1 /* crypto/bn/bn_gf2m.c */
2 /* ====================================================================
3 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
5 * The Elliptic Curve Public-Key Crypto Library (ECC Code) included
6 * herein is developed by SUN MICROSYSTEMS, INC., and is contributed
7 * to the OpenSSL project.
9 * The ECC Code is licensed pursuant to the OpenSSL open source
10 * license provided below.
12 * In addition, Sun covenants to all licensees who provide a reciprocal
13 * covenant with respect to their own patents if any, not to sue under
14 * current and future patent claims necessarily infringed by the making,
15 * using, practicing, selling, offering for sale and/or otherwise
16 * disposing of the ECC Code as delivered hereunder (or portions thereof),
17 * provided that such covenant shall not apply:
18 * 1) for code that a licensee deletes from the ECC Code;
19 * 2) separates from the ECC Code; or
20 * 3) for infringements caused by:
21 * i) the modification of the ECC Code or
22 * ii) the combination of the ECC Code with other software or
23 * devices where such combination causes the infringement.
25 * The software is originally written by Sheueling Chang Shantz and
26 * Douglas Stebila of Sun Microsystems Laboratories.
30 /* NOTE: This file is licensed pursuant to the OpenSSL license below
31 * and may be modified; but after modifications, the above covenant
32 * may no longer apply! In such cases, the corresponding paragraph
33 * ["In addition, Sun covenants ... causes the infringement."] and
34 * this note can be edited out; but please keep the Sun copyright
35 * notice and attribution. */
37 /* ====================================================================
38 * Copyright (c) 1998-2002 The OpenSSL Project. All rights reserved.
40 * Redistribution and use in source and binary forms, with or without
41 * modification, are permitted provided that the following conditions
44 * 1. Redistributions of source code must retain the above copyright
45 * notice, this list of conditions and the following disclaimer.
47 * 2. Redistributions in binary form must reproduce the above copyright
48 * notice, this list of conditions and the following disclaimer in
49 * the documentation and/or other materials provided with the
52 * 3. All advertising materials mentioning features or use of this
53 * software must display the following acknowledgment:
54 * "This product includes software developed by the OpenSSL Project
55 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
57 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
58 * endorse or promote products derived from this software without
59 * prior written permission. For written permission, please contact
60 * openssl-core@openssl.org.
62 * 5. Products derived from this software may not be called "OpenSSL"
63 * nor may "OpenSSL" appear in their names without prior written
64 * permission of the OpenSSL Project.
66 * 6. Redistributions of any form whatsoever must retain the following
68 * "This product includes software developed by the OpenSSL Project
69 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
71 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
72 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
73 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
74 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
75 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
76 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
77 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
78 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
79 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
80 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
81 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
82 * OF THE POSSIBILITY OF SUCH DAMAGE.
83 * ====================================================================
85 * This product includes cryptographic software written by Eric Young
86 * (eay@cryptsoft.com). This product includes software written by Tim
87 * Hudson (tjh@cryptsoft.com).
91 #define OPENSSL_FIPSAPI
99 #ifndef OPENSSL_NO_EC2M
101 /* Maximum number of iterations before BN_GF2m_mod_solve_quad_arr should fail. */
102 #define MAX_ITERATIONS 50
105 static const BN_ULONG SQR_tb
[16] =
106 { 0, 1, 4, 5, 16, 17, 20, 21,
107 64, 65, 68, 69, 80, 81, 84, 85 };
108 /* Platform-specific macros to accelerate squaring. */
109 #if defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG)
111 SQR_tb[(w) >> 60 & 0xF] << 56 | SQR_tb[(w) >> 56 & 0xF] << 48 | \
112 SQR_tb[(w) >> 52 & 0xF] << 40 | SQR_tb[(w) >> 48 & 0xF] << 32 | \
113 SQR_tb[(w) >> 44 & 0xF] << 24 | SQR_tb[(w) >> 40 & 0xF] << 16 | \
114 SQR_tb[(w) >> 36 & 0xF] << 8 | SQR_tb[(w) >> 32 & 0xF]
116 SQR_tb[(w) >> 28 & 0xF] << 56 | SQR_tb[(w) >> 24 & 0xF] << 48 | \
117 SQR_tb[(w) >> 20 & 0xF] << 40 | SQR_tb[(w) >> 16 & 0xF] << 32 | \
118 SQR_tb[(w) >> 12 & 0xF] << 24 | SQR_tb[(w) >> 8 & 0xF] << 16 | \
119 SQR_tb[(w) >> 4 & 0xF] << 8 | SQR_tb[(w) & 0xF]
121 #ifdef THIRTY_TWO_BIT
123 SQR_tb[(w) >> 28 & 0xF] << 24 | SQR_tb[(w) >> 24 & 0xF] << 16 | \
124 SQR_tb[(w) >> 20 & 0xF] << 8 | SQR_tb[(w) >> 16 & 0xF]
126 SQR_tb[(w) >> 12 & 0xF] << 24 | SQR_tb[(w) >> 8 & 0xF] << 16 | \
127 SQR_tb[(w) >> 4 & 0xF] << 8 | SQR_tb[(w) & 0xF]
130 #if !defined(OPENSSL_BN_ASM_GF2m)
131 /* Product of two polynomials a, b each with degree < BN_BITS2 - 1,
132 * result is a polynomial r with degree < 2 * BN_BITS - 1
133 * The caller MUST ensure that the variables have the right amount
134 * of space allocated.
