1/*
2 * Copyright (c) 2007, 2017, Oracle and/or its affiliates. All rights reserved.
3 * Use is subject to license terms.
4 *
5 * This library is free software; you can redistribute it and/or
6 * modify it under the terms of the GNU Lesser General Public
7 * License as published by the Free Software Foundation; either
8 * version 2.1 of the License, or (at your option) any later version.
9 *
10 * This library is distributed in the hope that it will be useful,
11 * but WITHOUT ANY WARRANTY; without even the implied warranty of
12 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
13 * Lesser General Public License for more details.
14 *
15 * You should have received a copy of the GNU Lesser General Public License
16 * along with this library; if not, write to the Free Software Foundation,
17 * Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
18 *
19 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
20 * or visit www.oracle.com if you need additional information or have any
21 * questions.
22 */
23
24/* *********************************************************************
25 *
26 * The Original Code is the elliptic curve math library for binary polynomial field curves.
27 *
28 * The Initial Developer of the Original Code is
29 * Sun Microsystems, Inc.
30 * Portions created by the Initial Developer are Copyright (C) 2003
31 * the Initial Developer. All Rights Reserved.
32 *
33 * Contributor(s):
34 *   Douglas Stebila <douglas@stebila.ca>, Sun Microsystems Laboratories
35 *
36 * Last Modified Date from the Original Code: May 2017
37 *********************************************************************** */
38
39#include "ec2.h"
40#include "mplogic.h"
41#include "mp_gf2m.h"
42#ifndef _KERNEL
43#include <stdlib.h>
44#endif
45
46/* Checks if point P(px, py) is at infinity.  Uses affine coordinates. */
47mp_err
48ec_GF2m_pt_is_inf_aff(const mp_int *px, const mp_int *py)
49{
50
51        if ((mp_cmp_z(px) == 0) && (mp_cmp_z(py) == 0)) {
52                return MP_YES;
53        } else {
54                return MP_NO;
55        }
56
57}
58
59/* Sets P(px, py) to be the point at infinity.  Uses affine coordinates. */
60mp_err
61ec_GF2m_pt_set_inf_aff(mp_int *px, mp_int *py)
62{
63        mp_zero(px);
64        mp_zero(py);
65        return MP_OKAY;
66}
67
68/* Computes R = P + Q based on IEEE P1363 A.10.2. Elliptic curve points P,
69 * Q, and R can all be identical. Uses affine coordinates. */
70mp_err
71ec_GF2m_pt_add_aff(const mp_int *px, const mp_int *py, const mp_int *qx,
72                                   const mp_int *qy, mp_int *rx, mp_int *ry,
73                                   const ECGroup *group)
74{
75        mp_err res = MP_OKAY;
76        mp_int lambda, tempx, tempy;
77
78        MP_DIGITS(&lambda) = 0;
79        MP_DIGITS(&tempx) = 0;
80        MP_DIGITS(&tempy) = 0;
81        MP_CHECKOK(mp_init(&lambda, FLAG(px)));
82        MP_CHECKOK(mp_init(&tempx, FLAG(px)));
83        MP_CHECKOK(mp_init(&tempy, FLAG(px)));
84        /* if P = inf, then R = Q */
85        if (ec_GF2m_pt_is_inf_aff(px, py) == 0) {
86                MP_CHECKOK(mp_copy(qx, rx));
87                MP_CHECKOK(mp_copy(qy, ry));
88                res = MP_OKAY;
89                goto CLEANUP;
90        }
91        /* if Q = inf, then R = P */
92        if (ec_GF2m_pt_is_inf_aff(qx, qy) == 0) {
93                MP_CHECKOK(mp_copy(px, rx));
94                MP_CHECKOK(mp_copy(py, ry));
95                res = MP_OKAY;
96                goto CLEANUP;
97        }
98        /* if px != qx, then lambda = (py+qy) / (px+qx), tempx = a + lambda^2
