + qx */
106f9fbec18Smcpowers if (mp_cmp(px, qx) != 0) {
107f9fbec18Smcpowers MP_CHECKOK(group->meth->field_add(py, qy, &tempy, group->meth));
108f9fbec18Smcpowers MP_CHECKOK(group->meth->field_add(px, qx, &tempx, group->meth));
109f9fbec18Smcpowers MP_CHECKOK(group->meth->
110f9fbec18Smcpowers field_div(&tempy, &tempx, &lambda, group->meth));
111f9fbec18Smcpowers MP_CHECKOK(group->meth->field_sqr(&lambda, &tempx, group->meth));
112f9fbec18Smcpowers MP_CHECKOK(group->meth->
113f9fbec18Smcpowers field_add(&tempx, &lambda, &tempx, group->meth));
114f9fbec18Smcpowers MP_CHECKOK(group->meth->
115f9fbec18Smcpowers field_add(&tempx, &group->curvea, &tempx, group->meth));
116f9fbec18Smcpowers MP_CHECKOK(group->meth->
117f9fbec18Smcpowers field_add(&tempx, px, &tempx, group->meth));
118f9fbec18Smcpowers MP_CHECKOK(group->meth->
119f9fbec18Smcpowers field_add(&tempx, qx, &tempx, group->meth));
120f9fbec18Smcpowers } else {
121f9fbec18Smcpowers /* if py != qy or qx = 0, then R = inf */
122f9fbec18Smcpowers if (((mp_cmp(py, qy) != 0)) || (mp_cmp_z(qx) == 0)) {
123f9fbec18Smcpowers mp_zero(rx);
124f9fbec18Smcpowers mp_zero(ry);
125f9fbec18Smcpowers res = MP_OKAY;
126f9fbec18Smcpowers goto CLEANUP;
127f9fbec18Smcpowers }
128f9fbec18Smcpowers /* lambda = qx + qy / qx */
129f9fbec18Smcpowers MP_CHECKOK(group->meth->field_div(qy, qx, &lambda, group->meth));
130f9fbec18Smcpowers MP_CHECKOK(group->meth->
131f9fbec18Smcpowers field_add(&lambda, qx, &lambda, group->meth));
132f9fbec18Smcpowers /* tempx = a + lambda^2 + lambda */
133f9fbec18Smcpowers MP_CHECKOK(group->meth->field_sqr(&lambda, &tempx, group->meth));
134f9fbec18Smcpowers MP_CHECKOK(group->meth->
135f9fbec18Smcpowers field_add(&tempx, &lambda, &tempx, group->meth));
136f9fbec18Smcpowers MP_CHECKOK(group->meth->
137f9fbec18Smcpowers field_add(&tempx, &group->curvea, &tempx, group->meth));
138f9fbec18Smcpowers }
139f9fbec18Smcpowers /* ry = (qx + tempx) * lambda + tempx + qy */
140f9fbec18Smcpowers MP_CHECKOK(group->meth->field_add(qx, &tempx, &tempy, group->meth));
141f9fbec18Smcpowers MP_CHECKOK(group->meth->
142f9fbec18Smcpowers field_mul(&tempy, &lambda, &tempy, group->meth));
143f9fbec18Smcpowers MP_CHECKOK(group->meth->
144f9fbec18Smcpowers field_add(&tempy, &tempx, &tempy, group->meth));
145f9fbec18Smcpowers MP_CHECKOK(group->meth->field_add(&tempy, qy, ry, group->meth));
146f9fbec18Smcpowers /* rx = tempx */
147f9fbec18Smcpowers MP_CHECKOK(mp_copy(&tempx, rx));
148f9fbec18Smcpowers
149f9fbec18Smcpowers CLEANUP:
150f9fbec18Smcpowers mp_clear(&lambda);
151f9fbec18Smcpowers mp_clear(&tempx);
152f9fbec18Smcpowers mp_clear(&tempy);
153f9fbec18Smcpowers return res;
154f9fbec18Smcpowers }
155f9fbec18Smcpowers
156f9fbec18Smcpowers /* Computes R = P - Q. Elliptic curve points P, Q, and R can all be
157f9fbec18Smcpowers * identical. Uses affine coordinates. */
158f9fbec18Smcpowers 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)159f9fbec18Smcpowers ec_GF2m_pt_sub_aff(const mp_int *px, const mp_int *py, const mp_int *qx,
160f9fbec18Smcpowers const mp_int *qy, mp_int *rx, mp_int *ry,
161f9fbec18Smcpowers const ECGroup *group)
162f9fbec18Smcpowers {
163f9fbec18Smcpowers mp_err res = MP_OKAY;
164f9fbec18Smcpowers mp_int nqy;
165f9fbec18Smcpowers
166f9fbec18Smcpowers MP_DIGITS(&nqy) = 0;
167f9fbec18Smcpowers MP_CHECKOK(mp_init(&nqy, FLAG(px)));
168f9fbec18Smcpowers /* nqy = qx+qy */
