/security/nss/lib/freebl/ecl/ecp_aff.c

  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#include "ecp.h"
 45#include "mplogic.h"
 46#include <stdlib.h>
 47
 48/* Checks if point P(px, py) is at infinity.  Uses affine coordinates. */
 49mp_err
 50ec_GFp_pt_is_inf_aff(const mp_int *px, const mp_int *py)
 51{
 52
 53	if ((mp_cmp_z(px) == 0) && (mp_cmp_z(py) == 0)) {
 54		return MP_YES;
 55	} else {
 56		return MP_NO;
 57	}
 58
 59}
 60
 61/* Sets P(px, py) to be the point at infinity.  Uses affine coordinates. */
 62mp_err
 63ec_GFp_pt_set_inf_aff(mp_int *px, mp_int *py)
 64{
 65	mp_zero(px);
 66	mp_zero(py);
 67	return MP_OKAY;
 68}
 69
 70/* Computes R = P + Q based on IEEE P1363 A.10.1. Elliptic curve points P, 
 71 * Q, and R can all be identical. Uses affine coordinates. Assumes input
 72 * is already field-encoded using field_enc, and returns output that is
 73 * still field-encoded. */
 74mp_err
 75ec_GFp_pt_add_aff(const mp_int *px, const mp_int *py, const mp_int *qx,
 76				  const mp_int *qy, mp_int *rx, mp_int *ry,
 77				  const ECGroup *group)
 78{
 79	mp_err res = MP_OKAY;
 80	mp_int lambda, temp, tempx, tempy;
 81
 82	MP_DIGITS(&lambda) = 0;
 83	MP_DIGITS(&temp) = 0;
 84	MP_DIGITS(&tempx) = 0;
 85	MP_DIGITS(&tempy) = 0;
 86	MP_CHECKOK(mp_init(&lambda));
 87	MP_CHECKOK(mp_init(&temp));
 88	MP_CHECKOK(mp_init(&tempx));
 89	MP_CHECKOK(mp_init(&tempy));
 90	/* if P = inf, then R = Q */
 91	if (ec_GFp_pt_is_inf_aff(px, py) == 0) {
 92		MP_CHECKOK(mp_copy(qx, rx));
 93		MP_CHECKOK(mp_copy(qy, ry));
 94		res = MP_OKAY;
 95		goto CLEANUP;
 96	}
 97	/* if Q = inf, then R = P */
 98	if (ec_GFp_pt_is_inf_aff(qx, qy) == 0) {
 99		MP_CHECKOK(mp_copy(px, rx));
100		MP_CHECKOK(mp_copy(py, ry));
101		res = MP_OKAY;
102		goto CLEANUP;
103	}
104	/* if px != qx, then lambda = (py-qy) / (px-qx) */
105	if (mp_cmp(px, qx) != 0) {
106		MP_CHECKOK(group->meth->field_sub(py, qy, &tempy, group->meth));
107		MP_CHECKOK(group->meth->field_sub(px, qx, &tempx, group->meth));
108		MP_CHECKOK(group->meth->
109				   field_div(&tempy, &tempx, &lambda, group->meth));
110	} else {
111		/* if py != qy or qy = 0, then R = inf */
112		if (((mp_cmp(py, qy) != 0)) || (mp_cmp_z(qy) == 0)) {
113			mp_zero(rx);
114			mp_zero(ry);
115			res = MP_OKAY;
116			goto CLEANUP;
117		}
118		/* lambda = (3qx^2+a) / (2qy) */
119		MP_CHECKOK(group->meth->field_sqr(qx, &tempx, group->meth));
120		MP_CHECKOK(mp_set_int(&temp, 3));
121		if (group->meth->field_enc) {
122			MP_CHECKOK(group->meth->field_enc(&temp, &temp, group->meth));
123		}
124		MP_CHECKOK(group->meth->
125				   field_mul(&tempx, &temp, &tempx, group->meth));
126		MP_CHECKOK(group->meth->
127				   field_add(&tempx, &group->curvea, &tempx, group->meth));
128		MP_CHECKOK(mp_set_int(&temp, 2));
129		if (group->meth->field_enc) {
130			MP_CHECKOK(group->meth->field_enc(&temp, &temp, group->meth));
131		}
132		MP_CHECKOK(group->meth->field_mul(qy, &temp, &tempy, group->meth));
133		MP_CHECKOK(group->meth->
134				   field_div(&tempx, &tempy, &lambda, group->meth));
135	}
136	/* rx = lambda^2 - px - qx */
137	MP_CHECKOK(group->meth->field_sqr(&lambda, &tempx, group->meth));
138	MP_CHECKOK(group->meth->field_sub(&tempx, px, &tempx, group->meth));
139	MP_CHECKOK(group->meth->field_sub(&tempx, qx, &tempx, group->meth));