99         * + lambda + px + qx */
100        if (mp_cmp(px, qx) != 0) {
101                MP_CHECKOK(group->meth->field_add(py, qy, &tempy, group->meth));
102                MP_CHECKOK(group->meth->field_add(px, qx, &tempx, group->meth));
103                MP_CHECKOK(group->meth->
104                                   field_div(&tempy, &tempx, &lambda, group->meth));
105                MP_CHECKOK(group->meth->field_sqr(&lambda, &tempx, group->meth));
106                MP_CHECKOK(group->meth->
107                                   field_add(&tempx, &lambda, &tempx, group->meth));
108                MP_CHECKOK(group->meth->
109                                   field_add(&tempx, &group->curvea, &tempx, group->meth));
110                MP_CHECKOK(group->meth->
111                                   field_add(&tempx, px, &tempx, group->meth));
112                MP_CHECKOK(group->meth->
113                                   field_add(&tempx, qx, &tempx, group->meth));
114        } else {
115                /* if py != qy or qx = 0, then R = inf */
116                if (((mp_cmp(py, qy) != 0)) || (mp_cmp_z(qx) == 0)) {
117                        mp_zero(rx);
118                        mp_zero(ry);
119                        res = MP_OKAY;
120                        goto CLEANUP;
121                }
122                /* lambda = qx + qy / qx */
123                MP_CHECKOK(group->meth->field_div(qy, qx, &lambda, group->meth));
124                MP_CHECKOK(group->meth->
125                                   field_add(&lambda, qx, &lambda, group->meth));
126                /* tempx = a + lambda^2 + lambda */
127                MP_CHECKOK(group->meth->field_sqr(&lambda, &tempx, group->meth));
128                MP_CHECKOK(group->meth->
129                                   field_add(&tempx, &lambda, &tempx, group->meth));
130                MP_CHECKOK(group->meth->
131                                   field_add(&tempx, &group->curvea, &tempx, group->meth));
132        }
133        /* ry = (qx + tempx) * lambda + tempx + qy */
134        MP_CHECKOK(group->meth->field_add(qx, &tempx, &tempy, group->meth));
135        MP_CHECKOK(group->meth->
136                           field_mul(&tempy, &lambda, &tempy, group->meth));
137        MP_CHECKOK(group->meth->
138                           field_add(&tempy, &tempx, &tempy, group->meth));
139        MP_CHECKOK(group->meth->field_add(&tempy, qy, ry, group->meth));
140        /* rx = tempx */
141        MP_CHECKOK(mp_copy(&tempx, rx));
142
143  CLEANUP:
144        mp_clear(&lambda);
145        mp_clear(&tempx);
146        mp_clear(&tempy);
147        return res;
148}
149
150/* Computes R = P - Q. Elliptic curve points P, Q, and R can all be
151 * identical. Uses affine coordinates. */
152mp_err
153ec_GF2m_pt_sub_aff(const mp_int *px, const mp_int *py, const mp_int *qx,
154                                   const mp_int *qy, mp_int *rx, mp_int *ry,
155                                   const ECGroup *group)
156{
157        mp_err res = MP_OKAY;
158        mp_int nqy;
159
160        MP_DIGITS(&nqy) = 0;
161        MP_CHECKOK(mp_init(&nqy, FLAG(px)));
162        /* nqy = qx+qy */
163        MP_CHECKOK(group->meth->field_add(qx, qy, &nqy, group->meth));
164        MP_CHECKOK(group->point_add(px, py, qx, &nqy, rx, ry, group));
165  CLEANUP:
166        mp_clear(&nqy);
167        return res;
168}
169
170/* Computes R = 2P. Elliptic curve points P and R can be identical. Uses
171 * affine coordinates. */
172mp_err
173ec_GF2m_pt_dbl_aff(const mp_int *px, const mp_int *py, mp_int *rx,
