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 * Douglas Stebila <douglas@stebila.ca>, 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 "mpi.h"
49 #include "mplogic.h"
50 #include "mpi-priv.h"
51 #ifndef _KERNEL
52 #include <stdlib.h>
53 #endif
54
55 #define ECP224_DIGITS ECL_CURVE_DIGITS(224)
56
57 /* Fast modular reduction for p224 = 2^224 - 2^96 + 1. a can be r. Uses
58 * algorithm 7 from Brown, Hankerson, Lopez, Menezes. Software
59 * Implementation of the NIST Elliptic Curves over Prime Fields. */
60 mp_err
ec_GFp_nistp224_mod(const mp_int * a,mp_int * r,const GFMethod * meth)61 ec_GFp_nistp224_mod(const mp_int *a, mp_int *r, const GFMethod *meth)
62 {
63 mp_err res = MP_OKAY;
64 mp_size a_used = MP_USED(a);
65
66 int r3b;
67 mp_digit carry;
68 #ifdef ECL_THIRTY_TWO_BIT
69 mp_digit a6a = 0, a6b = 0,
70 a5a = 0, a5b = 0, a4a = 0, a4b = 0, a3a = 0, a3b = 0;
71 mp_digit r0a, r0b, r1a, r1b, r2a, r2b, r3a;
72 #else
73 mp_digit a6 = 0, a5 = 0, a4 = 0, a3b = 0, a5a = 0;
74 mp_digit a6b = 0, a6a_a5b = 0, a5b = 0, a5a_a4b = 0, a4a_a3b = 0;
75 mp_digit r0, r1, r2, r3;
76 #endif
77
78 /* reduction not needed if a is not larger than field size */
79 if (a_used < ECP224_DIGITS) {
80 if (a == r) return MP_OKAY;
81 return mp_copy(a, r);
82 }
83 /* for polynomials larger than twice the field size, use regular
84 * reduction */
85 if (a_used > ECL_CURVE_DIGITS(224*2)) {
86 MP_CHECKOK(mp_mod(a, &meth->irr, r));
87 } else {
88 #ifdef ECL_THIRTY_TWO_BIT
89 /* copy out upper words of a */
90 switch (a_used) {
91 case 14:
92 a6b = MP_DIGIT(a, 13);
93 case 13:
94 a6a = MP_DIGIT(a, 12);
95 case 12:
96 a5b = MP_DIGIT(a, 11);
97 case 11:
98 a5a = MP_DIGIT(a, 10);
99 case 10:
100 a4b = MP_DIGIT(a, 9);
101 case 9:
102 a4a = MP_DIGIT(a, 8);
103 case 8:
104 a3b = MP_DIGIT(a, 7);
105 }
106 r3a = MP_DIGIT(a, 6);
107 r2b= MP_DIGIT(a, 5);
108 r2a= MP_DIGIT(a, 4);
109 r1b = MP_DIGIT(a, 3);
110 r1a = MP_DIGIT(a, 2);
111 r0b = MP_DIGIT(a, 1);
112 r0a = MP_DIGIT(a, 0);
113
114
115 /* implement r = (a3a,a2,a1,a0)
116 +(a5a, a4,a3b, 0)
117 +( 0, a6,a5b, 0)
118 -( 0 0, 0|a6b, a6a|a5b )
119 -( a6b, a6a|a5b, a5a|a4b, a4a|a3b ) */
120 MP_ADD_CARRY (r1b, a3b, r1b, 0, carry);
121 MP_ADD_CARRY (r2a, a4a, r2a, carry, carry);
122 MP_ADD_CARRY (r2b, a4b, r2b, carry, carry);
123 MP_ADD_CARRY (r3a, a5a, r3a, carry, carry);
124 r3b = carry;
125 MP_ADD_CARRY (r1b, a5b, r1b, 0, carry);
126 MP_ADD_CARRY (r2a, a6a, r2a, carry, carry);
127 MP_ADD_CARRY (r2b, a6b, r2b, carry, carry);
128 MP_ADD_CARRY (r3a, 0, r3a, carry, carry);
129 r3b += carry;
130 MP_SUB_BORROW(r0a, a3b, r0a, 0, carry);
131 MP_SUB_BORROW(r0b, a4a, r0b, carry, carry);
132 MP_SUB_BORROW(r1a, a4b, r1a, carry, carry);
133 MP_SUB_BORROW(r1b, a5a, r1b, carry, carry);
