xref: /illumos-gate/usr/src/common/crypto/ecc/ecp_256.c (revision 38a641c5)
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>
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 /* Fast modular reduction for p256 = 2^256 - 2^224 + 2^192+ 2^96 - 1.  a can be r.
54  * Uses algorithm 2.29 from Hankerson, Menezes, Vanstone. Guide to
55  * Elliptic Curve Cryptography. */
56 mp_err
ec_GFp_nistp256_mod(const mp_int * a,mp_int * r,const GFMethod * meth)57 ec_GFp_nistp256_mod(const mp_int *a, mp_int *r, const GFMethod *meth)
58 {
59 	mp_err res = MP_OKAY;
60 	mp_size a_used = MP_USED(a);
61 	int a_bits = mpl_significant_bits(a);
62 	mp_digit carry;
63 
64 #ifdef ECL_THIRTY_TWO_BIT
65 	mp_digit a8=0, a9=0, a10=0, a11=0, a12=0, a13=0, a14=0, a15=0;
66 	mp_digit r0, r1, r2, r3, r4, r5, r6, r7;
67 	int r8; /* must be a signed value ! */
68 #else
69 	mp_digit a4=0, a5=0, a6=0, a7=0;
70 	mp_digit a4h, a4l, a5h, a5l, a6h, a6l, a7h, a7l;
71 	mp_digit r0, r1, r2, r3;
72 	int r4; /* must be a signed value ! */
73 #endif
74 	/* for polynomials larger than twice the field size
75 	 * use regular reduction */
76 	if (a_bits < 256) {
77 		if (a == r) return MP_OKAY;
78 		return mp_copy(a,r);
79 	}
80 	if (a_bits > 512)  {
81 		MP_CHECKOK(mp_mod(a, &meth->irr, r));
82 	} else {
83 
84 #ifdef ECL_THIRTY_TWO_BIT
85 		switch (a_used) {
86 		case 16:
87 			a15 = MP_DIGIT(a,15);
88 			/* FALLTHROUGH */
89 		case 15:
90 			a14 = MP_DIGIT(a,14);
91 			/* FALLTHROUGH */
92 		case 14:
93 			a13 = MP_DIGIT(a,13);
94 			/* FALLTHROUGH */
95 		case 13:
96 			a12 = MP_DIGIT(a,12);
97 			/* FALLTHROUGH */
98 		case 12:
99 			a11 = MP_DIGIT(a,11);
100 			/* FALLTHROUGH */
101 		case 11:
102 			a10 = MP_DIGIT(a,10);
103 			/* FALLTHROUGH */
104 		case 10:
105 			a9 = MP_DIGIT(a,9);
106 			/* FALLTHROUGH */
107 		case 9:
108 			a8 = MP_DIGIT(a,8);
109 		}
110 
111 		r0 = MP_DIGIT(a,0);
112 		r1 = MP_DIGIT(a,1);
113 		r2 = MP_DIGIT(a,2);
114 		r3 = MP_DIGIT(a,3);
115 		r4 = MP_DIGIT(a,4);
116 		r5 = MP_DIGIT(a,5);
117 		r6 = MP_DIGIT(a,6);
118 		r7 = MP_DIGIT(a,7);
119 
120 		/* sum 1 */
121 		MP_ADD_CARRY(r3, a11, r3, 0,     carry);
122 		MP_ADD_CARRY(r4, a12, r4, carry, carry);
123 		MP_ADD_CARRY(r5, a13, r5, carry, carry);
124 		MP_ADD_CARRY(r6, a14, r6, carry, carry);
125 		MP_ADD_CARRY(r7, a15, r7, carry, carry);
126 		r8 = carry;
127 		MP_ADD_CARRY(r3, a11, r3, 0,     carry);
128 		MP_ADD_CARRY(r4, a12, r4, carry, carry);
129 		MP_ADD_CARRY(r5, a13, r5, carry, carry);
130 		MP_ADD_CARRY(r6, a14, r6, carry, carry);
131 		MP_ADD_CARRY(r7, a15, r7, carry, carry);
132 		r8 += carry;
133 		/* sum 2 */
134 		MP_ADD_CARRY(r3, a12, r3, 0,     carry);
135 		MP_ADD_CARRY(r4, a13, r4, carry, carry);
