xref: /illumos-gate/usr/src/common/crypto/ecc/ecp_jm.c (revision c40a6cd785e883b3f052b122c332e21174fc1871)
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 	/* C = A - px, D = B - py */
176 	MP_CHECKOK(group->meth->field_sub(A, px, C, group->meth));
177 	MP_CHECKOK(group->meth->field_sub(B, py, D, group->meth));
178 
179 	/* C2 = C^2, C3 = C^3 */
180 	MP_CHECKOK(group->meth->field_sqr(C, C2, group->meth));
181 	MP_CHECKOK(group->meth->field_mul(C, C2, C3, group->meth));
182 
183 	/* rz = pz * C */
184 	MP_CHECKOK(group->meth->field_mul(pz, C, rz, group->meth));
185 
186 	/* C = px * C^2 */
187 	MP_CHECKOK(group->meth->field_mul(px, C2, C, group->meth));
188 	/* A = D^2 */
189 	MP_CHECKOK(group->meth->field_sqr(D, A, group->meth));
190 
191 	/* rx = D^2 - (C^3 + 2 * (px * C^2)) */
192 	MP_CHECKOK(group->meth->field_add(C, C, rx, group->meth));
193 	MP_CHECKOK(group->meth->field_add(C3, rx, rx, group->meth));
194 	MP_CHECKOK(group->meth->field_sub(A, rx, rx, group->meth));
195 
196 	/* C3 = py * C^3 */
197 	MP_CHECKOK(group->meth->field_mul(py, C3, C3, group->meth));
198 
199 	/* ry = D * (px * C^2 - rx) - py * C^3 */
200 	MP_CHECKOK(group->meth->field_sub(C, rx, ry, group->meth));
201 	MP_CHECKOK(group->meth->field_mul(D, ry, ry, group->meth));
202 	MP_CHECKOK(group->meth->field_sub(ry, C3, ry, group->meth));
203 
204 	/* raz4 = a * rz^4 */
205 	MP_CHECKOK(group->meth->field_sqr(rz, raz4, group->meth));
206 	MP_CHECKOK(group->meth->field_sqr(raz4, raz4, group->meth));
207 	MP_CHECKOK(group->meth->
208 			   field_mul(raz4, &group->curvea, raz4, group->meth));
209 CLEANUP:
210 	return res;
211 }
212 
213 /* Computes R = nP where R is (rx, ry) and P is the base point. Elliptic
214  * curve points P and R can be identical. Uses mixed Modified-Jacobian
215  * co-ordinates for doubling and Chudnovsky Jacobian coordinates for
216  * additions. Assumes input is already field-encoded using field_enc, and
217  * returns output that is still field-encoded. Uses 5-bit window NAF
218  * method (algorithm 11) for scalar-point multiplication from Brown,
219  * Hankerson, Lopez, Menezes. Software Implementation of the NIST Elliptic
220  * Curves Over Prime Fields. */
221 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)222 ec_GFp_pt_mul_jm_wNAF(const mp_int *n, const mp_int *px, const mp_int *py,
223 					  mp_int *rx, mp_int *ry, const ECGroup *group)
224 {
225 	mp_err res = MP_OKAY;
226 	mp_int precomp[16][2], rz, tpx, tpy;
227 	mp_int raz4;
228 	mp_int scratch[MAX_SCRATCH];
229 	signed char *naf = NULL;
230 	int i, orderBitSize;
231 
232 	MP_DIGITS(&rz) = 0;
233 	MP_DIGITS(&raz4) = 0;
234 	MP_DIGITS(&tpx) = 0;
235 	MP_DIGITS(&tpy) = 0;
236 	for (i = 0; i < 16; i++) {
237 		MP_DIGITS(&precomp[i][0]) = 0;
238 		MP_DIGITS(&precomp[i][1]) = 0;
239 	}
240 	for (i = 0; i < MAX_SCRATCH; i++) {
