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 #include "ecp.h"
46 #include "mpi.h"
47 #include "mplogic.h"
48 #include "mpi-priv.h"
49 #ifndef _KERNEL
50 #include <stdlib.h>
51 #endif
52
53 #define ECP224_DIGITS ECL_CURVE_DIGITS(224)
54
55 /* Fast modular reduction for p224 = 2^224 - 2^96 + 1. a can be r. Uses
56 * algorithm 7 from Brown, Hankerson, Lopez, Menezes. Software
57 * Implementation of the NIST Elliptic Curves over Prime Fields. */
58 mp_err
ec_GFp_nistp224_mod(const mp_int * a,mp_int * r,const GFMethod * meth)59 ec_GFp_nistp224_mod(const mp_int *a, mp_int *r, const GFMethod *meth)
60 {
61 mp_err res = MP_OKAY;
62 mp_size a_used = MP_USED(a);
63
64 int r3b;
65 mp_digit carry;
66 #ifdef ECL_THIRTY_TWO_BIT
67 mp_digit a6a = 0, a6b = 0,
68 a5a = 0, a5b = 0, a4a = 0, a4b = 0, a3a = 0, a3b = 0;
69 mp_digit r0a, r0b, r1a, r1b, r2a, r2b, r3a;
70 #else
71 mp_digit a6 = 0, a5 = 0, a4 = 0, a3b = 0, a5a = 0;
72 mp_digit a6b = 0, a6a_a5b = 0, a5b = 0, a5a_a4b = 0, a4a_a3b = 0;
73 mp_digit r0, r1, r2, r3;
74 #endif
75
76 /* reduction not needed if a is not larger than field size */
77 if (a_used < ECP224_DIGITS) {
78 if (a == r) return MP_OKAY;
79 return mp_copy(a, r);
80 }
81 /* for polynomials larger than twice the field size, use regular
82 * reduction */
83 if (a_used > ECL_CURVE_DIGITS(224*2)) {
84 MP_CHECKOK(mp_mod(a, &meth->irr, r));
85 } else {
86 #ifdef ECL_THIRTY_TWO_BIT
87 /* copy out upper words of a */
88 switch (a_used) {
89 case 14:
90 a6b = MP_DIGIT(a, 13);
91 /* FALLTHROUGH */
92 case 13:
93 a6a = MP_DIGIT(a, 12);
94 /* FALLTHROUGH */
95 case 12:
96 a5b = MP_DIGIT(a, 11);
97 /* FALLTHROUGH */
98 case 11:
99 a5a = MP_DIGIT(a, 10);
100 /* FALLTHROUGH */
101 case 10:
102 a4b = MP_DIGIT(a, 9);
103 /* FALLTHROUGH */
104 case 9:
105 a4a = MP_DIGIT(a, 8);
106 /* FALLTHROUGH */
107 case 8:
108 a3b = MP_DIGIT(a, 7);
109 }
110 r3a = MP_DIGIT(a, 6);
111 r2b= MP_DIGIT(a, 5);
112 r2a= MP_DIGIT(a, 4);
113 r1b = MP_DIGIT(a, 3);
114 r1a = MP_DIGIT(a, 2);
115 r0b = MP_DIGIT(a, 1);
116 r0a = MP_DIGIT(a, 0);
117
118
119 /* implement r = (a3a,a2,a1,a0)
120 +(a5a, a4,a3b, 0)
121 +( 0, a6,a5b, 0)
122 -( 0 0, 0|a6b, a6a|a5b )
123 -( a6b, a6a|a5b, a5a|a4b, a4a|a3b ) */
124 MP_ADD_CARRY (r1b, a3b, r1b, 0, carry);
125 MP_ADD_CARRY (r2a, a4a, r2a, carry, carry);
126 MP_ADD_CARRY (r2b, a4b, r2b, carry, carry);
127 MP_ADD_CARRY (r3a, a5a, r3a, carry, carry);
128 r3b = carry;
129 MP_ADD_CARRY (r1b, a5b, r1b, 0, carry);
130 MP_ADD_CARRY (r2a, a6a, r2a, carry, carry);
131 MP_ADD_CARRY (r2b, a6b, r2b, carry, carry);
132 MP_ADD_CARRY (r3a, 0, r3a, carry, carry);
133 r3b += carry;
134 MP_SUB_BORROW(r0a, a3b, r0a, 0, carry);
135 MP_SUB_BORROW(r0b, a4a, r0b, carry, carry);
136 MP_SUB_BORROW(r1a, a4b, r1a, carry, carry);
137 MP_SUB_BORROW(r1b, a5a, r1b, carry, carry);