136 		MP_ADD_CARRY(r5, a14, r5, carry, carry);
137 		MP_ADD_CARRY(r6, a15, r6, carry, carry);
138 		MP_ADD_CARRY(r7,   0, r7, carry, carry);
139 		r8 += carry;
140 		/* combine last bottom of sum 3 with second sum 2 */
141 		MP_ADD_CARRY(r0, a8,  r0, 0,     carry);
142 		MP_ADD_CARRY(r1, a9,  r1, carry, carry);
143 		MP_ADD_CARRY(r2, a10, r2, carry, carry);
144 		MP_ADD_CARRY(r3, a12, r3, carry, carry);
145 		MP_ADD_CARRY(r4, a13, r4, carry, carry);
146 		MP_ADD_CARRY(r5, a14, r5, carry, carry);
147 		MP_ADD_CARRY(r6, a15, r6, carry, carry);
148 		MP_ADD_CARRY(r7, a15, r7, carry, carry); /* from sum 3 */
149 		r8 += carry;
150 		/* sum 3 (rest of it)*/
151 		MP_ADD_CARRY(r6, a14, r6, 0,     carry);
152 		MP_ADD_CARRY(r7,   0, r7, carry, carry);
153 		r8 += carry;
154 		/* sum 4 (rest of it)*/
155 		MP_ADD_CARRY(r0, a9,  r0, 0,     carry);
156 		MP_ADD_CARRY(r1, a10, r1, carry, carry);
157 		MP_ADD_CARRY(r2, a11, r2, carry, carry);
158 		MP_ADD_CARRY(r3, a13, r3, carry, carry);
159 		MP_ADD_CARRY(r4, a14, r4, carry, carry);
160 		MP_ADD_CARRY(r5, a15, r5, carry, carry);
161 		MP_ADD_CARRY(r6, a13, r6, carry, carry);
162 		MP_ADD_CARRY(r7, a8,  r7, carry, carry);
163 		r8 += carry;
164 		/* diff 5 */
165 		MP_SUB_BORROW(r0, a11, r0, 0,     carry);
166 		MP_SUB_BORROW(r1, a12, r1, carry, carry);
167 		MP_SUB_BORROW(r2, a13, r2, carry, carry);
168 		MP_SUB_BORROW(r3,   0, r3, carry, carry);
169 		MP_SUB_BORROW(r4,   0, r4, carry, carry);
170 		MP_SUB_BORROW(r5,   0, r5, carry, carry);
171 		MP_SUB_BORROW(r6, a8,  r6, carry, carry);
172 		MP_SUB_BORROW(r7, a10, r7, carry, carry);
173 		r8 -= carry;
174 		/* diff 6 */
175 		MP_SUB_BORROW(r0, a12, r0, 0,     carry);
176 		MP_SUB_BORROW(r1, a13, r1, carry, carry);
177 		MP_SUB_BORROW(r2, a14, r2, carry, carry);
178 		MP_SUB_BORROW(r3, a15, r3, carry, carry);
179 		MP_SUB_BORROW(r4,   0, r4, carry, carry);
180 		MP_SUB_BORROW(r5,   0, r5, carry, carry);
181 		MP_SUB_BORROW(r6, a9,  r6, carry, carry);
182 		MP_SUB_BORROW(r7, a11, r7, carry, carry);
183 		r8 -= carry;
184 		/* diff 7 */
185 		MP_SUB_BORROW(r0, a13, r0, 0,     carry);
186 		MP_SUB_BORROW(r1, a14, r1, carry, carry);
187 		MP_SUB_BORROW(r2, a15, r2, carry, carry);
188 		MP_SUB_BORROW(r3, a8,  r3, carry, carry);
189 		MP_SUB_BORROW(r4, a9,  r4, carry, carry);
190 		MP_SUB_BORROW(r5, a10, r5, carry, carry);
191 		MP_SUB_BORROW(r6, 0,   r6, carry, carry);
192 		MP_SUB_BORROW(r7, a12, r7, carry, carry);
193 		r8 -= carry;
194 		/* diff 8 */
195 		MP_SUB_BORROW(r0, a14, r0, 0,     carry);
196 		MP_SUB_BORROW(r1, a15, r1, carry, carry);
197 		MP_SUB_BORROW(r2, 0,   r2, carry, carry);
198 		MP_SUB_BORROW(r3, a9,  r3, carry, carry);
199 		MP_SUB_BORROW(r4, a10, r4, carry, carry);