140	/* ry = (x1-x2) * lambda - y1 */
141	MP_CHECKOK(group->meth->field_sub(qx, &tempx, &tempy, group->meth));
142	MP_CHECKOK(group->meth->
143			   field_mul(&tempy, &lambda, &tempy, group->meth));
144	MP_CHECKOK(group->meth->field_sub(&tempy, qy, &tempy, group->meth));
145	MP_CHECKOK(mp_copy(&tempx, rx));
146	MP_CHECKOK(mp_copy(&tempy, ry));
147
148  CLEANUP:
149	mp_clear(&lambda);
150	mp_clear(&temp);
151	mp_clear(&tempx);
152	mp_clear(&tempy);
153	return res;
154}
155
156/* Computes R = P - Q. Elliptic curve points P, Q, and R can all be
157 * identical. Uses affine coordinates. Assumes input is already
158 * field-encoded using field_enc, and returns output that is still
159 * field-encoded. */
160mp_err
161ec_GFp_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));
170	/* nqy = -qy */
171	MP_CHECKOK(group->meth->field_neg(qy, &nqy, group->meth));
172	res = 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. Assumes input is already field-encoded using
180 * field_enc, and returns output that is still field-encoded. */
181mp_err
182ec_GFp_pt_dbl_aff(const mp_int *px, const mp_int *py, mp_int *rx,
183				  mp_int *ry, const ECGroup *group)
184{
185	return ec_GFp_pt_add_aff(px, py, px, py, rx, ry, group);
186}
187
188/* by default, this routine is unused and thus doesn't need to be compiled */
189#ifdef ECL_ENABLE_GFP_PT_MUL_AFF
190/* Computes R = nP based on IEEE P1363 A.10.3. Elliptic curve points P and 
191 * R can be identical. Uses affine coordinates. Assumes input is already
192 * field-encoded using field_enc, and returns output that is still
193 * field-encoded. */
194mp_err
195ec_GFp_pt_mul_aff(const mp_int *n, const mp_int *px, const mp_int *py,
196				  mp_int *rx, mp_int *ry, const ECGroup *group)
197{
198	mp_err res = MP_OKAY;
199	mp_int k, k3, qx, qy, sx, sy;
200	int b1, b3, i, l;
201
202	MP_DIGITS(&k) = 0;
203	MP_DIGITS(&k3) = 0;
204	MP_DIGITS(&qx) = 0;
205	MP_DIGITS(&qy) = 0;
206	MP_DIGITS(&sx) = 0;
207	MP_DIGITS(&sy) = 0;
208	MP_CHECKOK(mp_init(&k));
209	MP_CHECKOK(mp_init(&k3));
210	MP_CHECKOK(mp_init(&qx));
211	MP_CHECKOK(mp_init(&qy));
212	MP_CHECKOK(mp_init(&sx));
213	MP_CHECKOK(mp_init(&sy));
214
215	/* if n = 0 then r = inf */
216	if (mp_cmp_z(n) == 0) {
217		mp_zero(rx);
218		mp_zero(ry);
219		res = MP_OKAY;
220		goto CLEANUP;
221	}
222	/* Q = P, k = n */
223	MP_CHECKOK(mp_copy(px, &qx));
224	MP_CHECKOK(mp_copy(py, &qy));
225	MP_CHECKOK(mp_copy(n, &k));
226	/* if n < 0 then Q = -Q, k = -k */
227	if (mp_cmp_z(n) < 0) {
228		MP_CHECKOK(group->meth->field_neg(&qy, &qy, group->meth));
229		MP_CHECKOK(mp_neg(&k, &k));
230	}
231#ifdef ECL_DEBUG				/* basic double and add method */
232	l = mpl_significant_bits(&k) - 1;
233	MP_CHECKOK(mp_copy(&qx, &sx));
234	MP_CHECKOK(mp_copy(&qy, &sy));
235	for (i = l - 1; i >= 0; i--) {
236		/* S = 2S */
237		MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group));
238		/* if k_i = 1, then S = S + Q */
239		if (mpl_get_bit(&k, i) != 0) {
240			MP_CHECKOK(group->
241					   point_add(&sx, &sy, &qx, &qy, &sx, &sy, group));
242		}
243	}
244#else							/* double and add/subtract method from
245								 * standard */
246	/* k3 = 3 * k */
247	MP_CHECKOK(mp_set_int(&k3, 3));
248	MP_CHECKOK(mp_mul(&k, &k3, &k3));
249	/* S = Q */
250	MP_CHECKOK(mp_copy(&qx, &sx));
251	MP_CHECKOK(mp_copy(&qy, &sy));
