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
104 static const BN_ULONG SQR_tb
[16] =
105 { 0, 1, 4, 5, 16, 17, 20, 21,
106 64, 65, 68, 69, 80, 81, 84, 85 };
107 /* Platform-specific macros to accelerate squaring. */
108 #if defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG)
110 SQR_tb[(w) >> 60 & 0xF] << 56 | SQR_tb[(w) >> 56 & 0xF] << 48 | \
111 SQR_tb[(w) >> 52 & 0xF] << 40 | SQR_tb[(w) >> 48 & 0xF] << 32 | \
112 SQR_tb[(w) >> 44 & 0xF] << 24 | SQR_tb[(w) >> 40 & 0xF] << 16 | \
113 SQR_tb[(w) >> 36 & 0xF] << 8 | SQR_tb[(w) >> 32 & 0xF]
115 SQR_tb[(w) >> 28 & 0xF] << 56 | SQR_tb[(w) >> 24 & 0xF] << 48 | \
116 SQR_tb[(w) >> 20 & 0xF] << 40 | SQR_tb[(w) >> 16 & 0xF] << 32 | \
117 SQR_tb[(w) >> 12 & 0xF] << 24 | SQR_tb[(w) >> 8 & 0xF] << 16 | \
118 SQR_tb[(w) >> 4 & 0xF] << 8 | SQR_tb[(w) & 0xF]
120 #ifdef THIRTY_TWO_BIT
122 SQR_tb[(w) >> 28 & 0xF] << 24 | SQR_tb[(w) >> 24 & 0xF] << 16 | \
123 SQR_tb[(w) >> 20 & 0xF] << 8 | SQR_tb[(w) >> 16 & 0xF]
125 SQR_tb[(w) >> 12 & 0xF] << 24 | SQR_tb[(w) >> 8 & 0xF] << 16 | \
126 SQR_tb[(w) >> 4 & 0xF] << 8 | SQR_tb[(w) & 0xF]
129 #if !defined(OPENSSL_BN_ASM_GF2m)
130 /* Product of two polynomials a, b each with degree < BN_BITS2 - 1,
131 * result is a polynomial r with degree < 2 * BN_BITS - 1
132 * The caller MUST ensure that the variables have the right amount
133 * of space allocated.
135 #ifdef THIRTY_TWO_BIT
136 static void bn_GF2m_mul_1x1(BN_ULONG
*r1
, BN_ULONG
*r0
, const BN_ULONG a
, const BN_ULONG b
)
138 register BN_ULONG h
, l
, s
;
139 BN_ULONG tab
[8], top2b
= a
>> 30;
140 register BN_ULONG a1
, a2
, a4
;
142 a1
= a
& (0x3FFFFFFF); a2
= a1
<< 1; a4
= a2
<< 1;
144 tab
[0] = 0; tab
[1] = a1
; tab
[2] = a2
; tab
[3] = a1
^a2
;
145 tab
[4] = a4
; tab
[5] = a1
^a4
; tab
[6] = a2
^a4
; tab
[7] = a1
^a2
^a4
;
147 s
= tab
[b
& 0x7]; l
= s
;
148 s
= tab
[b
>> 3 & 0x7]; l
^= s
<< 3; h
= s
>> 29;
149 s
= tab
[b
>> 6 & 0x7]; l
^= s
<< 6; h
^= s
>> 26;
150 s
= tab
[b
>> 9 & 0x7]; l
^= s
<< 9; h
^= s
>> 23;
151 s
= tab
[b
>> 12 & 0x7]; l
^= s
<< 12; h
^= s
>> 20;
152 s
= tab
[b
>> 15 & 0x7]; l
^= s
<< 15; h
^= s
>> 17;
153 s
= tab
[b
>> 18 & 0x7]; l
^= s
<< 18; h
^= s
>> 14;
154 s
= tab
[b
>> 21 & 0x7]; l
^= s
<< 21; h
^= s
>> 11;
155 s
= tab
[b
>> 24 & 0x7]; l
^= s
<< 24; h
^= s
>> 8;
156 s
= tab
[b
>> 27 & 0x7]; l
^= s
<< 27; h
^= s
>> 5;
157 s
= tab
[b
>> 30 ]; l
^= s
<< 30; h
^= s
>> 2;
159 /* compensate for the top two bits of a */
161 if (top2b
& 01) { l
^= b
<< 30; h
^= b
>> 2; }
162 if (top2b
& 02) { l
^= b
<< 31; h
^= b
>> 1; }
167 #if defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG)