136 #ifdef THIRTY_TWO_BIT
137 static void bn_GF2m_mul_1x1(BN_ULONG
*r1
, BN_ULONG
*r0
, const BN_ULONG a
, const BN_ULONG b
)
139 register BN_ULONG h
, l
, s
;
140 BN_ULONG tab
[8], top2b
= a
>> 30;
141 register BN_ULONG a1
, a2
, a4
;
143 a1
= a
& (0x3FFFFFFF); a2
= a1
<< 1; a4
= a2
<< 1;
145 tab
[0] = 0; tab
[1] = a1
; tab
[2] = a2
; tab
[3] = a1
^a2
;
146 tab
[4] = a4
; tab
[5] = a1
^a4
; tab
[6] = a2
^a4
; tab
[7] = a1
^a2
^a4
;
148 s
= tab
[b
& 0x7]; l
= s
;
149 s
= tab
[b
>> 3 & 0x7]; l
^= s
<< 3; h
= s
>> 29;
150 s
= tab
[b
>> 6 & 0x7]; l
^= s
<< 6; h
^= s
>> 26;
151 s
= tab
[b
>> 9 & 0x7]; l
^= s
<< 9; h
^= s
>> 23;
152 s
= tab
[b
>> 12 & 0x7]; l
^= s
<< 12; h
^= s
>> 20;
153 s
= tab
[b
>> 15 & 0x7]; l
^= s
<< 15; h
^= s
>> 17;
154 s
= tab
[b
>> 18 & 0x7]; l
^= s
<< 18; h
^= s
>> 14;
155 s
= tab
[b
>> 21 & 0x7]; l
^= s
<< 21; h
^= s
>> 11;
156 s
= tab
[b
>> 24 & 0x7]; l
^= s
<< 24; h
^= s
>> 8;
157 s
= tab
[b
>> 27 & 0x7]; l
^= s
<< 27; h
^= s
>> 5;
158 s
= tab
[b
>> 30 ]; l
^= s
<< 30; h
^= s
>> 2;
160 /* compensate for the top two bits of a */
162 if (top2b
& 01) { l
^= b
<< 30; h
^= b
>> 2; }
163 if (top2b
& 02) { l
^= b
<< 31; h
^= b
>> 1; }
168 #if defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG)
169 static void bn_GF2m_mul_1x1(BN_ULONG
*r1
, BN_ULONG
*r0
, const BN_ULONG a
, const BN_ULONG b
)
171 register BN_ULONG h
, l
, s
;
172 BN_ULONG tab
[16], top3b
= a
>> 61;
173 register BN_ULONG a1
, a2
, a4
, a8
;
175 a1
= a
& (0x1FFFFFFFFFFFFFFFULL
); a2
= a1
<< 1; a4
= a2
<< 1; a8
= a4
<< 1;
177 tab
[ 0] = 0; tab
[ 1] = a1
; tab
[ 2] = a2
; tab
[ 3] = a1
^a2
;
178 tab
[ 4] = a4
; tab
[ 5] = a1
^a4
; tab
[ 6] = a2
^a4
; tab
[ 7] = a1
^a2
^a4
;
179 tab
[ 8] = a8
; tab
[ 9] = a1
^a8
; tab
[10] = a2
^a8
; tab
[11] = a1
^a2
^a8
;
180 tab
[12] = a4
^a8
; tab
[13] = a1
^a4
^a8
; tab
[14] = a2
^a4
^a8
; tab
[15] = a1
^a2
^a4
^a8
;
182 s
= tab
[b
& 0xF]; l
= s
;
183 s
= tab
[b
>> 4 & 0xF]; l
^= s
<< 4; h
= s
>> 60;
184 s
= tab
[b
>> 8 & 0xF]; l
^= s
<< 8; h
^= s
>> 56;
185 s
= tab
[b
>> 12 & 0xF]; l
^= s
<< 12; h
^= s
>> 52;
186 s
= tab
[b
>> 16 & 0xF]; l
^= s
<< 16; h
^= s
>> 48;
187 s
= tab
[b
>> 20 & 0xF]; l
^= s
<< 20; h
^= s
>> 44;
188 s
= tab
[b
>> 24 & 0xF]; l
^= s
<< 24; h
^= s
>> 40;
189 s
= tab
[b
>> 28 & 0xF]; l
^= s
<< 28; h
^= s
>> 36;
190 s
= tab
[b
>> 32 & 0xF]; l
^= s
<< 32; h
^= s
>> 32;
191 s
= tab
[b
>> 36 & 0xF]; l
^= s
<< 36; h
^= s