200 		MP_SUB_BORROW(r5, a11, r5, carry, carry);
201 		MP_SUB_BORROW(r6, 0,   r6, carry, carry);
202 		MP_SUB_BORROW(r7, a13, r7, carry, carry);
203 		r8 -= carry;
204 
205 		/* reduce the overflows */
206 		while (r8 > 0) {
207 			mp_digit r8_d = r8;
208 			MP_ADD_CARRY(r0, r8_d,         r0, 0,     carry);
209 			MP_ADD_CARRY(r1, 0,            r1, carry, carry);
210 			MP_ADD_CARRY(r2, 0,            r2, carry, carry);
211 			MP_ADD_CARRY(r3, -r8_d,        r3, carry, carry);
212 			MP_ADD_CARRY(r4, MP_DIGIT_MAX, r4, carry, carry);
213 			MP_ADD_CARRY(r5, MP_DIGIT_MAX, r5, carry, carry);
214 			MP_ADD_CARRY(r6, -(r8_d+1),    r6, carry, carry);
215 			MP_ADD_CARRY(r7, (r8_d-1),     r7, carry, carry);
216 			r8 = carry;
217 		}
218 
219 		/* reduce the underflows */
220 		while (r8 < 0) {
221 			mp_digit r8_d = -r8;
222 			MP_SUB_BORROW(r0, r8_d,         r0, 0,     carry);
223 			MP_SUB_BORROW(r1, 0,            r1, carry, carry);
224 			MP_SUB_BORROW(r2, 0,            r2, carry, carry);
225 			MP_SUB_BORROW(r3, -r8_d,        r3, carry, carry);
226 			MP_SUB_BORROW(r4, MP_DIGIT_MAX, r4, carry, carry);
227 			MP_SUB_BORROW(r5, MP_DIGIT_MAX, r5, carry, carry);
228 			MP_SUB_BORROW(r6, -(r8_d+1),    r6, carry, carry);
229 			MP_SUB_BORROW(r7, (r8_d-1),     r7, carry, carry);
230 			r8 = -carry;
231 		}
232 		if (a != r) {
233 			MP_CHECKOK(s_mp_pad(r,8));
234 		}
235 		MP_SIGN(r) = MP_ZPOS;
236 		MP_USED(r) = 8;
237 
238 		MP_DIGIT(r,7) = r7;
239 		MP_DIGIT(r,6) = r6;
240 		MP_DIGIT(r,5) = r5;
241 		MP_DIGIT(r,4) = r4;
242 		MP_DIGIT(r,3) = r3;
243 		MP_DIGIT(r,2) = r2;
244 		MP_DIGIT(r,1) = r1;
245 		MP_DIGIT(r,0) = r0;
246 
247 		/* final reduction if necessary */
248 		if ((r7 == MP_DIGIT_MAX) &&
249 			((r6 > 1) || ((r6 == 1) &&
250 			(r5 || r4 || r3 ||
251 				((r2 == MP_DIGIT_MAX) && (r1 == MP_DIGIT_MAX)
252 				  && (r0 == MP_DIGIT_MAX)))))) {
253 			MP_CHECKOK(mp_sub(r, &meth->irr, r));
254 		}
255 #ifdef notdef
256 
257 
258 		/* smooth the negatives */
259 		while (MP_SIGN(r) != MP_ZPOS) {
260 			MP_CHECKOK(mp_add(r, &meth->irr, r));
261 		}
262 		while (MP_USED(r) > 8) {
263 			MP_CHECKOK(mp_sub(r, &meth->irr, r));
264 		}
265 
266 		/* final reduction if necessary */
267 		if (MP_DIGIT(r,7) >= MP_DIGIT(&meth->irr,7)) {
268 		    if (mp_cmp(r,&meth->irr) != MP_LT) {
269 			MP_CHECKOK(mp_sub(r, &meth->irr, r));
270 		    }
271 		}
272 #endif
273 		s_mp_clamp(r);
274 #else
275 		switch (a_used) {
276 		case 8:
277 			a7 = MP_DIGIT(a,7);
278 			/* FALLTHROUGH */
279 		case 7:
280 			a6 = MP_DIGIT(a,6);
281 			/* FALLTHROUGH */
282 		case 6:
283 			a5 = MP_DIGIT(a,5);
284 			/* FALLTHROUGH */
285 		case 5:
286 			a4 = MP_DIGIT(a,4);
287 		}
288 		a7l = a7 << 32;
289 		a7h = a7 >> 32;