169f9fbec18Smcpowers MP_CHECKOK(group->meth->field_add(qx, qy, &nqy, group->meth));
170f9fbec18Smcpowers MP_CHECKOK(group->point_add(px, py, qx, &nqy, rx, ry, group));
171f9fbec18Smcpowers CLEANUP:
172f9fbec18Smcpowers mp_clear(&nqy);
173f9fbec18Smcpowers return res;
174f9fbec18Smcpowers }
175f9fbec18Smcpowers
176f9fbec18Smcpowers /* Computes R = 2P. Elliptic curve points P and R can be identical. Uses
177f9fbec18Smcpowers * affine coordinates. */
178f9fbec18Smcpowers mp_err
ec_GF2m_pt_dbl_aff(const mp_int * px,const mp_int * py,mp_int * rx,mp_int * ry,const ECGroup * group)179f9fbec18Smcpowers ec_GF2m_pt_dbl_aff(const mp_int *px, const mp_int *py, mp_int *rx,
180f9fbec18Smcpowers mp_int *ry, const ECGroup *group)
181f9fbec18Smcpowers {
182f9fbec18Smcpowers return group->point_add(px, py, px, py, rx, ry, group);
183f9fbec18Smcpowers }
184f9fbec18Smcpowers
185f9fbec18Smcpowers /* by default, this routine is unused and thus doesn't need to be compiled */
186f9fbec18Smcpowers #ifdef ECL_ENABLE_GF2M_PT_MUL_AFF
187*c40a6cd7SToomas Soome /* Computes R = nP based on IEEE P1363 A.10.3. Elliptic curve points P and
188f9fbec18Smcpowers * R can be identical. Uses affine coordinates. */
189f9fbec18Smcpowers 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)190f9fbec18Smcpowers ec_GF2m_pt_mul_aff(const mp_int *n, const mp_int *px, const mp_int *py,
191f9fbec18Smcpowers mp_int *rx, mp_int *ry, const ECGroup *group)
192f9fbec18Smcpowers {
193f9fbec18Smcpowers mp_err res = MP_OKAY;
194f9fbec18Smcpowers mp_int k, k3, qx, qy, sx, sy;
195f9fbec18Smcpowers int b1, b3, i, l;
196f9fbec18Smcpowers
197f9fbec18Smcpowers MP_DIGITS(&k) = 0;
198f9fbec18Smcpowers MP_DIGITS(&k3) = 0;
199f9fbec18Smcpowers MP_DIGITS(&qx) = 0;
200f9fbec18Smcpowers MP_DIGITS(&qy) = 0;
201f9fbec18Smcpowers MP_DIGITS(&sx) = 0;
202f9fbec18Smcpowers MP_DIGITS(&sy) = 0;
203f9fbec18Smcpowers MP_CHECKOK(mp_init(&k));
204f9fbec18Smcpowers MP_CHECKOK(mp_init(&k3));
205f9fbec18Smcpowers MP_CHECKOK(mp_init(&qx));
206f9fbec18Smcpowers MP_CHECKOK(mp_init(&qy));
207f9fbec18Smcpowers MP_CHECKOK(mp_init(&sx));
208f9fbec18Smcpowers MP_CHECKOK(mp_init(&sy));
209f9fbec18Smcpowers
210f9fbec18Smcpowers /* if n = 0 then r = inf */
211f9fbec18Smcpowers if (mp_cmp_z(n) == 0) {
212f9fbec18Smcpowers mp_zero(rx);
213f9fbec18Smcpowers mp_zero(ry);
214f9fbec18Smcpowers res = MP_OKAY;
215f9fbec18Smcpowers goto CLEANUP;
216f9fbec18Smcpowers }
217f9fbec18Smcpowers /* Q = P, k = n */
218f9fbec18Smcpowers MP_CHECKOK(mp_copy(px, &qx));
219f9fbec18Smcpowers MP_CHECKOK(mp_copy(py, &qy));
220f9fbec18Smcpowers MP_CHECKOK(mp_copy(n, &k));
221f9fbec18Smcpowers /* if n < 0 then Q = -Q, k = -k */
222f9fbec18Smcpowers if (mp_cmp_z(n) < 0) {
223f9fbec18Smcpowers MP_CHECKOK(group->meth->field_add(&qx, &qy, &qy, group->meth));
224f9fbec18Smcpowers MP_CHECKOK(mp_neg(&k, &k));
225f9fbec18Smcpowers }
226f9fbec18Smcpowers #ifdef ECL_DEBUG /* basic double and add method */
227f9fbec18Smcpowers l = mpl_significant_bits(&k) - 1;
228f9fbec18Smcpowers MP_CHECKOK(mp_copy(&qx, &sx));
229f9fbec18Smcpowers MP_CHECKOK(mp_copy(&qy, &sy));
230f9fbec18Smcpowers for (i = l - 1; i >= 0; i--) {
231f9fbec18Smcpowers /* S = 2S */
232f9fbec18Smcpowers MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group));
233f9fbec18Smcpowers /* if k_i = 1, then S = S + Q */
234f9fbec18Smcpowers if (mpl_get_bit(&k, i) != 0) {