168 static void bn_GF2m_mul_1x1(BN_ULONG
*r1
, BN_ULONG
*r0
, const BN_ULONG a
, const BN_ULONG b
)
170 register BN_ULONG h
, l
, s
;
171 BN_ULONG tab
[16], top3b
= a
>> 61;
172 register BN_ULONG a1
, a2
, a4
, a8
;
174 a1
= a
& (0x1FFFFFFFFFFFFFFFULL
); a2
= a1
<< 1; a4
= a2
<< 1; a8
= a4
<< 1;
176 tab
[ 0] = 0; tab
[ 1] = a1
; tab
[ 2] = a2
; tab
[ 3] = a1
^a2
;
177 tab
[ 4] = a4
; tab
[ 5] = a1
^a4
; tab
[ 6] = a2
^a4
; tab
[ 7] = a1
^a2
^a4
;
178 tab
[ 8] = a8
; tab
[ 9] = a1
^a8
; tab
[10] = a2
^a8
; tab
[11] = a1
^a2
^a8
;
179 tab
[12] = a4
^a8
; tab
[13] = a1
^a4
^a8
; tab
[14] = a2
^a4
^a8
; tab
[15] = a1
^a2
^a4
^a8
;
181 s
= tab
[b
& 0xF]; l
= s
;
182 s
= tab
[b
>> 4 & 0xF]; l
^= s
<< 4; h
= s
>> 60;
183 s
= tab
[b
>> 8 & 0xF]; l
^= s
<< 8; h
^= s
>> 56;
184 s
= tab
[b
>> 12 & 0xF]; l
^= s
<< 12; h
^= s
>> 52;
185 s
= tab
[b
>> 16 & 0xF]; l
^= s
<< 16; h
^= s
>> 48;
186 s
= tab
[b
>> 20 & 0xF]; l
^= s
<< 20; h
^= s
>> 44;
187 s
= tab
[b
>> 24 & 0xF]; l
^= s
<< 24; h
^= s
>> 40;
188 s
= tab
[b
>> 28 & 0xF]; l
^= s
<< 28; h
^= s
>> 36;
189 s
= tab
[b
>> 32 & 0xF]; l
^= s
<< 32; h
^= s
>> 32;
190 s
= tab
[b
>> 36 & 0xF]; l
^= s
<< 36; h
^= s
>> 28;
191 s
= tab
[b
>> 40 & 0xF]; l
^= s
<< 40; h
^= s
>> 24;
192 s
= tab
[b
>> 44 & 0xF]; l
^= s
<< 44; h
^= s
>> 20;
193 s
= tab
[b
>> 48 & 0xF]; l
^= s
<< 48; h
^= s
>> 16;
194 s
= tab
[b
>> 52 & 0xF]; l
^= s
<< 52; h
^= s
>> 12;
195 s
= tab
[b
>> 56 & 0xF]; l
^= s
<< 56; h
^= s
>> 8;
196 s
= tab
[b
>> 60 ]; l
^= s
<< 60; h
^= s
>> 4;
198 /* compensate for the top three bits of a */
200 if (top3b
& 01) { l
^= b
<< 61; h
^= b
>> 3; }
201 if (top3b
& 02) { l
^= b
<< 62; h
^= b
>> 2; }
202 if (top3b
& 04) { l
^= b
<< 63; h
^= b
>> 1; }
208 /* Product of two polynomials a, b each with degree < 2 * BN_BITS2 - 1,
209 * result is a polynomial r with degree < 4 * BN_BITS2 - 1
210 * The caller MUST ensure that the variables have the right amount
211 * of space allocated.
213 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
)
216 /* r[3] = h1, r[2] = h0; r[1] = l1; r[0] = l0 */
217 bn_GF2m_mul_1x1(r
+3, r
+2, a1
, b1
);
218 bn_GF2m_mul_1x1(r
+1, r
, a0
, b0
);
219 bn_GF2m_mul_1x1(&m1
, &m0
, a0
^ a1
, b0
^ b1
);
220 /* Correction on m1 ^= l1 ^ h1; m0 ^= l0 ^ h0; */
221 r
[2] ^= m1
^ r
[1] ^ r
[3]; /* h0 ^= m1 ^ l1 ^ h1; */
222 r
[1] = r
[3] ^ r
[2] ^ r
[0] ^ m1
^ m0
; /* l1 ^= l0 ^ h0 ^ m0; */
225 void bn_GF2m_mul_2x2(BN_ULONG
*r
, BN_ULONG a1
, BN_ULONG a0
, BN_ULONG b1
, BN_ULONG b0
);
228 /* Add polynomials a and b and store result in r; r could be a or b, a and b
229 * could be equal; r is the bitwise XOR of a and b.