134 MP_SUB_BORROW(r2a, a5b, r2a, carry, carry);
135 MP_SUB_BORROW(r2b, a6a, r2b, carry, carry);
136 MP_SUB_BORROW(r3a, a6b, r3a, carry, carry);
137 r3b -= carry;
138 MP_SUB_BORROW(r0a, a5b, r0a, 0, carry);
139 MP_SUB_BORROW(r0b, a6a, r0b, carry, carry);
140 MP_SUB_BORROW(r1a, a6b, r1a, carry, carry);
141 if (carry) {
142 MP_SUB_BORROW(r1b, 0, r1b, carry, carry);
143 MP_SUB_BORROW(r2a, 0, r2a, carry, carry);
144 MP_SUB_BORROW(r2b, 0, r2b, carry, carry);
145 MP_SUB_BORROW(r3a, 0, r3a, carry, carry);
146 r3b -= carry;
147 }
148
149 while (r3b > 0) {
150 int tmp;
151 MP_ADD_CARRY(r1b, r3b, r1b, 0, carry);
152 if (carry) {
153 MP_ADD_CARRY(r2a, 0, r2a, carry, carry);
154 MP_ADD_CARRY(r2b, 0, r2b, carry, carry);
155 MP_ADD_CARRY(r3a, 0, r3a, carry, carry);
156 }
157 tmp = carry;
158 MP_SUB_BORROW(r0a, r3b, r0a, 0, carry);
159 if (carry) {
160 MP_SUB_BORROW(r0b, 0, r0b, carry, carry);
161 MP_SUB_BORROW(r1a, 0, r1a, carry, carry);
162 MP_SUB_BORROW(r1b, 0, r1b, carry, carry);
163 MP_SUB_BORROW(r2a, 0, r2a, carry, carry);
164 MP_SUB_BORROW(r2b, 0, r2b, carry, carry);
165 MP_SUB_BORROW(r3a, 0, r3a, carry, carry);
166 tmp -= carry;
167 }
168 r3b = tmp;
169 }
170
171 while (r3b < 0) {
172 mp_digit maxInt = MP_DIGIT_MAX;
173 MP_ADD_CARRY (r0a, 1, r0a, 0, carry);
174 MP_ADD_CARRY (r0b, 0, r0b, carry, carry);
175 MP_ADD_CARRY (r1a, 0, r1a, carry, carry);
176 MP_ADD_CARRY (r1b, maxInt, r1b, carry, carry);
177 MP_ADD_CARRY (r2a, maxInt, r2a, carry, carry);
178 MP_ADD_CARRY (r2b, maxInt, r2b, carry, carry);
179 MP_ADD_CARRY (r3a, maxInt, r3a, carry, carry);
180 r3b += carry;
181 }
182 /* check for final reduction */
183 /* now the only way we are over is if the top 4 words are all ones */
184 if ((r3a == MP_DIGIT_MAX) && (r2b == MP_DIGIT_MAX)
185 && (r2a == MP_DIGIT_MAX) && (r1b == MP_DIGIT_MAX) &&
186 ((r1a != 0) || (r0b != 0) || (r0a != 0)) ) {
187 /* one last subraction */
188 MP_SUB_BORROW(r0a, 1, r0a, 0, carry);
189 MP_SUB_BORROW(r0b, 0, r0b, carry, carry);
190 MP_SUB_BORROW(r1a, 0, r1a, carry, carry);
191 r1b = r2a = r2b = r3a = 0;
192 }
193
194
195 if (a != r) {
196 MP_CHECKOK(s_mp_pad(r, 7));
197 }
198 /* set the lower words of r */
199 MP_SIGN(r) = MP_ZPOS;
200 MP_USED(r) = 7;
201 MP_DIGIT(r, 6) = r3a;
202 MP_DIGIT(r, 5) = r2b;
203 MP_DIGIT(r, 4) = r2a;
204 MP_DIGIT(r, 3) = r1b;
205 MP_DIGIT(r, 2) = r1a;
206 MP_DIGIT(r, 1) = r0b;
207 MP_DIGIT(r, 0) = r0a;
208 #else
209 /* copy out upper words of a */
210 switch (a_used) {
211 case 7:
212 a6 = MP_DIGIT(a, 6);
213 a6b = a6 >> 32;
214 a6a_a5b = a6 << 32;
215 case 6:
216 a5 = MP_DIGIT(a, 5);
217 a5b = a5 >> 32;
218 a6a_a5b |= a5b;
219 a5b = a5b << 32;
220 a5a_a4b = a5 << 32;
221 a5a = a5 & 0xffffffff;
222 case 5:
223 a4 = MP_DIGIT(a, 4);
224 a5a_a4b |= a4 >> 32;