>> 28;
192 s
= tab
[b
>> 40 & 0xF]; l
^= s
<< 40; h
^= s
>> 24;
193 s
= tab
[b
>> 44 & 0xF]; l
^= s
<< 44; h
^= s
>> 20;
194 s
= tab
[b
>> 48 & 0xF]; l
^= s
<< 48; h
^= s
>> 16;
195 s
= tab
[b
>> 52 & 0xF]; l
^= s
<< 52; h
^= s
>> 12;
196 s
= tab
[b
>> 56 & 0xF]; l
^= s
<< 56; h
^= s
>> 8;
197 s
= tab
[b
>> 60 ]; l
^= s
<< 60; h
^= s
>> 4;
199 /* compensate for the top three bits of a */
201 if (top3b
& 01) { l
^= b
<< 61; h
^= b
>> 3; }
202 if (top3b
& 02) { l
^= b
<< 62; h
^= b
>> 2; }
203 if (top3b
& 04) { l
^= b
<< 63; h
^= b
>> 1; }
209 /* Product of two polynomials a, b each with degree < 2 * BN_BITS2 - 1,
210 * result is a polynomial r with degree < 4 * BN_BITS2 - 1
211 * The caller MUST ensure that the variables have the right amount
212 * of space allocated.
214 static void bn_GF2m_mul_2x2(BN_ULONG
*r
, const BN_ULONG a1
, const BN_ULONG a0
, const BN_ULONG b1
, const BN_ULONG b0
)
217 /* r[3] = h1, r[2] = h0; r[1] = l1; r[0] = l0 */
218 bn_GF2m_mul_1x1(r
+3, r
+2, a1
, b1
);
219 bn_GF2m_mul_1x1(r
+1, r
, a0
, b0
);
220 bn_GF2m_mul_1x1(&m1
, &m0
, a0
^ a1
, b0
^ b1
);
221 /* Correction on m1 ^= l1 ^ h1; m0 ^= l0 ^ h0; */
222 r
[2] ^= m1
^ r
[1] ^ r
[3]; /* h0 ^= m1 ^ l1 ^ h1; */
223 r
[1] = r
[3] ^ r
[2] ^ r
[0] ^ m1
^ m0
; /* l1 ^= l0 ^ h0 ^ m0; */
226 void bn_GF2m_mul_2x2(BN_ULONG
*r
, BN_ULONG a1
, BN_ULONG a0
, BN_ULONG b1
, BN_ULONG b0
);
229 /* Add polynomials a and b and store result in r; r could be a or b, a and b
230 * could be equal; r is the bitwise XOR of a and b.
232 int BN_GF2m_add(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
)
235 const BIGNUM
*at
, *bt
;
240 if (a
->top
< b
->top
) { at
= b
; bt
= a
; }
241 else { at
= a
; bt
= b
; }
243 if(bn_wexpand(r
, at
->top
) == NULL
)
246 for (i
= 0; i
< bt
->top
; i
++)
248 r
->d
[i
] = at
->d
[i
] ^ bt
->d
[i
];
250 for (; i
< at
->top
; i
++)
262 /* Some functions allow for representation of the irreducible polynomials
263 * as an int[], say p. The irreducible f(t) is then of the form:
264 * t^p[0] + t^p[1] + ... + t^p[k]
265 * where m = p[0] > p[1] > ... > p[k] = 0.
269 /* Performs modular reduction of a and store result in r. r could be a. */
270 int BN_GF2m_mod_arr(BIGNUM
*r
, const BIGNUM
*a
, const int p
[])
280 /* reduction mod 1 => return 0 */
285 /* Since the algorithm does reduction in the r value, if a != r, copy
286 * the contents of a into r so we can do reduction in r.
