xref: /titanic_51/usr/src/common/crypto/ecc/ecp_224.c (revision 37714ae43602c675f9dc59b070bfdf9fa702872c)
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
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
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
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
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
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