xref: /illumos-gate/usr/src/common/crypto/ecc/ec2_aff.c (revision f9fbec18)
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 binary polynomial 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  *   Douglas Stebila <douglas@stebila.ca>, Sun Microsystems Laboratories
24  *
25  * Alternatively, the contents of this file may be used under the terms of
26  * either the GNU General Public License Version 2 or later (the "GPL"), or
27  * the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
28  * in which case the provisions of the GPL or the LGPL are applicable instead
29  * of those above. If you wish to allow use of your version of this file only
30  * under the terms of either the GPL or the LGPL, and not to allow others to
31  * use your version of this file under the terms of the MPL, indicate your
32  * decision by deleting the provisions above and replace them with the notice
33  * and other provisions required by the GPL or the LGPL. If you do not delete
34  * the provisions above, a recipient may use your version of this file under
35  * the terms of any one of the MPL, the GPL or the LGPL.
36  *
37  * ***** END LICENSE BLOCK ***** */
38 /*
39  * Copyright 2007 Sun Microsystems, Inc.  All rights reserved.
40  * Use is subject to license terms.
41  *
42  * Sun elects to use this software under the MPL license.
43  */
44 
45 #pragma ident	"%Z%%M%	%I%	%E% SMI"
46 
47 #include "ec2.h"
48 #include "mplogic.h"
49 #include "mp_gf2m.h"
50 #ifndef _KERNEL
51 #include <stdlib.h>
52 #endif
53 
54 /* Checks if point P(px, py) is at infinity.  Uses affine coordinates. */
55 mp_err
ec_GF2m_pt_is_inf_aff(const mp_int * px,const mp_int * py)56 ec_GF2m_pt_is_inf_aff(const mp_int *px, const mp_int *py)
57 {
58 
59 	if ((mp_cmp_z(px) == 0) && (mp_cmp_z(py) == 0)) {
60 		return MP_YES;
61 	} else {
62 		return MP_NO;
63 	}
64 
65 }
66 
67 /* Sets P(px, py) to be the point at infinity.  Uses affine coordinates. */
68 mp_err
ec_GF2m_pt_set_inf_aff(mp_int * px,mp_int * py)69 ec_GF2m_pt_set_inf_aff(mp_int *px, mp_int *py)
70 {
71 	mp_zero(px);
72 	mp_zero(py);
73 	return MP_OKAY;
74 }
75 
76 /* Computes R = P + Q based on IEEE P1363 A.10.2. Elliptic curve points P,
77  * Q, and R can all be identical. Uses affine coordinates. */
78 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)79 ec_GF2m_pt_add_aff(const mp_int *px, const mp_int *py, const mp_int *qx,
80 				   const mp_int *qy, mp_int *rx, mp_int *ry,
81 				   const ECGroup *group)
82 {
83 	mp_err res = MP_OKAY;
84 	mp_int lambda, tempx, tempy;
85 
86 	MP_DIGITS(&lambda) = 0;
87 	MP_DIGITS(&tempx) = 0;
88 	MP_DIGITS(&tempy) = 0;
89 	MP_CHECKOK(mp_init(&lambda, FLAG(px)));
90 	MP_CHECKOK(mp_init(&tempx, FLAG(px)));
91 	MP_CHECKOK(mp_init(&tempy, FLAG(px)));
92 	/* if P = inf, then R = Q */
93 	if (ec_GF2m_pt_is_inf_aff(px, py) == 0) {
94 		MP_CHECKOK(mp_copy(qx, rx));
95 		MP_CHECKOK(mp_copy(qy, ry));
96 		res = MP_OKAY;
97 		goto CLEANUP;
98 	}
99 	/* if Q = inf, then R = P */
100 	if (ec_GF2m_pt_is_inf_aff(qx, qy) == 0) {