290 if (!bn_wexpand(r
, a
->top
)) return 0;
291 for (j
= 0; j
< a
->top
; j
++)
299 /* start reduction */
300 dN
= p
[0] / BN_BITS2
;
301 for (j
= r
->top
- 1; j
> dN
;)
304 if (z
[j
] == 0) { j
--; continue; }
307 for (k
= 1; p
[k
] != 0; k
++)
309 /* reducing component t^p[k] */
311 d0
= n
% BN_BITS2
; d1
= BN_BITS2
- d0
;
314 if (d0
) z
[j
-n
-1] ^= (zz
<<d1
);
317 /* reducing component t^0 */
319 d0
= p
[0] % BN_BITS2
;
321 z
[j
-n
] ^= (zz
>> d0
);
322 if (d0
) z
[j
-n
-1] ^= (zz
<< d1
);
325 /* final round of reduction */
329 d0
= p
[0] % BN_BITS2
;
334 /* clear up the top d1 bits */
336 z
[dN
] = (z
[dN
] << d1
) >> d1
;
339 z
[0] ^= zz
; /* reduction t^0 component */
341 for (k
= 1; p
[k
] != 0; k
++)
345 /* reducing component t^p[k]*/
347 d0
= p
[k
] % BN_BITS2
;
350 tmp_ulong
= zz
>> d1
;
362 /* Performs modular reduction of a by p and store result in r. r could be a.
364 * This function calls down to the BN_GF2m_mod_arr implementation; this wrapper
365 * function is only provided for convenience; for best performance, use the
366 * BN_GF2m_mod_arr function.
368 int BN_GF2m_mod(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
)
374 ret
= BN_GF2m_poly2arr(p
, arr
, sizeof(arr
)/sizeof(arr
[0]));
375 if (!ret
|| ret
> (int)(sizeof(arr
)/sizeof(arr
[0])))
377 BNerr(BN_F_BN_GF2M_MOD
,BN_R_INVALID_LENGTH
);
380 ret
= BN_GF2m_mod_arr(r
, a
, arr
);
386 /* Compute the product of two polynomials a and b, reduce modulo p, and store
387 * the result in r. r could be a or b; a could be b.
389 int BN_GF2m_mod_mul_arr(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
, const int p
[], BN_CTX
*ctx
)
391 int zlen
, i
, j
, k
, ret
= 0;
393 BN_ULONG x1
, x0
, y1
, y0
, zz
[4];
400 return BN_GF2m_mod_sqr_arr(r
, a
, p
, ctx
);
404 if ((s
= BN_CTX_get(ctx
)) == NULL
) goto err
;
406 zlen
= a
->top
+ b
->top
+ 4;
407 if (!bn_wexpand(s
, zlen
)) goto err
;
410 for (i
= 0; i
< zlen
; i
++) s
->d
[i
] = 0;
412 for (j
= 0; j
< b
->top
; j
+= 2)
415 y1
= ((j
+1) == b
->top
) ? 0 : b
->d
[j
+1];
416 for (i
= 0; i
< a
->top
; i
+= 2)
419 x1
= ((i
+1) == a
->top
) ? 0 : a
->d
[i
+1];
420 bn_GF2m_mul_2x2(zz
, x1
, x0
, y1
, y0
);
421 for (k
= 0; k
< 4; k
++) s
->d
[i
+j
+k
] ^= zz
[k
];
426 if (BN_GF2m_mod_arr(r
, s
, p
))
435 /* Compute the product of two polynomials a and b, reduce modulo p, and store
436 * the result in r. r could be a or b; a could equal b.
438 * This function calls down to the BN_GF2m_mod_mul_arr implementation; this wrapper
439 * function is only provided for convenience; for best performance, use the
440 * BN_GF2m_mod_mul_arr function.
442 int BN_GF2m_mod_mul(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
, const BIGNUM
*p
, BN_CTX
*ctx
)
445 const int max
= BN_num_bits(p
) + 1;
450 if ((arr
= (int *)OPENSSL_malloc(sizeof(int) * max
)) == NULL
) goto err
;
451 ret
= BN_GF2m_poly2arr(p
, arr
, max
);
452 if (!ret
|| ret
> max
)
454 BNerr(BN_F_BN_GF2M_MOD_MUL
,BN_R_INVALID_LENGTH
);
457 ret
= BN_GF2m_mod_mul_arr(r
, a
, b
, arr
, ctx
);
460 if (arr
) OPENSSL_free(arr
);
465 /* Square a, reduce the result mod p, and store it in a. r could be a. */
466 int BN_GF2m_mod_sqr_arr(BIGNUM
*r
, const BIGNUM
*a
, const int p
[], BN_CTX
*ctx
)
473 if ((s
= BN_CTX_get(ctx
)) == NULL
) return 0;
474 if (!bn_wexpand(s
, 2 * a
->top
)) goto err
;
476 for (i
= a
->top
- 1; i
>= 0; i
--)
478 s
->d
[2*i
+1] = SQR1(a
->d
[i
]);
479 s
->d
[2*i
] = SQR0(a
->d
[i
]);
484 if (!BN_GF2m_mod_arr(r
, s
, p
)) goto err
;
492 /* Square a, reduce the result mod p, and store it in a. r could be a.