138 MP_SUB_BORROW(r2a, a5b, r2a, carry, carry);
139 MP_SUB_BORROW(r2b, a6a, r2b, carry, carry);
140 MP_SUB_BORROW(r3a, a6b, r3a, carry, carry);
141 r3b -= carry;
142 MP_SUB_BORROW(r0a, a5b, r0a, 0, carry);
143 MP_SUB_BORROW(r0b, a6a, r0b, carry, carry);
144 MP_SUB_BORROW(r1a, a6b, r1a, carry, carry);
145 if (carry) {
146 MP_SUB_BORROW(r1b, 0, r1b, carry, carry);
147 MP_SUB_BORROW(r2a, 0, r2a, carry, carry);
148 MP_SUB_BORROW(r2b, 0, r2b, carry, carry);
149 MP_SUB_BORROW(r3a, 0, r3a, carry, carry);
150 r3b -= carry;
151 }
152
153 while (r3b > 0) {
154 int tmp;
155 MP_ADD_CARRY(r1b, r3b, r1b, 0, carry);
156 if (carry) {
157 MP_ADD_CARRY(r2a, 0, r2a, carry, carry);
158 MP_ADD_CARRY(r2b, 0, r2b, carry, carry);
159 MP_ADD_CARRY(r3a, 0, r3a, carry, carry);
160 }
161 tmp = carry;
162 MP_SUB_BORROW(r0a, r3b, r0a, 0, carry);
163 if (carry) {
164 MP_SUB_BORROW(r0b, 0, r0b, carry, carry);
165 MP_SUB_BORROW(r1a, 0, r1a, carry, carry);
166 MP_SUB_BORROW(r1b, 0, r1b, carry, carry);
167 MP_SUB_BORROW(r2a, 0, r2a, carry, carry);
168 MP_SUB_BORROW(r2b, 0, r2b, carry, carry);
169 MP_SUB_BORROW(r3a, 0, r3a, carry, carry);
170 tmp -= carry;
171 }
172 r3b = tmp;
173 }
174
175 while (r3b < 0) {
176 mp_digit maxInt = MP_DIGIT_MAX;
177 MP_ADD_CARRY (r0a, 1, r0a, 0, carry);
178 MP_ADD_CARRY (r0b, 0, r0b, carry, carry);
179 MP_ADD_CARRY (r1a, 0, r1a, carry, carry);
180 MP_ADD_CARRY (r1b, maxInt, r1b, carry, carry);
181 MP_ADD_CARRY (r2a, maxInt, r2a, carry, carry);
182 MP_ADD_CARRY (r2b, maxInt, r2b, carry, carry);
183 MP_ADD_CARRY (r3a, maxInt, r3a, carry, carry);
184 r3b += carry;
185 }
186 /* check for final reduction */
187 /* now the only way we are over is if the top 4 words are all ones */
188 if ((r3a == MP_DIGIT_MAX) && (r2b == MP_DIGIT_MAX)
189 && (r2a == MP_DIGIT_MAX) && (r1b == MP_DIGIT_MAX) &&
190 ((r1a != 0) || (r0b != 0) || (r0a != 0)) ) {
191 /* one last subraction */
192 MP_SUB_BORROW(r0a, 1, r0a, 0, carry);
193 MP_SUB_BORROW(r0b, 0, r0b, carry, carry);
194 MP_SUB_BORROW(r1a, 0, r1a, carry, carry);
195 r1b = r2a = r2b = r3a = 0;
196 }
197
198
199 if (a != r) {
200 MP_CHECKOK(s_mp_pad(r, 7));
201 }
202 /* set the lower words of r */
203 MP_SIGN(r) = MP_ZPOS;
204 MP_USED(r) = 7;
205 MP_DIGIT(r, 6) = r3a;
206 MP_DIGIT(r, 5) = r2b;
207 MP_DIGIT(r, 4) = r2a;
208 MP_DIGIT(r, 3) = r1b;
209 MP_DIGIT(r, 2) = r1a;
210 MP_DIGIT(r, 1) = r0b;
211 MP_DIGIT(r, 0) = r0a;
212 #else
213 /* copy out upper words of a */
214 switch (a_used) {
215 case 7:
216 a6 = MP_DIGIT(a, 6);
217 a6b = a6 >> 32;
218 a6a_a5b = a6 << 32;
219 /* FALLTHROUGH */
220 case 6:
221 a5 = MP_DIGIT(a, 5);
222 a5b = a5 >> 32;
223 a6a_a5b |= a5b;
224 a5b = a5b << 32;
225 a5a_a4b = a5 << 32;
226 a5a = a5 & 0xffffffff;
227 /* FALLTHROUGH */
228 case 5:
229 a4 = MP_DIGIT(a, 4);