290 		a6l = a6 << 32;
291 		a6h = a6 >> 32;
292 		a5l = a5 << 32;
293 		a5h = a5 >> 32;
294 		a4l = a4 << 32;
295 		a4h = a4 >> 32;
296 		r3 = MP_DIGIT(a,3);
297 		r2 = MP_DIGIT(a,2);
298 		r1 = MP_DIGIT(a,1);
299 		r0 = MP_DIGIT(a,0);
300 
301 		/* sum 1 */
302 		MP_ADD_CARRY(r1, a5h << 32, r1, 0,     carry);
303 		MP_ADD_CARRY(r2, a6,        r2, carry, carry);
304 		MP_ADD_CARRY(r3, a7,        r3, carry, carry);
305 		r4 = carry;
306 		MP_ADD_CARRY(r1, a5h << 32, r1, 0,     carry);
307 		MP_ADD_CARRY(r2, a6,        r2, carry, carry);
308 		MP_ADD_CARRY(r3, a7,        r3, carry, carry);
309 		r4 += carry;
310 		/* sum 2 */
311 		MP_ADD_CARRY(r1, a6l,       r1, 0,     carry);
312 		MP_ADD_CARRY(r2, a6h | a7l, r2, carry, carry);
313 		MP_ADD_CARRY(r3, a7h,       r3, carry, carry);
314 		r4 += carry;
315 		MP_ADD_CARRY(r1, a6l,       r1, 0,     carry);
316 		MP_ADD_CARRY(r2, a6h | a7l, r2, carry, carry);
317 		MP_ADD_CARRY(r3, a7h,       r3, carry, carry);
318 		r4 += carry;
319 
320 		/* sum 3 */
321 		MP_ADD_CARRY(r0, a4,        r0, 0,     carry);
322 		MP_ADD_CARRY(r1, a5l >> 32, r1, carry, carry);
323 		MP_ADD_CARRY(r2, 0,         r2, carry, carry);
324 		MP_ADD_CARRY(r3, a7,        r3, carry, carry);
325 		r4 += carry;
326 		/* sum 4 */
327 		MP_ADD_CARRY(r0, a4h | a5l,     r0, 0,     carry);
328 		MP_ADD_CARRY(r1, a5h|(a6h<<32), r1, carry, carry);
329 		MP_ADD_CARRY(r2, a7,            r2, carry, carry);
330 		MP_ADD_CARRY(r3, a6h | a4l,     r3, carry, carry);
331 		r4 += carry;
332 		/* diff 5 */
333 		MP_SUB_BORROW(r0, a5h | a6l,    r0, 0,     carry);
334 		MP_SUB_BORROW(r1, a6h,          r1, carry, carry);
335 		MP_SUB_BORROW(r2, 0,            r2, carry, carry);
336 		MP_SUB_BORROW(r3, (a4l>>32)|a5l,r3, carry, carry);
337 		r4 -= carry;
338 		/* diff 6 */
339 		MP_SUB_BORROW(r0, a6,  		r0, 0,     carry);
340 		MP_SUB_BORROW(r1, a7,           r1, carry, carry);
341 		MP_SUB_BORROW(r2, 0,            r2, carry, carry);
342 		MP_SUB_BORROW(r3, a4h|(a5h<<32),r3, carry, carry);
343 		r4 -= carry;
344 		/* diff 7 */
345 		MP_SUB_BORROW(r0, a6h|a7l,	r0, 0,     carry);
346 		MP_SUB_BORROW(r1, a7h|a4l,      r1, carry, carry);
347 		MP_SUB_BORROW(r2, a4h|a5l,      r2, carry, carry);
348 		MP_SUB_BORROW(r3, a6l,          r3, carry, carry);
349 		r4 -= carry;
350 		/* diff 8 */
351 		MP_SUB_BORROW(r0, a7,	        r0, 0,     carry);
352 		MP_SUB_BORROW(r1, a4h<<32,      r1, carry, carry);
353 		MP_SUB_BORROW(r2, a5,           r2, carry, carry);
354 		MP_SUB_BORROW(r3, a6h<<32,      r3, carry, carry);
355 		r4 -= carry;
356 
357 		/* reduce the overflows */
358 		while (r4 > 0) {
359 			mp_digit r4_long = r4;
360 			mp_digit r4l = (r4_long << 32);
361 			MP_ADD_CARRY(r0, r4_long,      r0, 0,     carry);