494 * This function calls down to the BN_GF2m_mod_sqr_arr implementation; this wrapper
495 * function is only provided for convenience; for best performance, use the
496 * BN_GF2m_mod_sqr_arr function.
498 int BN_GF2m_mod_sqr(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
, BN_CTX
*ctx
)
501 const int max
= BN_num_bits(p
) + 1;
506 if ((arr
= (int *)OPENSSL_malloc(sizeof(int) * max
)) == NULL
) goto err
;
507 ret
= BN_GF2m_poly2arr(p
, arr
, max
);
508 if (!ret
|| ret
> max
)
510 BNerr(BN_F_BN_GF2M_MOD_SQR
,BN_R_INVALID_LENGTH
);
513 ret
= BN_GF2m_mod_sqr_arr(r
, a
, arr
, ctx
);
516 if (arr
) OPENSSL_free(arr
);
521 /* Invert a, reduce modulo p, and store the result in r. r could be a.
522 * Uses Modified Almost Inverse Algorithm (Algorithm 10) from
523 * Hankerson, D., Hernandez, J.L., and Menezes, A. "Software Implementation
524 * of Elliptic Curve Cryptography Over Binary Fields".
526 int BN_GF2m_mod_inv(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
, BN_CTX
*ctx
)
528 BIGNUM
*b
, *c
, *u
, *v
, *tmp
;
536 if ((b
= BN_CTX_get(ctx
))==NULL
) goto err
;
537 if ((c
= BN_CTX_get(ctx
))==NULL
) goto err
;
538 if ((u
= BN_CTX_get(ctx
))==NULL
) goto err
;
539 if ((v
= BN_CTX_get(ctx
))==NULL
) goto err
;
541 if (!BN_GF2m_mod(u
, a
, p
)) goto err
;
542 if (BN_is_zero(u
)) goto err
;
544 if (!BN_copy(v
, p
)) goto err
;
546 if (!BN_one(b
)) goto err
;
550 while (!BN_is_odd(u
))
552 if (BN_is_zero(u
)) goto err
;
553 if (!BN_rshift1(u
, u
)) goto err
;
556 if (!BN_GF2m_add(b
, b
, p
)) goto err
;
558 if (!BN_rshift1(b
, b
)) goto err
;
561 if (BN_abs_is_word(u
, 1)) break;
563 if (BN_num_bits(u
) < BN_num_bits(v
))
565 tmp
= u
; u
= v
; v
= tmp
;
566 tmp
= b
; b
= c
; c
= tmp
;
569 if (!BN_GF2m_add(u
, u
, v
)) goto err
;
570 if (!BN_GF2m_add(b
, b
, c
)) goto err
;
574 int i
, ubits
= BN_num_bits(u
),
575 vbits
= BN_num_bits(v
), /* v is copy of p */
577 BN_ULONG
*udp
,*bdp
,*vdp
,*cdp
;
579 bn_wexpand(u
,top
); udp
= u
->d
;
580 for (i
=u
->top
;i
<top
;i
++) udp
[i
] = 0;
582 bn_wexpand(b
,top
); bdp
= b
->d
;
584 for (i
=1;i
<top
;i
++) bdp
[i
] = 0;
586 bn_wexpand(c
,top
); cdp
= c
->d
;
587 for (i
=0;i
<top
;i
++) cdp
[i
] = 0;
589 vdp
= v
->d
; /* It pays off to "cache" *->d pointers, because
590 * it allows optimizer to be more aggressive.