230 a5a_a4b |= a4 >> 32;
231 a4a_a3b = a4 << 32;
232 /* FALLTHROUGH */
233 case 4:
234 a3b = MP_DIGIT(a, 3) >> 32;
235 a4a_a3b |= a3b;
236 a3b = a3b << 32;
237 }
238
239 r3 = MP_DIGIT(a, 3) & 0xffffffff;
240 r2 = MP_DIGIT(a, 2);
241 r1 = MP_DIGIT(a, 1);
242 r0 = MP_DIGIT(a, 0);
243
244 /* implement r = (a3a,a2,a1,a0)
245 +(a5a, a4,a3b, 0)
246 +( 0, a6,a5b, 0)
247 -( 0 0, 0|a6b, a6a|a5b )
248 -( a6b, a6a|a5b, a5a|a4b, a4a|a3b ) */
249 MP_ADD_CARRY (r1, a3b, r1, 0, carry);
250 MP_ADD_CARRY (r2, a4 , r2, carry, carry);
251 MP_ADD_CARRY (r3, a5a, r3, carry, carry);
252 MP_ADD_CARRY (r1, a5b, r1, 0, carry);
253 MP_ADD_CARRY (r2, a6 , r2, carry, carry);
254 MP_ADD_CARRY (r3, 0, r3, carry, carry);
255
256 MP_SUB_BORROW(r0, a4a_a3b, r0, 0, carry);
257 MP_SUB_BORROW(r1, a5a_a4b, r1, carry, carry);
258 MP_SUB_BORROW(r2, a6a_a5b, r2, carry, carry);
259 MP_SUB_BORROW(r3, a6b , r3, carry, carry);
260 MP_SUB_BORROW(r0, a6a_a5b, r0, 0, carry);
261 MP_SUB_BORROW(r1, a6b , r1, carry, carry);
262 if (carry) {
263 MP_SUB_BORROW(r2, 0, r2, carry, carry);
264 MP_SUB_BORROW(r3, 0, r3, carry, carry);
265 }
266
267
268 /* if the value is negative, r3 has a 2's complement
269 * high value */
270 r3b = (int)(r3 >>32);
271 while (r3b > 0) {
272 r3 &= 0xffffffff;
273 MP_ADD_CARRY(r1,((mp_digit)r3b) << 32, r1, 0, carry);
274 if (carry) {
275 MP_ADD_CARRY(r2, 0, r2, carry, carry);
276 MP_ADD_CARRY(r3, 0, r3, carry, carry);
277 }
278 MP_SUB_BORROW(r0, r3b, r0, 0, carry);
279 if (carry) {
280 MP_SUB_BORROW(r1, 0, r1, carry, carry);
281 MP_SUB_BORROW(r2, 0, r2, carry, carry);
282 MP_SUB_BORROW(r3, 0, r3, carry, carry);
283 }
284 r3b = (int)(r3 >>32);
285 }
286
287 while (r3b < 0) {
288 MP_ADD_CARRY (r0, 1, r0, 0, carry);
289 MP_ADD_CARRY (r1, MP_DIGIT_MAX <<32, r1, carry, carry);
290 MP_ADD_CARRY (r2, MP_DIGIT_MAX, r2, carry, carry);
291 MP_ADD_CARRY (r3, MP_DIGIT_MAX >> 32, r3, carry, carry);
292 r3b = (int)(r3 >>32);
293 }
294 /* check for final reduction */
295 /* now the only way we are over is if the top 4 words are all ones */
296 if ((r3 == (MP_DIGIT_MAX >> 32)) && (r2 == MP_DIGIT_MAX)
297 && ((r1 & MP_DIGIT_MAX << 32)== MP_DIGIT_MAX << 32) &&
298 ((r1 != MP_DIGIT_MAX << 32 ) || (r0 != 0)) ) {
299 /* one last subraction */
300 MP_SUB_BORROW(r0, 1, r0, 0, carry);
301 MP_SUB_BORROW(r1, 0, r1, carry, carry);
302 r2 = r3 = 0;
303 }
304
305
306 if (a != r) {
307 MP_CHECKOK(s_mp_pad(r, 4));
308 }
309 /* set the lower words of r */
310 MP_SIGN(r) = MP_ZPOS;
311 MP_USED(r) = 4;
312 MP_DIGIT(r, 3) = r3;
313 MP_DIGIT(r, 2) = r2;
314 MP_DIGIT(r, 1) = r1;
315 MP_DIGIT(r, 0) = r0;
316 #endif
317 }
318
319 CLEANUP:
320 return res;
321 }
322
323 /* Compute the square of polynomial a, reduce modulo p224. Store the
324 * result in r. r could be a. Uses optimized modular reduction for p224.