241 		MP_DIGITS(&scratch[i]) = 0;
242 	}
243 
244 	ARGCHK(group != NULL, MP_BADARG);
245 	ARGCHK((n != NULL) && (px != NULL) && (py != NULL), MP_BADARG);
246 
247 	/* initialize precomputation table */
248 	MP_CHECKOK(mp_init(&tpx, FLAG(n)));
249 	MP_CHECKOK(mp_init(&tpy, FLAG(n)));;
250 	MP_CHECKOK(mp_init(&rz, FLAG(n)));
251 	MP_CHECKOK(mp_init(&raz4, FLAG(n)));
252 
253 	for (i = 0; i < 16; i++) {
254 		MP_CHECKOK(mp_init(&precomp[i][0], FLAG(n)));
255 		MP_CHECKOK(mp_init(&precomp[i][1], FLAG(n)));
256 	}
257 	for (i = 0; i < MAX_SCRATCH; i++) {
258 		MP_CHECKOK(mp_init(&scratch[i], FLAG(n)));
259 	}
260 
261 	/* Set out[8] = P */
262 	MP_CHECKOK(mp_copy(px, &precomp[8][0]));
263 	MP_CHECKOK(mp_copy(py, &precomp[8][1]));
264 
265 	/* Set (tpx, tpy) = 2P */
266 	MP_CHECKOK(group->
267 			   point_dbl(&precomp[8][0], &precomp[8][1], &tpx, &tpy,
268 						 group));
269 
270 	/* Set 3P, 5P, ..., 15P */
271 	for (i = 8; i < 15; i++) {
272 		MP_CHECKOK(group->
273 				   point_add(&precomp[i][0], &precomp[i][1], &tpx, &tpy,
274 							 &precomp[i + 1][0], &precomp[i + 1][1],
275 							 group));
276 	}
277 
278 	/* Set -15P, -13P, ..., -P */
279 	for (i = 0; i < 8; i++) {
280 		MP_CHECKOK(mp_copy(&precomp[15 - i][0], &precomp[i][0]));
281 		MP_CHECKOK(group->meth->
282 				   field_neg(&precomp[15 - i][1], &precomp[i][1],
283 							 group->meth));
284 	}
285 
286 	/* R = inf */
287 	MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, &rz));
288 
289 	orderBitSize = mpl_significant_bits(&group->order);
290 
291 	/* Allocate memory for NAF */
292 #ifdef _KERNEL
293 	naf = (signed char *) kmem_alloc((orderBitSize + 1), FLAG(n));
294 #else
295 	naf = (signed char *) malloc(sizeof(signed char) * (orderBitSize + 1));
296 	if (naf == NULL) {
297 		res = MP_MEM;
298 		goto CLEANUP;
299 	}
300 #endif
301 
302 	/* Compute 5NAF */
303 	ec_compute_wNAF(naf, orderBitSize, n, 5);
304 
305 	/* wNAF method */
306 	for (i = orderBitSize; i >= 0; i--) {
307 		/* R = 2R */
308 		ec_GFp_pt_dbl_jm(rx, ry, &rz, &raz4, rx, ry, &rz,
309 					     &raz4, scratch, group);
310 		if (naf[i] != 0) {
311 			ec_GFp_pt_add_jm_aff(rx, ry, &rz, &raz4,
312 								 &precomp[(naf[i] + 15) / 2][0],
313 								 &precomp[(naf[i] + 15) / 2][1], rx, ry,
314 								 &rz, &raz4, scratch, group);
315 		}
316 	}
317 
318 	/* convert result S to affine coordinates */
319 	MP_CHECKOK(ec_GFp_pt_jac2aff(rx, ry, &rz, rx, ry, group));
320 
321   CLEANUP:
322 	for (i = 0; i < MAX_SCRATCH; i++) {
323 		mp_clear(&scratch[i]);
324 	}
325 	for (i = 0; i < 16; i++) {
326 		mp_clear(&precomp[i][0]);
327 		mp_clear(&precomp[i][1]);
328 	}
329 	mp_clear(&tpx);
330 	mp_clear(&tpy);
331 	mp_clear(&rz);
332 	mp_clear(&raz4);
333 #ifdef _KERNEL
334 	kmem_free(naf, (orderBitSize + 1));
335 #else
336 	free(naf);
337 #endif
338 	return res;
339 }
340