591 * But we don't have to "cache" p->d, because *p
592 * is declared 'const'... */
595 while (ubits
&& !(udp
[0]&1))
597 BN_ULONG u0
,u1
,b0
,b1
,mask
;
601 mask
= (BN_ULONG
)0-(b0
&1);
603 for (i
=0;i
<top
-1;i
++)
606 udp
[i
] = ((u0
>>1)|(u1
<<(BN_BITS2
-1)))&BN_MASK2
;
608 b1
= bdp
[i
+1]^(p
->d
[i
+1]&mask
);
609 bdp
[i
] = ((b0
>>1)|(b1
<<(BN_BITS2
-1)))&BN_MASK2
;
617 if (ubits
<=BN_BITS2
&& udp
[0]==1) break;
621 i
= ubits
; ubits
= vbits
; vbits
= i
;
622 tmp
= u
; u
= v
; v
= tmp
;
623 tmp
= b
; b
= c
; c
= tmp
;
624 udp
= vdp
; vdp
= v
->d
;
625 bdp
= cdp
; cdp
= c
->d
;
635 ubits
= BN_num_bits(u
);
642 if (!BN_copy(r
, b
)) goto err
;
647 #ifdef BN_DEBUG /* BN_CTX_end would complain about the expanded form */
654 /* Invert xx, reduce modulo p, and store the result in r. r could be xx.
656 * This function calls down to the BN_GF2m_mod_inv implementation; this wrapper
657 * function is only provided for convenience; for best performance, use the
658 * BN_GF2m_mod_inv function.
660 int BN_GF2m_mod_inv_arr(BIGNUM
*r
, const BIGNUM
*xx
, const int p
[], BN_CTX
*ctx
)
667 if ((field
= BN_CTX_get(ctx
)) == NULL
) goto err
;
668 if (!BN_GF2m_arr2poly(p
, field
)) goto err
;
670 ret
= BN_GF2m_mod_inv(r
, xx
, field
, ctx
);
679 #ifndef OPENSSL_SUN_GF2M_DIV
680 /* Divide y by x, reduce modulo p, and store the result in r. r could be x
681 * or y, x could equal y.
683 int BN_GF2m_mod_div(BIGNUM
*r
, const BIGNUM
*y
, const BIGNUM
*x
, const BIGNUM
*p
, BN_CTX
*ctx
)
693 xinv
= BN_CTX_get(ctx
);
694 if (xinv
== NULL
) goto err
;
696 if (!BN_GF2m_mod_inv(xinv
, x
, p
, ctx
)) goto err
;
697 if (!BN_GF2m_mod_mul(r
, y
, xinv
, p
, ctx
)) goto err
;
706 /* Divide y by x, reduce modulo p, and store the result in r. r could be x
707 * or y, x could equal y.
708 * Uses algorithm Modular_Division_GF(2^m) from
709 * Chang-Shantz, S. "From Euclid's GCD to Montgomery Multiplication to
712 int BN_GF2m_mod_div(BIGNUM
*r
, const BIGNUM
*y
, const BIGNUM
*x
, const BIGNUM
*p
, BN_CTX
*ctx
)
714 BIGNUM
*a
, *b
, *u
, *v
;
727 if (v
== NULL
) goto err
;
729 /* reduce x and y mod p */
730 if (!BN_GF2m_mod(u
, y
, p
)) goto err
;
731 if (!BN_GF2m_mod(a
, x
, p
)) goto err
;
732 if (!BN_copy(b
, p
)) goto err
;
734 while (!BN_is_odd(a
))
736 if (!BN_rshift1(a
, a
)) goto err
;
737 if (BN_is_odd(u
)) if (!BN_GF2m_add(u
, u
, p
)) goto err
;
738 if (!BN_rshift1(u
, u
)) goto err
;
743 if (BN_GF2m_cmp(b
, a
) > 0)
745 if (!BN_GF2m_add(b
, b
, a
)) goto err
;
746 if (!BN_GF2m_add(v
, v
, u
)) goto err
;
749 if (!BN_rshift1(b
, b
)) goto err
;
750 if (BN_is_odd(v
)) if (!BN_GF2m_add(v
, v
, p
)) goto err
;
751 if (!BN_rshift1(v
, v
)) goto err
;
752 } while (!BN_is_odd(b
));
754 else if (BN_abs_is_word(a
, 1))
758 if (!BN_GF2m_add(a
, a
, b
)) goto err
;
759 if (!BN_GF2m_add(u
, u
, v
)) goto err
;
762 if (!BN_rshift1(a
, a
)) goto err
;
763 if (BN_is_odd(u
)) if (!BN_GF2m_add(u
, u
, p
)) goto err
;
764 if (!BN_rshift1(u
, u
)) goto err
;
765 } while (!BN_is_odd(a
));
769 if (!BN_copy(r
, u
)) goto err
;
779 /* Divide yy by xx, reduce modulo p, and store the result in r. r could be xx
780 * or yy, xx could equal yy.