101 		MP_CHECKOK(mp_copy(px, rx));
102 		MP_CHECKOK(mp_copy(py, ry));
103 		res = MP_OKAY;
104 		goto CLEANUP;
105 	}
106 	/* if px != qx, then lambda = (py+qy) / (px+qx), tempx = a + lambda^2
107 	 * + lambda + px + qx */
108 	if (mp_cmp(px, qx) != 0) {
109 		MP_CHECKOK(group->meth->field_add(py, qy, &tempy, group->meth));
110 		MP_CHECKOK(group->meth->field_add(px, qx, &tempx, group->meth));
111 		MP_CHECKOK(group->meth->
112 				   field_div(&tempy, &tempx, &lambda, group->meth));
113 		MP_CHECKOK(group->meth->field_sqr(&lambda, &tempx, group->meth));
114 		MP_CHECKOK(group->meth->
115 				   field_add(&tempx, &lambda, &tempx, group->meth));
116 		MP_CHECKOK(group->meth->
117 				   field_add(&tempx, &group->curvea, &tempx, group->meth));
118 		MP_CHECKOK(group->meth->
119 				   field_add(&tempx, px, &tempx, group->meth));
120 		MP_CHECKOK(group->meth->
121 				   field_add(&tempx, qx, &tempx, group->meth));
122 	} else {
123 		/* if py != qy or qx = 0, then R = inf */
124 		if (((mp_cmp(py, qy) != 0)) || (mp_cmp_z(qx) == 0)) {
125 			mp_zero(rx);
126 			mp_zero(ry);
127 			res = MP_OKAY;
128 			goto CLEANUP;
129 		}
130 		/* lambda = qx + qy / qx */
131 		MP_CHECKOK(group->meth->field_div(qy, qx, &lambda, group->meth));
132 		MP_CHECKOK(group->meth->
133 				   field_add(&lambda, qx, &lambda, group->meth));
134 		/* tempx = a + lambda^2 + lambda */
135 		MP_CHECKOK(group->meth->field_sqr(&lambda, &tempx, group->meth));
136 		MP_CHECKOK(group->meth->
137 				   field_add(&tempx, &lambda, &tempx, group->meth));
138 		MP_CHECKOK(group->meth->
139 				   field_add(&tempx, &group->curvea, &tempx, group->meth));
140 	}
141 	/* ry = (qx + tempx) * lambda + tempx + qy */
142 	MP_CHECKOK(group->meth->field_add(qx, &tempx, &tempy, group->meth));
143 	MP_CHECKOK(group->meth->
144 			   field_mul(&tempy, &lambda, &tempy, group->meth));
145 	MP_CHECKOK(group->meth->
146 			   field_add(&tempy, &tempx, &tempy, group->meth));
147 	MP_CHECKOK(group->meth->field_add(&tempy, qy, ry, group->meth));
148 	/* rx = tempx */
149 	MP_CHECKOK(mp_copy(&tempx, rx));
150 
151   CLEANUP:
152 	mp_clear(&lambda);
153 	mp_clear(&tempx);
154 	mp_clear(&tempy);
155 	return res;
156 }
157 
158 /* Computes R = P - Q. Elliptic curve points P, Q, and R can all be
159  * identical. Uses affine coordinates. */
160 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)161 ec_GF2m_pt_sub_aff(const mp_int *px, const mp_int *py, const mp_int *qx,
162 				   const mp_int *qy, mp_int *rx, mp_int *ry,
163 				   const ECGroup *group)
164 {
165 	mp_err res = MP_OKAY;
166 	mp_int nqy;
167 
168 	MP_DIGITS(&nqy) = 0;
169 	MP_CHECKOK(mp_init(&nqy, FLAG(px)));
170 	/* nqy = qx+qy */
171 	MP_CHECKOK(group->meth->field_add(qx, qy, &nqy, group->meth));
172 	MP_CHECKOK(group->point_add(px, py, qx, &nqy, rx, ry, group));
173   CLEANUP:
174 	mp_clear(&nqy);
175 	return res;
176 }
177 
178 /* Computes R = 2P. Elliptic curve points P and R can be identical. Uses
179  * affine coordinates. */
180 mp_err