225 a4a_a3b = a4 << 32;
226 case 4:
227 a3b = MP_DIGIT(a, 3) >> 32;
228 a4a_a3b |= a3b;
229 a3b = a3b << 32;
230 }
231
232 r3 = MP_DIGIT(a, 3) & 0xffffffff;
233 r2 = MP_DIGIT(a, 2);
234 r1 = MP_DIGIT(a, 1);
235 r0 = MP_DIGIT(a, 0);
236
237 /* implement r = (a3a,a2,a1,a0)
238 +(a5a, a4,a3b, 0)
239 +( 0, a6,a5b, 0)
240 -( 0 0, 0|a6b, a6a|a5b )
241 -( a6b, a6a|a5b, a5a|a4b, a4a|a3b ) */
242 MP_ADD_CARRY (r1, a3b, r1, 0, carry);
243 MP_ADD_CARRY (r2, a4 , r2, carry, carry);
244 MP_ADD_CARRY (r3, a5a, r3, carry, carry);
245 MP_ADD_CARRY (r1, a5b, r1, 0, carry);
246 MP_ADD_CARRY (r2, a6 , r2, carry, carry);
247 MP_ADD_CARRY (r3, 0, r3, carry, carry);
248
249 MP_SUB_BORROW(r0, a4a_a3b, r0, 0, carry);
250 MP_SUB_BORROW(r1, a5a_a4b, r1, carry, carry);
251 MP_SUB_BORROW(r2, a6a_a5b, r2, carry, carry);
252 MP_SUB_BORROW(r3, a6b , r3, carry, carry);
253 MP_SUB_BORROW(r0, a6a_a5b, r0, 0, carry);
254 MP_SUB_BORROW(r1, a6b , r1, carry, carry);
255 if (carry) {
256 MP_SUB_BORROW(r2, 0, r2, carry, carry);
257 MP_SUB_BORROW(r3, 0, r3, carry, carry);
258 }
259
260
261 /* if the value is negative, r3 has a 2's complement
262 * high value */
263 r3b = (int)(r3 >>32);
264 while (r3b > 0) {
265 r3 &= 0xffffffff;
266 MP_ADD_CARRY(r1,((mp_digit)r3b) << 32, r1, 0, carry);
267 if (carry) {
268 MP_ADD_CARRY(r2, 0, r2, carry, carry);
269 MP_ADD_CARRY(r3, 0, r3, carry, carry);
270 }
271 MP_SUB_BORROW(r0, r3b, r0, 0, carry);
272 if (carry) {
273 MP_SUB_BORROW(r1, 0, r1, carry, carry);
274 MP_SUB_BORROW(r2, 0, r2, carry, carry);
275 MP_SUB_BORROW(r3, 0, r3, carry, carry);
276 }
277 r3b = (int)(r3 >>32);
278 }
279
280 while (r3b < 0) {
281 MP_ADD_CARRY (r0, 1, r0, 0, carry);
282 MP_ADD_CARRY (r1, MP_DIGIT_MAX <<32, r1, carry, carry);
283 MP_ADD_CARRY (r2, MP_DIGIT_MAX, r2, carry, carry);
284 MP_ADD_CARRY (r3, MP_DIGIT_MAX >> 32, r3, carry, carry);
285 r3b = (int)(r3 >>32);
286 }
287 /* check for final reduction */
288 /* now the only way we are over is if the top 4 words are all ones */
289 if ((r3 == (MP_DIGIT_MAX >> 32)) && (r2 == MP_DIGIT_MAX)
290 && ((r1 & MP_DIGIT_MAX << 32)== MP_DIGIT_MAX << 32) &&
291 ((r1 != MP_DIGIT_MAX << 32 ) || (r0 != 0)) ) {
292 /* one last subraction */
293 MP_SUB_BORROW(r0, 1, r0, 0, carry);
294 MP_SUB_BORROW(r1, 0, r1, carry, carry);
295 r2 = r3 = 0;
296 }
297
298
299 if (a != r) {
300 MP_CHECKOK(s_mp_pad(r, 4));
301 }
302 /* set the lower words of r */
303 MP_SIGN(r) = MP_ZPOS;
304 MP_USED(r) = 4;
305 MP_DIGIT(r, 3) = r3;
306 MP_DIGIT(r, 2) = r2;
307 MP_DIGIT(r, 1) = r1;
308 MP_DIGIT(r, 0) = r0;
309 #endif
310 }
311
312 CLEANUP:
313 return res;
314 }
315
316 /* Compute the square of polynomial a, reduce modulo p224. Store the
317 * result in r. r could be a. Uses optimized modular reduction for p224.