782 * This function calls down to the BN_GF2m_mod_div implementation; this wrapper
783 * function is only provided for convenience; for best performance, use the
784 * BN_GF2m_mod_div function.
786 int BN_GF2m_mod_div_arr(BIGNUM
*r
, const BIGNUM
*yy
, const BIGNUM
*xx
, const int p
[], BN_CTX
*ctx
)
795 if ((field
= BN_CTX_get(ctx
)) == NULL
) goto err
;
796 if (!BN_GF2m_arr2poly(p
, field
)) goto err
;
798 ret
= BN_GF2m_mod_div(r
, yy
, xx
, field
, ctx
);
807 /* Compute the bth power of a, reduce modulo p, and store
808 * the result in r. r could be a.
809 * Uses simple square-and-multiply algorithm A.5.1 from IEEE P1363.
811 int BN_GF2m_mod_exp_arr(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
, const int p
[], BN_CTX
*ctx
)
822 if (BN_abs_is_word(b
, 1))
823 return (BN_copy(r
, a
) != NULL
);
826 if ((u
= BN_CTX_get(ctx
)) == NULL
) goto err
;
828 if (!BN_GF2m_mod_arr(u
, a
, p
)) goto err
;
830 n
= BN_num_bits(b
) - 1;
831 for (i
= n
- 1; i
>= 0; i
--)
833 if (!BN_GF2m_mod_sqr_arr(u
, u
, p
, ctx
)) goto err
;
834 if (BN_is_bit_set(b
, i
))
836 if (!BN_GF2m_mod_mul_arr(u
, u
, a
, p
, ctx
)) goto err
;
839 if (!BN_copy(r
, u
)) goto err
;
847 /* Compute the bth power of a, reduce modulo p, and store
848 * the result in r. r could be a.
850 * This function calls down to the BN_GF2m_mod_exp_arr implementation; this wrapper
851 * function is only provided for convenience; for best performance, use the
852 * BN_GF2m_mod_exp_arr function.
854 int BN_GF2m_mod_exp(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
, const BIGNUM
*p
, BN_CTX
*ctx
)
857 const int max
= BN_num_bits(p
) + 1;
862 if ((arr
= (int *)OPENSSL_malloc(sizeof(int) * max
)) == NULL
) goto err
;
863 ret
= BN_GF2m_poly2arr(p
, arr
, max
);
864 if (!ret
|| ret
> max
)
866 BNerr(BN_F_BN_GF2M_MOD_EXP
,BN_R_INVALID_LENGTH
);
869 ret
= BN_GF2m_mod_exp_arr(r
, a
, b
, arr
, ctx
);
872 if (arr
) OPENSSL_free(arr
);
876 /* Compute the square root of a, reduce modulo p, and store
877 * the result in r. r could be a.
878 * Uses exponentiation as in algorithm A.4.1 from IEEE P1363.
880 int BN_GF2m_mod_sqrt_arr(BIGNUM
*r
, const BIGNUM
*a
, const int p
[], BN_CTX
*ctx
)
889 /* reduction mod 1 => return 0 */
895 if ((u
= BN_CTX_get(ctx
)) == NULL
) goto err
;
897 if (!BN_set_bit(u
, p
[0] - 1)) goto err
;
898 ret
= BN_GF2m_mod_exp_arr(r
, a
, u
, p
, ctx
);
906 /* Compute the square root of a, reduce modulo p, and store
907 * the result in r. r could be a.
909 * This function calls down to the BN_GF2m_mod_sqrt_arr implementation; this wrapper
910 * function is only provided for convenience; for best performance, use the
911 * BN_GF2m_mod_sqrt_arr function.
913 int BN_GF2m_mod_sqrt(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
, BN_CTX
*ctx
)
916 const int max
= BN_num_bits(p
) + 1;
920 if ((arr
= (int *)OPENSSL_malloc(sizeof(int) * max
)) == NULL
) goto err
;
921 ret
= BN_GF2m_poly2arr(p
, arr
, max
);
922 if (!ret
|| ret
> max
)
924 BNerr(BN_F_BN_GF2M_MOD_SQRT
,BN_R_INVALID_LENGTH
);
927 ret
= BN_GF2m_mod_sqrt_arr(r
, a
, arr
, ctx
);
930 if (arr
) OPENSSL_free(arr
);
934 /* Find r such that r^2 + r = a mod p. r could be a. If no r exists returns 0.
935 * Uses algorithms A.4.7 and A.4.6 from IEEE P1363.