235f9fbec18Smcpowers MP_CHECKOK(group->
236f9fbec18Smcpowers point_add(&sx, &sy, &qx, &qy, &sx, &sy, group));
237f9fbec18Smcpowers }
238f9fbec18Smcpowers }
239f9fbec18Smcpowers #else /* double and add/subtract method from
240f9fbec18Smcpowers * standard */
241f9fbec18Smcpowers /* k3 = 3 * k */
242f9fbec18Smcpowers MP_CHECKOK(mp_set_int(&k3, 3));
243f9fbec18Smcpowers MP_CHECKOK(mp_mul(&k, &k3, &k3));
244f9fbec18Smcpowers /* S = Q */
245f9fbec18Smcpowers MP_CHECKOK(mp_copy(&qx, &sx));
246f9fbec18Smcpowers MP_CHECKOK(mp_copy(&qy, &sy));
247f9fbec18Smcpowers /* l = index of high order bit in binary representation of 3*k */
248f9fbec18Smcpowers l = mpl_significant_bits(&k3) - 1;
249f9fbec18Smcpowers /* for i = l-1 downto 1 */
250f9fbec18Smcpowers for (i = l - 1; i >= 1; i--) {
251f9fbec18Smcpowers /* S = 2S */
252f9fbec18Smcpowers MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group));
253f9fbec18Smcpowers b3 = MP_GET_BIT(&k3, i);
254f9fbec18Smcpowers b1 = MP_GET_BIT(&k, i);
255f9fbec18Smcpowers /* if k3_i = 1 and k_i = 0, then S = S + Q */
256f9fbec18Smcpowers if ((b3 == 1) && (b1 == 0)) {
257f9fbec18Smcpowers MP_CHECKOK(group->
258f9fbec18Smcpowers point_add(&sx, &sy, &qx, &qy, &sx, &sy, group));
259f9fbec18Smcpowers /* if k3_i = 0 and k_i = 1, then S = S - Q */
260f9fbec18Smcpowers } else if ((b3 == 0) && (b1 == 1)) {
261f9fbec18Smcpowers MP_CHECKOK(group->
262f9fbec18Smcpowers point_sub(&sx, &sy, &qx, &qy, &sx, &sy, group));
263f9fbec18Smcpowers }
264f9fbec18Smcpowers }
265f9fbec18Smcpowers #endif
266f9fbec18Smcpowers /* output S */
267f9fbec18Smcpowers MP_CHECKOK(mp_copy(&sx, rx));
268f9fbec18Smcpowers MP_CHECKOK(mp_copy(&sy, ry));
269f9fbec18Smcpowers
270f9fbec18Smcpowers CLEANUP:
271f9fbec18Smcpowers mp_clear(&k);
272f9fbec18Smcpowers mp_clear(&k3);
273f9fbec18Smcpowers mp_clear(&qx);
274f9fbec18Smcpowers mp_clear(&qy);
275f9fbec18Smcpowers mp_clear(&sx);
276f9fbec18Smcpowers mp_clear(&sy);
277f9fbec18Smcpowers return res;
278f9fbec18Smcpowers }
279f9fbec18Smcpowers #endif
280f9fbec18Smcpowers
281f9fbec18Smcpowers /* Validates a point on a GF2m curve. */
282*c40a6cd7SToomas Soome mp_err
ec_GF2m_validate_point(const mp_int * px,const mp_int * py,const ECGroup * group)283f9fbec18Smcpowers ec_GF2m_validate_point(const mp_int *px, const mp_int *py, const ECGroup *group)
284f9fbec18Smcpowers {
285f9fbec18Smcpowers mp_err res = MP_NO;
286f9fbec18Smcpowers mp_int accl, accr, tmp, pxt, pyt;
287f9fbec18Smcpowers
288f9fbec18Smcpowers MP_DIGITS(&accl) = 0;
289f9fbec18Smcpowers MP_DIGITS(&accr) = 0;
290f9fbec18Smcpowers MP_DIGITS(&tmp) = 0;
291f9fbec18Smcpowers MP_DIGITS(&pxt) = 0;
292f9fbec18Smcpowers MP_DIGITS(&pyt) = 0;
293f9fbec18Smcpowers MP_CHECKOK(mp_init(&accl, FLAG(px)));
294f9fbec18Smcpowers MP_CHECKOK(mp_init(&accr, FLAG(px)));
295f9fbec18Smcpowers MP_CHECKOK(mp_init(&tmp, FLAG(px)));
296f9fbec18Smcpowers MP_CHECKOK(mp_init(&pxt, FLAG(px)));
297f9fbec18Smcpowers MP_CHECKOK(mp_init(&pyt, FLAG(px)));
298f9fbec18Smcpowers
299f9fbec18Smcpowers /* 1: Verify that publicValue is not the point at infinity */
300f9fbec18Smcpowers if (ec_GF2m_pt_is_inf_aff(px, py) == MP_YES) {
301f9fbec18Smcpowers res = MP_NO;
302f9fbec18Smcpowers goto CLEANUP;
303f9fbec18Smcpowers }
304*c40a6cd7SToomas Soome /* 2: Verify that the coordinates of publicValue are elements
305f9fbec18Smcpowers * of the field.
