xref: /illumos-gate/usr/src/common/crypto/ecc/ecp_jm.c (revision f36d754ab42a9c0301f6a475a5895e22adb0bb1a)
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  *   Stephen Fung <fungstep@hotmail.com>, 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 #include "ecp.h"
46 #include "ecl-priv.h"
47 #include "mplogic.h"
48 #ifndef _KERNEL
49 #include <stdlib.h>
50 #endif
51 
52 #define MAX_SCRATCH 6
53 
54 /* Computes R = 2P.  Elliptic curve points P and R can be identical.  Uses
55  * Modified Jacobian coordinates.
56  *
57  * Assumes input is already field-encoded using field_enc, and returns
58  * output that is still field-encoded.
59  *
60  */
61 mp_err
ec_GFp_pt_dbl_jm(const mp_int * px,const mp_int * py,const mp_int * pz,const mp_int * paz4,mp_int * rx,mp_int * ry,mp_int * rz,mp_int * raz4,mp_int scratch[],const ECGroup * group)62 ec_GFp_pt_dbl_jm(const mp_int *px, const mp_int *py, const mp_int *pz,
63 				 const mp_int *paz4, mp_int *rx, mp_int *ry, mp_int *rz,
64 				 mp_int *raz4, mp_int scratch[], const ECGroup *group)
65 {
66 	mp_err res = MP_OKAY;
67 	mp_int *t0, *t1, *M, *S;
68 
69 	t0 = &scratch[0];
70 	t1 = &scratch[1];
71 	M = &scratch[2];
72 	S = &scratch[3];
73 
74 #if MAX_SCRATCH < 4
75 #error "Scratch array defined too small "
76 #endif
77 
78 	/* Check for point at infinity */
79 	if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {
80 		/* Set r = pt at infinity by setting rz = 0 */
81 
82 		MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, rz));
83 		goto CLEANUP;
84 	}
85 
86 	/* M = 3 (px^2) + a*(pz^4) */
87 	MP_CHECKOK(group->meth->field_sqr(px, t0, group->meth));
88 	MP_CHECKOK(group->meth->field_add(t0, t0, M, group->meth));
89 	MP_CHECKOK(group->meth->field_add(t0, M, t0, group->meth));
90 	MP_CHECKOK(group->meth->field_add(t0, paz4, M, group->meth));
91 
92 	/* rz = 2 * py * pz */
93 	MP_CHECKOK(group->meth->field_mul(py, pz, S, group->meth));
94 	MP_CHECKOK(group->meth->field_add(S, S, rz, group->meth));
95 
96 	/* t0 = 2y^2 , t1 = 8y^4 */
97 	MP_CHECKOK(group->meth->field_sqr(py, t0, group->meth));
98 	MP_CHECKOK(group->meth->field_add(t0, t0, t0, group->meth));
99 	MP_CHECKOK(group->meth->field_sqr(t0, t1, group->meth));
100 	MP_CHECKOK(group->meth->field_add(t1, t1, t1, group->meth));
101 
102 	/* S = 4 * px * py^2 = 2 * px * t0 */
103 	MP_CHECKOK(group->meth->field_mul(px, t0, S, group->meth));
104 	MP_CHECKOK(group->meth->field_add(S, S, S, group->meth));
105 
106 
107 	/* rx = M^2 - 2S */
108 	MP_CHECKOK(group->meth->field_sqr(M, rx, group->meth));
109 	MP_CHECKOK(group->meth->field_sub(rx, S, rx, group->meth));
110 	MP_CHECKOK(group->meth->field_sub(rx, S, rx, group->meth));
111 
112 	/* ry = M * (S - rx) - t1 */
113 	MP_CHECKOK(group->meth->field_sub(S, rx, S, group->meth));
114 	MP_CHECKOK(group->meth->field_mul(S, M, ry, group->meth));
115 	MP_CHECKOK(group->meth->field_sub(ry, t1, ry, group->meth));
116 
117 	/* ra*z^4 = 2*t1*(apz4) */
118 	MP_CHECKOK(group->meth->field_mul(paz4, t1, raz4, group->meth));
119 	MP_CHECKOK(group->meth->field_add(raz4, raz4, raz4, group->meth));
120 
121 
122   CLEANUP:
123 	return res;
124 }
125 
126 /* Computes R = P + Q where R is (rx, ry, rz), P is (px, py, pz) and Q is
127  * (qx, qy, 1).  Elliptic curve points P, Q, and R can all be identical.