937 int BN_GF2m_mod_solve_quad_arr(BIGNUM
*r
, const BIGNUM
*a_
, const int p
[], BN_CTX
*ctx
)
939 int ret
= 0, count
= 0, j
;
940 BIGNUM
*a
, *z
, *rho
, *w
, *w2
, *tmp
;
946 /* reduction mod 1 => return 0 */
955 if (w
== NULL
) goto err
;
957 if (!BN_GF2m_mod_arr(a
, a_
, p
)) goto err
;
966 if (p
[0] & 0x1) /* m is odd */
968 /* compute half-trace of a */
969 if (!BN_copy(z
, a
)) goto err
;
970 for (j
= 1; j
<= (p
[0] - 1) / 2; j
++)
972 if (!BN_GF2m_mod_sqr_arr(z
, z
, p
, ctx
)) goto err
;
973 if (!BN_GF2m_mod_sqr_arr(z
, z
, p
, ctx
)) goto err
;
974 if (!BN_GF2m_add(z
, z
, a
)) goto err
;
980 rho
= BN_CTX_get(ctx
);
981 w2
= BN_CTX_get(ctx
);
982 tmp
= BN_CTX_get(ctx
);
983 if (tmp
== NULL
) goto err
;
986 if (!BN_rand(rho
, p
[0], 0, 0)) goto err
;
987 if (!BN_GF2m_mod_arr(rho
, rho
, p
)) goto err
;
989 if (!BN_copy(w
, rho
)) goto err
;
990 for (j
= 1; j
<= p
[0] - 1; j
++)
992 if (!BN_GF2m_mod_sqr_arr(z
, z
, p
, ctx
)) goto err
;
993 if (!BN_GF2m_mod_sqr_arr(w2
, w
, p
, ctx
)) goto err
;
994 if (!BN_GF2m_mod_mul_arr(tmp
, w2
, a
, p
, ctx
)) goto err
;
995 if (!BN_GF2m_add(z
, z
, tmp
)) goto err
;
996 if (!BN_GF2m_add(w
, w2
, rho
)) goto err
;
999 } while (BN_is_zero(w
) && (count
< MAX_ITERATIONS
));
1002 BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR
,BN_R_TOO_MANY_ITERATIONS
);
1007 if (!BN_GF2m_mod_sqr_arr(w
, z
, p
, ctx
)) goto err
;
1008 if (!BN_GF2m_add(w
, z
, w
)) goto err
;
1009 if (BN_GF2m_cmp(w
, a
))
1011 BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR
, BN_R_NO_SOLUTION
);
1015 if (!BN_copy(r
, z
)) goto err
;
1025 /* Find r such that r^2 + r = a mod p. r could be a. If no r exists returns 0.
1027 * This function calls down to the BN_GF2m_mod_solve_quad_arr implementation; this wrapper
1028 * function is only provided for convenience; for best performance, use the
1029 * BN_GF2m_mod_solve_quad_arr function.
1031 int BN_GF2m_mod_solve_quad(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
, BN_CTX
*ctx
)
1034 const int max
= BN_num_bits(p
) + 1;
1038 if ((arr
= (int *)OPENSSL_malloc(sizeof(int) *
1039 max
)) == NULL
) goto err
;
1040 ret
= BN_GF2m_poly2arr(p
, arr
, max
);
1041 if (!ret
|| ret
> max
)
1043 BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD
,BN_R_INVALID_LENGTH
);
1046 ret
= BN_GF2m_mod_solve_quad_arr(r
, a
, arr
, ctx
);
1049 if (arr
) OPENSSL_free(arr
);
1053 /* Convert the bit-string representation of a polynomial
1054 * ( \sum_{i=0}^n a_i * x^i) into an array of integers corresponding
1055 * to the bits with non-zero coefficient. Array is terminated with -1.
1056 * Up to max elements of the array will be filled. Return value is total
1057 * number of array elements that would be filled if array was large enough.
1059 int BN_GF2m_poly2arr(const BIGNUM
*a
, int p
[], int max
)
1067 for (i
= a
->top
- 1; i
>= 0; i
--)
1070 /* skip word if a->d[i] == 0 */
1073 for (j
= BN_BITS2
- 1; j
>= 0; j
--)
1077 if (k
< max
) p
[k
] = BN_BITS2
* i
+ j
;
1092 /* Convert the coefficient array representation of a polynomial to a
1093 * bit-string. The array must be terminated by -1.
1095 int BN_GF2m_arr2poly(const int p
[], BIGNUM
*a
)
1101 for (i
= 0; p
[i
] != -1; i
++)
1103 if (BN_set_bit(a
, p
[i
]) == 0)