306f9fbec18Smcpowers */
307*c40a6cd7SToomas Soome if ((MP_SIGN(px) == MP_NEG) || (mp_cmp(px, &group->meth->irr) >= 0) ||
308f9fbec18Smcpowers (MP_SIGN(py) == MP_NEG) || (mp_cmp(py, &group->meth->irr) >= 0)) {
309f9fbec18Smcpowers res = MP_NO;
310f9fbec18Smcpowers goto CLEANUP;
311f9fbec18Smcpowers }
312f9fbec18Smcpowers /* 3: Verify that publicValue is on the curve. */
313f9fbec18Smcpowers if (group->meth->field_enc) {
314f9fbec18Smcpowers group->meth->field_enc(px, &pxt, group->meth);
315f9fbec18Smcpowers group->meth->field_enc(py, &pyt, group->meth);
316f9fbec18Smcpowers } else {
317f9fbec18Smcpowers mp_copy(px, &pxt);
318f9fbec18Smcpowers mp_copy(py, &pyt);
319f9fbec18Smcpowers }
320f9fbec18Smcpowers /* left-hand side: y^2 + x*y */
321f9fbec18Smcpowers MP_CHECKOK( group->meth->field_sqr(&pyt, &accl, group->meth) );
322f9fbec18Smcpowers MP_CHECKOK( group->meth->field_mul(&pxt, &pyt, &tmp, group->meth) );
323f9fbec18Smcpowers MP_CHECKOK( group->meth->field_add(&accl, &tmp, &accl, group->meth) );
324f9fbec18Smcpowers /* right-hand side: x^3 + a*x^2 + b */
325f9fbec18Smcpowers MP_CHECKOK( group->meth->field_sqr(&pxt, &tmp, group->meth) );
326f9fbec18Smcpowers MP_CHECKOK( group->meth->field_mul(&pxt, &tmp, &accr, group->meth) );
327f9fbec18Smcpowers MP_CHECKOK( group->meth->field_mul(&group->curvea, &tmp, &tmp, group->meth) );
328f9fbec18Smcpowers MP_CHECKOK( group->meth->field_add(&tmp, &accr, &accr, group->meth) );
329f9fbec18Smcpowers MP_CHECKOK( group->meth->field_add(&accr, &group->curveb, &accr, group->meth) );
330f9fbec18Smcpowers /* check LHS - RHS == 0 */
331f9fbec18Smcpowers MP_CHECKOK( group->meth->field_add(&accl, &accr, &accr, group->meth) );
332f9fbec18Smcpowers if (mp_cmp_z(&accr) != 0) {
333f9fbec18Smcpowers res = MP_NO;
334f9fbec18Smcpowers goto CLEANUP;
335f9fbec18Smcpowers }
336f9fbec18Smcpowers /* 4: Verify that the order of the curve times the publicValue
337f9fbec18Smcpowers * is the point at infinity.
338f9fbec18Smcpowers */
339f9fbec18Smcpowers MP_CHECKOK( ECPoint_mul(group, &group->order, px, py, &pxt, &pyt) );
340f9fbec18Smcpowers if (ec_GF2m_pt_is_inf_aff(&pxt, &pyt) != MP_YES) {
341f9fbec18Smcpowers res = MP_NO;
342f9fbec18Smcpowers goto CLEANUP;
343f9fbec18Smcpowers }
344f9fbec18Smcpowers
345f9fbec18Smcpowers res = MP_YES;
346f9fbec18Smcpowers
347f9fbec18Smcpowers CLEANUP:
348f9fbec18Smcpowers mp_clear(&accl);
349f9fbec18Smcpowers mp_clear(&accr);
350f9fbec18Smcpowers mp_clear(&tmp);
351f9fbec18Smcpowers mp_clear(&pxt);
352f9fbec18Smcpowers mp_clear(&pyt);
353f9fbec18Smcpowers return res;
354f9fbec18Smcpowers }
355