xref: /illumos-gate/usr/src/common/crypto/ecc/ecp_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 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