318 */
319 mp_err
ec_GFp_nistp224_sqr(const mp_int * a,mp_int * r,const GFMethod * meth)320 ec_GFp_nistp224_sqr(const mp_int *a, mp_int *r, const GFMethod *meth)
321 {
322 mp_err res = MP_OKAY;
323
324 MP_CHECKOK(mp_sqr(a, r));
325 MP_CHECKOK(ec_GFp_nistp224_mod(r, r, meth));
326 CLEANUP:
327 return res;
328 }
329
330 /* Compute the product of two polynomials a and b, reduce modulo p224.
331 * Store the result in r. r could be a or b; a could be b. Uses
332 * optimized modular reduction for p224. */
333 mp_err
ec_GFp_nistp224_mul(const mp_int * a,const mp_int * b,mp_int * r,const GFMethod * meth)334 ec_GFp_nistp224_mul(const mp_int *a, const mp_int *b, mp_int *r,
335 const GFMethod *meth)
336 {
337 mp_err res = MP_OKAY;
338
339 MP_CHECKOK(mp_mul(a, b, r));
340 MP_CHECKOK(ec_GFp_nistp224_mod(r, r, meth));
341 CLEANUP:
342 return res;
343 }
344
345 /* Divides two field elements. If a is NULL, then returns the inverse of
346 * b. */
347 mp_err
ec_GFp_nistp224_div(const mp_int * a,const mp_int * b,mp_int * r,const GFMethod * meth)348 ec_GFp_nistp224_div(const mp_int *a, const mp_int *b, mp_int *r,
349 const GFMethod *meth)
350 {
351 mp_err res = MP_OKAY;
352 mp_int t;
353
354 /* If a is NULL, then return the inverse of b, otherwise return a/b. */
355 if (a == NULL) {
356 return mp_invmod(b, &meth->irr, r);
357 } else {
358 /* MPI doesn't support divmod, so we implement it using invmod and
359 * mulmod. */
360 MP_CHECKOK(mp_init(&t, FLAG(b)));
361 MP_CHECKOK(mp_invmod(b, &meth->irr, &t));
362 MP_CHECKOK(mp_mul(a, &t, r));
363 MP_CHECKOK(ec_GFp_nistp224_mod(r, r, meth));
364 CLEANUP:
365 mp_clear(&t);
366 return res;
367 }
368 }
369
370 /* Wire in fast field arithmetic and precomputation of base point for
371 * named curves. */
372 mp_err
ec_group_set_gfp224(ECGroup * group,ECCurveName name)373 ec_group_set_gfp224(ECGroup *group, ECCurveName name)
374 {
375 if (name == ECCurve_NIST_P224) {
376 group->meth->field_mod = &ec_GFp_nistp224_mod;
377 group->meth->field_mul = &ec_GFp_nistp224_mul;
378 group->meth->field_sqr = &ec_GFp_nistp224_sqr;
379 group->meth->field_div = &ec_GFp_nistp224_div;
380 }
381 return MP_OKAY;
382 }
383