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