252	/* l = index of high order bit in binary representation of 3*k */
253	l = mpl_significant_bits(&k3) - 1;
254	/* for i = l-1 downto 1 */
255	for (i = l - 1; i >= 1; i--) {
256		/* S = 2S */
257		MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group));
258		b3 = MP_GET_BIT(&k3, i);
259		b1 = MP_GET_BIT(&k, i);
260		/* if k3_i = 1 and k_i = 0, then S = S + Q */
261		if ((b3 == 1) && (b1 == 0)) {
262			MP_CHECKOK(group->
263					   point_add(&sx, &sy, &qx, &qy, &sx, &sy, group));
264			/* if k3_i = 0 and k_i = 1, then S = S - Q */
265		} else if ((b3 == 0) && (b1 == 1)) {
266			MP_CHECKOK(group->
267					   point_sub(&sx, &sy, &qx, &qy, &sx, &sy, group));
268		}
269	}
270#endif
271	/* output S */
272	MP_CHECKOK(mp_copy(&sx, rx));
273	MP_CHECKOK(mp_copy(&sy, ry));
274
275  CLEANUP:
276	mp_clear(&k);
277	mp_clear(&k3);
278	mp_clear(&qx);
279	mp_clear(&qy);
280	mp_clear(&sx);
281	mp_clear(&sy);
282	return res;
283}
284#endif
285
286/* Validates a point on a GFp curve. */
287mp_err 
288ec_GFp_validate_point(const mp_int *px, const mp_int *py, const ECGroup *group)
289{
290	mp_err res = MP_NO;
291	mp_int accl, accr, tmp, pxt, pyt;
292
293	MP_DIGITS(&accl) = 0;
294	MP_DIGITS(&accr) = 0;
295	MP_DIGITS(&tmp) = 0;
296	MP_DIGITS(&pxt) = 0;
297	MP_DIGITS(&pyt) = 0;
298	MP_CHECKOK(mp_init(&accl));
299	MP_CHECKOK(mp_init(&accr));
300	MP_CHECKOK(mp_init(&tmp));
301	MP_CHECKOK(mp_init(&pxt));
302	MP_CHECKOK(mp_init(&pyt));
303
304    /* 1: Verify that publicValue is not the point at infinity */
305	if (ec_GFp_pt_is_inf_aff(px, py) == MP_YES) {
306		res = MP_NO;
307		goto CLEANUP;
308	}
309    /* 2: Verify that the coordinates of publicValue are elements 
310     *    of the field.
311     */
312	if ((MP_SIGN(px) == MP_NEG) || (mp_cmp(px, &group->meth->irr) >= 0) || 
313		(MP_SIGN(py) == MP_NEG) || (mp_cmp(py, &group->meth->irr) >= 0)) {
314		res = MP_NO;
315		goto CLEANUP;
316	}
317    /* 3: Verify that publicValue is on the curve. */
318	if (group->meth->field_enc) {
319		group->meth->field_enc(px, &pxt, group->meth);
320		group->meth->field_enc(py, &pyt, group->meth);
321	} else {
322		mp_copy(px, &pxt);
323		mp_copy(py, &pyt);
324	}
325	/* left-hand side: y^2  */
326	MP_CHECKOK( group->meth->field_sqr(&pyt, &accl, group->meth) );
327	/* right-hand side: x^3 + a*x + b */
328	MP_CHECKOK( group->meth->field_sqr(&pxt, &tmp, group->meth) );
329	MP_CHECKOK( group->meth->field_mul(&pxt, &tmp, &accr, group->meth) );
330	MP_CHECKOK( group->meth->field_mul(&group->curvea, &pxt, &tmp, group->meth) );
331	MP_CHECKOK( group->meth->field_add(&tmp, &accr, &accr, group->meth) );
332	MP_CHECKOK( group->meth->field_add(&accr, &group->curveb, &accr, group->meth) );
333	/* check LHS - RHS == 0 */
334	MP_CHECKOK( group->meth->field_sub(&accl, &accr, &accr, group->meth) );
335	if (mp_cmp_z(&accr) != 0) {
336		res = MP_NO;
337		goto CLEANUP;
338	}
339    /* 4: Verify that the order of the curve times the publicValue
340     *    is the point at infinity.
341     */
342	MP_CHECKOK( ECPoint_mul(group, &group->order, px, py, &pxt, &pyt) );
343	if (ec_GFp_pt_is_inf_aff(&pxt, &pyt) != MP_YES) {
344		res = MP_NO;
345		goto CLEANUP;
346	}
347
348	res = MP_YES;
349
350CLEANUP:
351	mp_clear(&accl);
352	mp_clear(&accr);
353	mp_clear(&tmp);
354	mp_clear(&pxt);
355	mp_clear(&pyt);
356	return res;
357}