128  * Uses mixed Modified_Jacobian-affine coordinates. Assumes input is
129  * already field-encoded using field_enc, and returns output that is still
130  * field-encoded. */
131 mp_err
ec_GFp_pt_add_jm_aff(const mp_int * px,const mp_int * py,const mp_int * pz,const mp_int * paz4,const mp_int * qx,const mp_int * qy,mp_int * rx,mp_int * ry,mp_int * rz,mp_int * raz4,mp_int scratch[],const ECGroup * group)132 ec_GFp_pt_add_jm_aff(const mp_int *px, const mp_int *py, const mp_int *pz,
133 					 const mp_int *paz4, const mp_int *qx,
134 					 const mp_int *qy, mp_int *rx, mp_int *ry, mp_int *rz,
135 					 mp_int *raz4, mp_int scratch[], const ECGroup *group)
136 {
137 	mp_err res = MP_OKAY;
138 	mp_int *A, *B, *C, *D, *C2, *C3;
139 
140 	A = &scratch[0];
141 	B = &scratch[1];
142 	C = &scratch[2];
143 	D = &scratch[3];
144 	C2 = &scratch[4];
145 	C3 = &scratch[5];
146 
147 #if MAX_SCRATCH < 6
148 #error "Scratch array defined too small "
149 #endif
150 
151 	/* If either P or Q is the point at infinity, then return the other
152 	 * point */
153 	if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {
154 		MP_CHECKOK(ec_GFp_pt_aff2jac(qx, qy, rx, ry, rz, group));
155 		MP_CHECKOK(group->meth->field_sqr(rz, raz4, group->meth));
156 		MP_CHECKOK(group->meth->field_sqr(raz4, raz4, group->meth));
157 		MP_CHECKOK(group->meth->
158 				   field_mul(raz4, &group->curvea, raz4, group->meth));
159 		goto CLEANUP;
160 	}
161 	if (ec_GFp_pt_is_inf_aff(qx, qy) == MP_YES) {
162 		MP_CHECKOK(mp_copy(px, rx));
163 		MP_CHECKOK(mp_copy(py, ry));
164 		MP_CHECKOK(mp_copy(pz, rz));
165 		MP_CHECKOK(mp_copy(paz4, raz4));
166 		goto CLEANUP;
167 	}
168 
169 	/* A = qx * pz^2, B = qy * pz^3 */
170 	MP_CHECKOK(group->meth->field_sqr(pz, A, group->meth));
171 	MP_CHECKOK(group->meth->field_mul(A, pz, B, group->meth));
172 	MP_CHECKOK(group->meth->field_mul(A, qx, A, group->meth));
173 	MP_CHECKOK(group->meth->field_mul(B, qy, B, group->meth));
174 
175 	/* Check P == Q */
176 	if (mp_cmp(A, px) == 0) {
177 		if (mp_cmp(B, py) == 0) {
178 			/* If Px == Qx && Py == Qy, double P. */
179 			return (ec_GFp_pt_dbl_jm(px, py, pz, paz4, rx, ry, rz,
180 			    raz4, scratch, group));
181 		}
182 		/* If Px == Qx && Py != Qy, return point at infinity. */
183 		return (ec_GFp_pt_set_inf_jac(rx, ry, rz));
184 	}
185 
186 	/* C = A - px, D = B - py */
187 	MP_CHECKOK(group->meth->field_sub(A, px, C, group->meth));
188 	MP_CHECKOK(group->meth->field_sub(B, py, D, group->meth));
189 
190 	/* C2 = C^2, C3 = C^3 */
191 	MP_CHECKOK(group->meth->field_sqr(C, C2, group->meth));
192 	MP_CHECKOK(group->meth->field_mul(C, C2, C3, group->meth));