ec_GF2m_pt_dbl_aff(const mp_int * px,const mp_int * py,mp_int * rx,mp_int * ry,const ECGroup * group)181 ec_GF2m_pt_dbl_aff(const mp_int *px, const mp_int *py, mp_int *rx,
182 				   mp_int *ry, const ECGroup *group)
183 {
184 	return group->point_add(px, py, px, py, rx, ry, group);
185 }
186 
187 /* by default, this routine is unused and thus doesn't need to be compiled */
188 #ifdef ECL_ENABLE_GF2M_PT_MUL_AFF
189 /* Computes R = nP based on IEEE P1363 A.10.3. Elliptic curve points P and
190  * R can be identical. Uses affine coordinates. */
191 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)192 ec_GF2m_pt_mul_aff(const mp_int *n, const mp_int *px, const mp_int *py,
193 				   mp_int *rx, mp_int *ry, const ECGroup *group)
194 {
195 	mp_err res = MP_OKAY;
196 	mp_int k, k3, qx, qy, sx, sy;
197 	int b1, b3, i, l;
198 
199 	MP_DIGITS(&k) = 0;
200 	MP_DIGITS(&k3) = 0;
201 	MP_DIGITS(&qx) = 0;
202 	MP_DIGITS(&qy) = 0;
203 	MP_DIGITS(&sx) = 0;
204 	MP_DIGITS(&sy) = 0;
205 	MP_CHECKOK(mp_init(&k));
206 	MP_CHECKOK(mp_init(&k3));
207 	MP_CHECKOK(mp_init(&qx));
208 	MP_CHECKOK(mp_init(&qy));
209 	MP_CHECKOK(mp_init(&sx));
210 	MP_CHECKOK(mp_init(&sy));
211 
212 	/* if n = 0 then r = inf */
213 	if (mp_cmp_z(n) == 0) {
214 		mp_zero(rx);
215 		mp_zero(ry);
216 		res = MP_OKAY;
217 		goto CLEANUP;
218 	}
219 	/* Q = P, k = n */
220 	MP_CHECKOK(mp_copy(px, &qx));
221 	MP_CHECKOK(mp_copy(py, &qy));
222 	MP_CHECKOK(mp_copy(n, &k));
223 	/* if n < 0 then Q = -Q, k = -k */
224 	if (mp_cmp_z(n) < 0) {
225 		MP_CHECKOK(group->meth->field_add(&qx, &qy, &qy, group->meth));
226 		MP_CHECKOK(mp_neg(&k, &k));
227 	}
228 #ifdef ECL_DEBUG				/* basic double and add method */
229 	l = mpl_significant_bits(&k) - 1;
230 	MP_CHECKOK(mp_copy(&qx, &sx));
231 	MP_CHECKOK(mp_copy(&qy, &sy));
232 	for (i = l - 1; i >= 0; i--) {
233 		/* S = 2S */
234 		MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group));
235 		/* if k_i = 1, then S = S + Q */
236 		if (mpl_get_bit(&k, i) != 0) {
237 			MP_CHECKOK(group->
238 					   point_add(&sx, &sy, &qx, &qy, &sx, &sy, group));
239 		}
240 	}
241 #else							/* double and add/subtract method from
242 								 * standard */
243 	/* k3 = 3 * k */
244 	MP_CHECKOK(mp_set_int(&k3, 3));
245 	MP_CHECKOK(mp_mul(&k, &k3, &k3));
246 	/* S = Q */
247 	MP_CHECKOK(mp_copy(&qx, &sx));
248 	MP_CHECKOK(mp_copy(&qy, &sy));
249 	/* l = index of high order bit in binary representation of 3*k */
250 	l = mpl_significant_bits(&k3) - 1;
251 	/* for i = l-1 downto 1 */
252 	for (i = l - 1; i >= 1; i--) {
253 		/* S = 2S */
254 		MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group));
255 		b3 = MP_GET_BIT(&k3, i);
256 		b1 = MP_GET_BIT(&k, i);
257 		/* if k3_i = 1 and k_i = 0, then S = S + Q */
258 		if ((b3 == 1) && (b1 == 0)) {
259 			MP_CHECKOK(group->
260 					   point_add(&sx, &sy, &qx, &qy, &sx, &sy, group));
261 			/* if k3_i = 0 and k_i = 1, then S = S - Q */
262 		} else if ((b3 == 0) && (b1 == 1)) {
263 			MP_CHECKOK(group->
264 					   point_sub(&sx, &sy, &qx, &qy, &sx, &sy, group));
265 		}