325 */
326 mp_err
ec_GFp_nistp224_sqr(const mp_int * a,mp_int * r,const GFMethod * meth)327 ec_GFp_nistp224_sqr(const mp_int *a, mp_int *r, const GFMethod *meth)
328 {
329 mp_err res = MP_OKAY;
330
331 MP_CHECKOK(mp_sqr(a, r));
332 MP_CHECKOK(ec_GFp_nistp224_mod(r, r, meth));
333 CLEANUP:
334 return res;
335 }
336
337 /* Compute the product of two polynomials a and b, reduce modulo p224.
338 * Store the result in r. r could be a or b; a could be b. Uses
339 * optimized modular reduction for p224. */
340 mp_err
ec_GFp_nistp224_mul(const mp_int * a,const mp_int * b,mp_int * r,const GFMethod * meth)341 ec_GFp_nistp224_mul(const mp_int *a, const mp_int *b, mp_int *r,
342 const GFMethod *meth)
343 {
344 mp_err res = MP_OKAY;
345
346 MP_CHECKOK(mp_mul(a, b, r));
347 MP_CHECKOK(ec_GFp_nistp224_mod(r, r, meth));
348 CLEANUP:
349 return res;
350 }
351
352 /* Divides two field elements. If a is NULL, then returns the inverse of
353 * b. */
354 mp_err
ec_GFp_nistp224_div(const mp_int * a,const mp_int * b,mp_int * r,const GFMethod * meth)355 ec_GFp_nistp224_div(const mp_int *a, const mp_int *b, mp_int *r,
356 const GFMethod *meth)
357 {
358 mp_err res = MP_OKAY;
359 mp_int t;
360
361 /* If a is NULL, then return the inverse of b, otherwise return a/b. */
362 if (a == NULL) {
363 return mp_invmod(b, &meth->irr, r);
364 } else {
365 /* MPI doesn't support divmod, so we implement it using invmod and
366 * mulmod. */
367 MP_CHECKOK(mp_init(&t, FLAG(b)));
368 MP_CHECKOK(mp_invmod(b, &meth->irr, &t));
369 MP_CHECKOK(mp_mul(a, &t, r));
370 MP_CHECKOK(ec_GFp_nistp224_mod(r, r, meth));
371 CLEANUP:
372 mp_clear(&t);
373 return res;
374 }
375 }
376
377 /* Wire in fast field arithmetic and precomputation of base point for
378 * named curves. */
379 mp_err
ec_group_set_gfp224(ECGroup * group,ECCurveName name)380 ec_group_set_gfp224(ECGroup *group, ECCurveName name)
381 {
382 if (name == ECCurve_NIST_P224) {
383 group->meth->field_mod = &ec_GFp_nistp224_mod;
384 group->meth->field_mul = &ec_GFp_nistp224_mul;
385 group->meth->field_sqr = &ec_GFp_nistp224_sqr;
386 group->meth->field_div = &ec_GFp_nistp224_div;
387 }
388 return MP_OKAY;
389 }
390