193 
194 	/* rz = pz * C */
195 	MP_CHECKOK(group->meth->field_mul(pz, C, rz, group->meth));
196 
197 	/* C = px * C^2 */
198 	MP_CHECKOK(group->meth->field_mul(px, C2, C, group->meth));
199 	/* A = D^2 */
200 	MP_CHECKOK(group->meth->field_sqr(D, A, group->meth));
201 
202 	/* rx = D^2 - (C^3 + 2 * (px * C^2)) */
203 	MP_CHECKOK(group->meth->field_add(C, C, rx, group->meth));
204 	MP_CHECKOK(group->meth->field_add(C3, rx, rx, group->meth));
205 	MP_CHECKOK(group->meth->field_sub(A, rx, rx, group->meth));
206 
207 	/* C3 = py * C^3 */
208 	MP_CHECKOK(group->meth->field_mul(py, C3, C3, group->meth));
209 
210 	/* ry = D * (px * C^2 - rx) - py * C^3 */
211 	MP_CHECKOK(group->meth->field_sub(C, rx, ry, group->meth));
212 	MP_CHECKOK(group->meth->field_mul(D, ry, ry, group->meth));
213 	MP_CHECKOK(group->meth->field_sub(ry, C3, ry, group->meth));
214 
215 	/* raz4 = a * rz^4 */
216 	MP_CHECKOK(group->meth->field_sqr(rz, raz4, group->meth));
217 	MP_CHECKOK(group->meth->field_sqr(raz4, raz4, group->meth));
218 	MP_CHECKOK(group->meth->
219 			   field_mul(raz4, &group->curvea, raz4, group->meth));
220 CLEANUP:
221 	return res;
222 }
223 
224 /* Computes R = nP where R is (rx, ry) and P is the base point. Elliptic
225  * curve points P and R can be identical. Uses mixed Modified-Jacobian
226  * co-ordinates for doubling and Chudnovsky Jacobian coordinates for
227  * additions. Assumes input is already field-encoded using field_enc, and
228  * returns output that is still field-encoded. Uses 5-bit window NAF
229  * method (algorithm 11) for scalar-point multiplication from Brown,
230  * Hankerson, Lopez, Menezes. Software Implementation of the NIST Elliptic
231  * Curves Over Prime Fields. */
232 mp_err
ec_GFp_pt_mul_jm_wNAF(const mp_int * n,const mp_int * px,const mp_int * py,mp_int * rx,mp_int * ry,const ECGroup * group)233 ec_GFp_pt_mul_jm_wNAF(const mp_int *n, const mp_int *px, const mp_int *py,
234 					  mp_int *rx, mp_int *ry, const ECGroup *group)
235 {
236 	mp_err res = MP_OKAY;
237 	mp_int precomp[16][2], rz, tpx, tpy;
238 	mp_int raz4;
239 	mp_int scratch[MAX_SCRATCH];
240 	signed char *naf = NULL;
241 	int i, orderBitSize;
242 
243 	MP_DIGITS(&rz) = 0;
244 	MP_DIGITS(&raz4) = 0;
245 	MP_DIGITS(&tpx) = 0;
246 	MP_DIGITS(&tpy) = 0;
247 	for (i = 0; i < 16; i++) {
248 		MP_DIGITS(&precomp[i][0]) = 0;
249 		MP_DIGITS(&precomp[i][1]) = 0;
250 	}
251 	for (i = 0; i < MAX_SCRATCH; i++) {
252 		MP_DIGITS(&scratch[i]) = 0;
253 	}
254 
255 	ARGCHK(group != NULL, MP_BADARG);
256 	ARGCHK((n != NULL) && (px != NULL) && (py != NULL), MP_BADARG);
257 
258 	/* initialize precomputation table */