266 	}
267 #endif
268 	/* output S */
269 	MP_CHECKOK(mp_copy(&sx, rx));
270 	MP_CHECKOK(mp_copy(&sy, ry));
271 
272   CLEANUP:
273 	mp_clear(&k);
274 	mp_clear(&k3);
275 	mp_clear(&qx);
276 	mp_clear(&qy);
277 	mp_clear(&sx);
278 	mp_clear(&sy);
279 	return res;
280 }
281 #endif
282 
283 /* Validates a point on a GF2m curve. */
284 mp_err
ec_GF2m_validate_point(const mp_int * px,const mp_int * py,const ECGroup * group)285 ec_GF2m_validate_point(const mp_int *px, const mp_int *py, const ECGroup *group)
286 {
287 	mp_err res = MP_NO;
288 	mp_int accl, accr, tmp, pxt, pyt;
289 
290 	MP_DIGITS(&accl) = 0;
291 	MP_DIGITS(&accr) = 0;
292 	MP_DIGITS(&tmp) = 0;
293 	MP_DIGITS(&pxt) = 0;
294 	MP_DIGITS(&pyt) = 0;
295 	MP_CHECKOK(mp_init(&accl, FLAG(px)));
296 	MP_CHECKOK(mp_init(&accr, FLAG(px)));
297 	MP_CHECKOK(mp_init(&tmp, FLAG(px)));
298 	MP_CHECKOK(mp_init(&pxt, FLAG(px)));
299 	MP_CHECKOK(mp_init(&pyt, FLAG(px)));
300 
301     /* 1: Verify that publicValue is not the point at infinity */
302 	if (ec_GF2m_pt_is_inf_aff(px, py) == MP_YES) {
303 		res = MP_NO;
304 		goto CLEANUP;
305 	}
306     /* 2: Verify that the coordinates of publicValue are elements
307      *    of the field.
308      */
309 	if ((MP_SIGN(px) == MP_NEG) || (mp_cmp(px, &group->meth->irr) >= 0) ||
310 		(MP_SIGN(py) == MP_NEG) || (mp_cmp(py, &group->meth->irr) >= 0)) {
311 		res = MP_NO;
312 		goto CLEANUP;
313 	}
314     /* 3: Verify that publicValue is on the curve. */
315 	if (group->meth->field_enc) {
316 		group->meth->field_enc(px, &pxt, group->meth);
317 		group->meth->field_enc(py, &pyt, group->meth);
318 	} else {
319 		mp_copy(px, &pxt);
320 		mp_copy(py, &pyt);
321 	}
322 	/* left-hand side: y^2 + x*y  */
323 	MP_CHECKOK( group->meth->field_sqr(&pyt, &accl, group->meth) );
324 	MP_CHECKOK( group->meth->field_mul(&pxt, &pyt, &tmp, group->meth) );
325 	MP_CHECKOK( group->meth->field_add(&accl, &tmp, &accl, group->meth) );
326 	/* right-hand side: x^3 + a*x^2 + b */
327 	MP_CHECKOK( group->meth->field_sqr(&pxt, &tmp, group->meth) );
328 	MP_CHECKOK( group->meth->field_mul(&pxt, &tmp, &accr, group->meth) );
329 	MP_CHECKOK( group->meth->field_mul(&group->curvea, &tmp, &tmp, group->meth) );
330 	MP_CHECKOK( group->meth->field_add(&tmp, &accr, &accr, group->meth) );
331 	MP_CHECKOK( group->meth->field_add(&accr, &group->curveb, &accr, group->meth) );
332 	/* check LHS - RHS == 0 */
333 	MP_CHECKOK( group->meth->field_add(&accl, &accr, &accr, group->meth) );
334 	if (mp_cmp_z(&accr) != 0) {
335 		res = MP_NO;
336 		goto CLEANUP;
337 	}
338     /* 4: Verify that the order of the curve times the publicValue
339      *    is the point at infinity.
340      */
341 	MP_CHECKOK( ECPoint_mul(group, &group->order, px, py, &pxt, &pyt) );
342 	if (ec_GF2m_pt_is_inf_aff(&pxt, &pyt) != MP_YES) {
343 		res = MP_NO;
344 		goto CLEANUP;
345 	}
346 
347 	res = MP_YES;
348 
349 CLEANUP:
350 	mp_clear(&accl);
351 	mp_clear(&accr);
352 	mp_clear(&tmp);
353 	mp_clear(&pxt);
354 	mp_clear(&pyt);
355 	return res;
356 }
357