362 			MP_ADD_CARRY(r1, -r4l,         r1, carry, carry);
363 			MP_ADD_CARRY(r2, MP_DIGIT_MAX, r2, carry, carry);
364 			MP_ADD_CARRY(r3, r4l-r4_long-1,r3, carry, carry);
365 			r4 = carry;
366 		}
367 
368 		/* reduce the underflows */
369 		while (r4 < 0) {
370 			mp_digit r4_long = -r4;
371 			mp_digit r4l = (r4_long << 32);
372 			MP_SUB_BORROW(r0, r4_long,      r0, 0,     carry);
373 			MP_SUB_BORROW(r1, -r4l,         r1, carry, carry);
374 			MP_SUB_BORROW(r2, MP_DIGIT_MAX, r2, carry, carry);
375 			MP_SUB_BORROW(r3, r4l-r4_long-1,r3, carry, carry);
376 			r4 = -carry;
377 		}
378 
379 		if (a != r) {
380 			MP_CHECKOK(s_mp_pad(r,4));
381 		}
382 		MP_SIGN(r) = MP_ZPOS;
383 		MP_USED(r) = 4;
384 
385 		MP_DIGIT(r,3) = r3;
386 		MP_DIGIT(r,2) = r2;
387 		MP_DIGIT(r,1) = r1;
388 		MP_DIGIT(r,0) = r0;
389 
390 		/* final reduction if necessary */
391 		if ((r3 > 0xFFFFFFFF00000001ULL) ||
392 			((r3 == 0xFFFFFFFF00000001ULL) &&
393 			(r2 || (r1 >> 32)||
394 			       (r1 == 0xFFFFFFFFULL && r0 == MP_DIGIT_MAX)))) {
395 			/* very rare, just use mp_sub */
396 			MP_CHECKOK(mp_sub(r, &meth->irr, r));
397 		}
398 
399 		s_mp_clamp(r);
400 #endif
401 	}
402 
403   CLEANUP:
404 	return res;
405 }
406 
407 /* Compute the square of polynomial a, reduce modulo p256. Store the
408  * result in r.  r could be a.  Uses optimized modular reduction for p256.
409  */
410 mp_err
ec_GFp_nistp256_sqr(const mp_int * a,mp_int * r,const GFMethod * meth)411 ec_GFp_nistp256_sqr(const mp_int *a, mp_int *r, const GFMethod *meth)
412 {
413 	mp_err res = MP_OKAY;
414 
415 	MP_CHECKOK(mp_sqr(a, r));
416 	MP_CHECKOK(ec_GFp_nistp256_mod(r, r, meth));
417   CLEANUP:
418 	return res;
419 }
420 
421 /* Compute the product of two polynomials a and b, reduce modulo p256.
422  * Store the result in r.  r could be a or b; a could be b.  Uses
423  * optimized modular reduction for p256. */
424 mp_err
ec_GFp_nistp256_mul(const mp_int * a,const mp_int * b,mp_int * r,const GFMethod * meth)425 ec_GFp_nistp256_mul(const mp_int *a, const mp_int *b, mp_int *r,
426 					const GFMethod *meth)
427 {
428 	mp_err res = MP_OKAY;
429 
430 	MP_CHECKOK(mp_mul(a, b, r));
431 	MP_CHECKOK(ec_GFp_nistp256_mod(r, r, meth));
432   CLEANUP:
433 	return res;
434 }
435 
436 /* Wire in fast field arithmetic and precomputation of base point for
437  * named curves. */
438 mp_err
ec_group_set_gfp256(ECGroup * group,ECCurveName name)439 ec_group_set_gfp256(ECGroup *group, ECCurveName name)
440 {
441 	if (name == ECCurve_NIST_P256) {
442 		group->meth->field_mod = &ec_GFp_nistp256_mod;
443 		group->meth->field_mul = &ec_GFp_nistp256_mul;
444 		group->meth->field_sqr = &ec_GFp_nistp256_sqr;
445 	}
446 	return MP_OKAY;
447 }
448