174                                   mp_int *ry, const ECGroup *group)
175{
176        return group->point_add(px, py, px, py, rx, ry, group);
177}
178
179/* by default, this routine is unused and thus doesn't need to be compiled */
180#ifdef ECL_ENABLE_GF2M_PT_MUL_AFF
181/* Computes R = nP based on IEEE P1363 A.10.3. Elliptic curve points P and
182 * R can be identical. Uses affine coordinates. */
183mp_err
184ec_GF2m_pt_mul_aff(const mp_int *n, const mp_int *px, const mp_int *py,
185                                   mp_int *rx, mp_int *ry, const ECGroup *group)
186{
187        mp_err res = MP_OKAY;
188        mp_int k, k3, qx, qy, sx, sy;
189        int b1, b3, i, l;
190
191        MP_DIGITS(&k) = 0;
192        MP_DIGITS(&k3) = 0;
193        MP_DIGITS(&qx) = 0;
194        MP_DIGITS(&qy) = 0;
195        MP_DIGITS(&sx) = 0;
196        MP_DIGITS(&sy) = 0;
197        MP_CHECKOK(mp_init(&k));
198        MP_CHECKOK(mp_init(&k3));
199        MP_CHECKOK(mp_init(&qx));
200        MP_CHECKOK(mp_init(&qy));
201        MP_CHECKOK(mp_init(&sx));
202        MP_CHECKOK(mp_init(&sy));
203
204        /* if n = 0 then r = inf */
205        if (mp_cmp_z(n) == 0) {
206                mp_zero(rx);
207                mp_zero(ry);
208                res = MP_OKAY;
209                goto CLEANUP;
210        }
211        /* Q = P, k = n */
212        MP_CHECKOK(mp_copy(px, &qx));
213        MP_CHECKOK(mp_copy(py, &qy));
214        MP_CHECKOK(mp_copy(n, &k));
215        /* if n < 0 then Q = -Q, k = -k */
216        if (mp_cmp_z(n) < 0) {
217                MP_CHECKOK(group->meth->field_add(&qx, &qy, &qy, group->meth));
218                MP_CHECKOK(mp_neg(&k, &k));
219        }
220#ifdef ECL_DEBUG                                /* basic double and add method */
221        l = mpl_significant_bits(&k) - 1;
222        MP_CHECKOK(mp_copy(&qx, &sx));
223        MP_CHECKOK(mp_copy(&qy, &sy));
224        for (i = l - 1; i >= 0; i--) {
225                /* S = 2S */
226                MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group));
227                /* if k_i = 1, then S = S + Q */
228                if (mpl_get_bit(&k, i) != 0) {
229                        MP_CHECKOK(group->
230                                           point_add(&sx, &sy, &qx, &qy, &sx, &sy, group));
231                }
232        }
233#else                                                   /* double and add/subtract method from
234                                                                 * standard */
235        /* k3 = 3 * k */
236        MP_CHECKOK(mp_set_int(&k3, 3));
237        MP_CHECKOK(mp_mul(&k, &k3, &k3));
238        /* S = Q */
239        MP_CHECKOK(mp_copy(&qx, &sx));
240        MP_CHECKOK(mp_copy(&qy, &sy));
241        /* l = index of high order bit in binary representation of 3*k */
242        l = mpl_significant_bits(&k3) - 1;
243        /* for i = l-1 downto 1 */
244        for (i = l - 1; i >= 1; i--) {
245                /* S = 2S */
246                MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group));
247                b3 = MP_GET_BIT(&k3, i);
248                b1 = MP_GET_BIT(&k, i);
249                /* if k3_i = 1 and k_i = 0, then S = S + Q */
250                if ((b3 == 1) && (b1 == 0)) {
251                        MP_CHECKOK(group->
252                                           point_add(&sx, &sy, &qx, &qy, &sx, &sy, group));
253                        /* if k3_i = 0 and k_i = 1, then S = S - Q */
254                } else if ((b3 == 0) && (b1 == 1)) {
255                        MP_CHECKOK(group->