259 	MP_CHECKOK(mp_init(&tpx, FLAG(n)));
260 	MP_CHECKOK(mp_init(&tpy, FLAG(n)));;
261 	MP_CHECKOK(mp_init(&rz, FLAG(n)));
262 	MP_CHECKOK(mp_init(&raz4, FLAG(n)));
263 
264 	for (i = 0; i < 16; i++) {
265 		MP_CHECKOK(mp_init(&precomp[i][0], FLAG(n)));
266 		MP_CHECKOK(mp_init(&precomp[i][1], FLAG(n)));
267 	}
268 	for (i = 0; i < MAX_SCRATCH; i++) {
269 		MP_CHECKOK(mp_init(&scratch[i], FLAG(n)));
270 	}
271 
272 	/* Set out[8] = P */
273 	MP_CHECKOK(mp_copy(px, &precomp[8][0]));
274 	MP_CHECKOK(mp_copy(py, &precomp[8][1]));
275 
276 	/* Set (tpx, tpy) = 2P */
277 	MP_CHECKOK(group->
278 			   point_dbl(&precomp[8][0], &precomp[8][1], &tpx, &tpy,
279 						 group));
280 
281 	/* Set 3P, 5P, ..., 15P */
282 	for (i = 8; i < 15; i++) {
283 		MP_CHECKOK(group->
284 				   point_add(&precomp[i][0], &precomp[i][1], &tpx, &tpy,
285 							 &precomp[i + 1][0], &precomp[i + 1][1],
286 							 group));
287 	}
288 
289 	/* Set -15P, -13P, ..., -P */
290 	for (i = 0; i < 8; i++) {
291 		MP_CHECKOK(mp_copy(&precomp[15 - i][0], &precomp[i][0]));
292 		MP_CHECKOK(group->meth->
293 				   field_neg(&precomp[15 - i][1], &precomp[i][1],
294 							 group->meth));
295 	}
296 
297 	/* R = inf */
298 	MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, &rz));
299 
300 	orderBitSize = mpl_significant_bits(&group->order);
301 
302 	/* Allocate memory for NAF */
303 #ifdef _KERNEL
304 	naf = (signed char *) kmem_alloc((orderBitSize + 1), FLAG(n));
305 #else
306 	naf = (signed char *) malloc(sizeof(signed char) * (orderBitSize + 1));
307 	if (naf == NULL) {
308 		res = MP_MEM;
309 		goto CLEANUP;
310 	}
311 #endif
312 
313 	/* Compute 5NAF */
314 	ec_compute_wNAF(naf, orderBitSize, n, 5);
315 
316 	/* wNAF method */
317 	for (i = orderBitSize; i >= 0; i--) {
318 		/* R = 2R */
319 		ec_GFp_pt_dbl_jm(rx, ry, &rz, &raz4, rx, ry, &rz,
320 					     &raz4, scratch, group);
321 		if (naf[i] != 0) {
322 			ec_GFp_pt_add_jm_aff(rx, ry, &rz, &raz4,
323 								 &precomp[(naf[i] + 15) / 2][0],
324 								 &precomp[(naf[i] + 15) / 2][1], rx, ry,
325 								 &rz, &raz4, scratch, group);
326 		}
327 	}
328 
329 	/* convert result S to affine coordinates */
330 	MP_CHECKOK(ec_GFp_pt_jac2aff(rx, ry, &rz, rx, ry, group));
331 
332   CLEANUP:
333 	for (i = 0; i < MAX_SCRATCH; i++) {
334 		mp_clear(&scratch[i]);
335 	}
336 	for (i = 0; i < 16; i++) {
337 		mp_clear(&precomp[i][0]);
338 		mp_clear(&precomp[i][1]);
339 	}
340 	mp_clear(&tpx);
341 	mp_clear(&tpy);
342 	mp_clear(&rz);
343 	mp_clear(&raz4);
344 #ifdef _KERNEL
345 	kmem_free(naf, (orderBitSize + 1));
346 #else
347 	free(naf);
348 #endif
349 	return res;
350 }
351