256                                           point_sub(&sx, &sy, &qx, &qy, &sx, &sy, group));
257                }
258        }
259#endif
260        /* output S */
261        MP_CHECKOK(mp_copy(&sx, rx));
262        MP_CHECKOK(mp_copy(&sy, ry));
263
264  CLEANUP:
265        mp_clear(&k);
266        mp_clear(&k3);
267        mp_clear(&qx);
268        mp_clear(&qy);
269        mp_clear(&sx);
270        mp_clear(&sy);
271        return res;
272}
273#endif
274
275/* Validates a point on a GF2m curve. */
276mp_err
277ec_GF2m_validate_point(const mp_int *px, const mp_int *py, const ECGroup *group)
278{
279        mp_err res = MP_NO;
280        mp_int accl, accr, tmp, pxt, pyt;
281
282        MP_DIGITS(&accl) = 0;
283        MP_DIGITS(&accr) = 0;
284        MP_DIGITS(&tmp) = 0;
285        MP_DIGITS(&pxt) = 0;
286        MP_DIGITS(&pyt) = 0;
287        MP_CHECKOK(mp_init(&accl, FLAG(px)));
288        MP_CHECKOK(mp_init(&accr, FLAG(px)));
289        MP_CHECKOK(mp_init(&tmp, FLAG(px)));
290        MP_CHECKOK(mp_init(&pxt, FLAG(px)));
291        MP_CHECKOK(mp_init(&pyt, FLAG(px)));
292
293    /* 1: Verify that publicValue is not the point at infinity */
294        if (ec_GF2m_pt_is_inf_aff(px, py) == MP_YES) {
295                res = MP_NO;
296                goto CLEANUP;
297        }
298    /* 2: Verify that the coordinates of publicValue are elements
299     *    of the field.
300     */
301        if ((MP_SIGN(px) == MP_NEG) || (mp_cmp(px, &group->meth->irr) >= 0) ||
302                (MP_SIGN(py) == MP_NEG) || (mp_cmp(py, &group->meth->irr) >= 0)) {
303                res = MP_NO;
304                goto CLEANUP;
305        }
306    /* 3: Verify that publicValue is on the curve. */
307        if (group->meth->field_enc) {
308                group->meth->field_enc(px, &pxt, group->meth);
309                group->meth->field_enc(py, &pyt, group->meth);
310        } else {
311                mp_copy(px, &pxt);
312                mp_copy(py, &pyt);
313        }
314        /* left-hand side: y^2 + x*y  */
315        MP_CHECKOK( group->meth->field_sqr(&pyt, &accl, group->meth) );
316        MP_CHECKOK( group->meth->field_mul(&pxt, &pyt, &tmp, group->meth) );
317        MP_CHECKOK( group->meth->field_add(&accl, &tmp, &accl, group->meth) );
318        /* right-hand side: x^3 + a*x^2 + b */
319        MP_CHECKOK( group->meth->field_sqr(&pxt, &tmp, group->meth) );
320        MP_CHECKOK( group->meth->field_mul(&pxt, &tmp, &accr, group->meth) );
321        MP_CHECKOK( group->meth->field_mul(&group->curvea, &tmp, &tmp, group->meth) );
322        MP_CHECKOK( group->meth->field_add(&tmp, &accr, &accr, group->meth) );
323        MP_CHECKOK( group->meth->field_add(&accr, &group->curveb, &accr, group->meth) );
324        /* check LHS - RHS == 0 */
325        MP_CHECKOK( group->meth->field_add(&accl, &accr, &accr, group->meth) );
326        if (mp_cmp_z(&accr) != 0) {
327                res = MP_NO;
328                goto CLEANUP;
329        }
330    /* 4: Verify that the order of the curve times the publicValue
331     *    is the point at infinity.
332     */
333        /* timing mitigation is not supported */
334        MP_CHECKOK( ECPoint_mul(group, &group->order, px, py, &pxt, &pyt, /*timing*/ 0) );
335        if (ec_GF2m_pt_is_inf_aff(&pxt, &pyt) != MP_YES) {
336                res = MP_NO;
337                goto CLEANUP;
338        }
339
340        res = MP_YES;
341
342CLEANUP:
343        mp_clear(&accl);
344        mp_clear(&accr);
345        mp_clear(&tmp);
346        mp_clear(&pxt);
347        mp_clear(&pyt);
348        return res;
349}
350