231 int BN_GF2m_add(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
)
234 const BIGNUM
*at
, *bt
;
239 if (a
->top
< b
->top
) { at
= b
; bt
= a
; }
240 else { at
= a
; bt
= b
; }
242 if(bn_wexpand(r
, at
->top
) == NULL
)
245 for (i
= 0; i
< bt
->top
; i
++)
247 r
->d
[i
] = at
->d
[i
] ^ bt
->d
[i
];
249 for (; i
< at
->top
; i
++)
261 /* Some functions allow for representation of the irreducible polynomials
262 * as an int[], say p. The irreducible f(t) is then of the form:
263 * t^p[0] + t^p[1] + ... + t^p[k]
264 * where m = p[0] > p[1] > ... > p[k] = 0.
268 /* Performs modular reduction of a and store result in r. r could be a. */
269 int BN_GF2m_mod_arr(BIGNUM
*r
, const BIGNUM
*a
, const int p
[])
279 /* reduction mod 1 => return 0 */
284 /* Since the algorithm does reduction in the r value, if a != r, copy
285 * the contents of a into r so we can do reduction in r.
289 if (!bn_wexpand(r
, a
->top
)) return 0;
290 for (j
= 0; j
< a
->top
; j
++)
298 /* start reduction */
299 dN
= p
[0] / BN_BITS2
;
300 for (j
= r
->top
- 1; j
> dN
;)
303 if (z
[j
] == 0) { j
--; continue; }
306 for (k
= 1; p
[k
] != 0; k
++)
308 /* reducing component t^p[k] */
310 d0
= n
% BN_BITS2
; d1
= BN_BITS2
- d0
;
313 if (d0
) z
[j
-n
-1] ^= (zz
<<d1
);
316 /* reducing component t^0 */
318 d0
= p
[0] % BN_BITS2
;
320 z
[j
-n
] ^= (zz
>> d0
);
321 if (d0
) z
[j
-n
-1] ^= (zz
<< d1
);
324 /* final round of reduction */
328 d0
= p
[0] % BN_BITS2
;
333 /* clear up the top d1 bits */
335 z
[dN
] = (z
[dN
] << d1
) >> d1
;
338 z
[0] ^= zz
; /* reduction t^0 component */
340 for (k
= 1; p
[k
] != 0; k
++)
344 /* reducing component t^p[k]*/
346 d0
= p
[k
] % BN_BITS2
;
349 tmp_ulong
= zz
>> d1
;
361 /* Performs modular reduction of a by p and store result in r. r could be a.
363 * This function calls down to the BN_GF2m_mod_arr implementation; this wrapper
364 * function is only provided for convenience; for best performance, use the
365 * BN_GF2m_mod_arr function.
367 int BN_GF2m_mod(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
)
373 ret
= BN_GF2m_poly2arr(p
, arr
, sizeof(arr
)/sizeof(arr
[0]));
374 if (!ret
|| ret
> (int)(sizeof(arr
)/sizeof(arr
[0])))
376 BNerr(BN_F_BN_GF2M_MOD
,BN_R_INVALID_LENGTH
);
379 ret
= BN_GF2m_mod_arr(r
, a
, arr
);
385 /* Compute the product of two polynomials a and b, reduce modulo p, and store
386 * the result in r. r could be a or b; a could be b.
388 int BN_GF2m_mod_mul_arr(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
, const int p
[], BN_CTX
*ctx
)
390 int zlen
, i
, j
, k
, ret
= 0;
392 BN_ULONG x1
, x0
, y1
, y0
, zz
[4];
399 return BN_GF2m_mod_sqr_arr(r
, a
, p
, ctx
);
403 if ((s
= BN_CTX_get(ctx
)) == NULL
) goto err
;
405 zlen
= a
->top
+ b
->top
+ 4;
406 if (!bn_wexpand(s
, zlen
)) goto err
;
409 for (i
= 0; i
< zlen
; i
++) s
->d
[i
] = 0;
411 for (j
= 0; j
< b
->top
; j
+= 2)
414 y1
= ((j
+1) == b
->top
) ? 0 : b
->d
[j
+1];
415 for (i
= 0; i
< a
->top
; i
+= 2)
418 x1
= ((i
+1) == a
->top
) ? 0 : a
->d
[i
+1];
419 bn_GF2m_mul_2x2(zz
, x1
, x0
, y1
, y0
);
420 for (k
= 0; k
< 4; k
++) s
->d
[i
+j
+k
] ^= zz
[k
];
425 if (BN_GF2m_mod_arr(r
, s
, p
))
434 /* Compute the product of two polynomials a and b, reduce modulo p, and store
435 * the result in r. r could be a or b; a could equal b.
437 * This function calls down to the BN_GF2m_mod_mul_arr implementation; this wrapper
438 * function is only provided for convenience; for best performance, use the
439 * BN_GF2m_mod_mul_arr function.
441 int BN_GF2m_mod_mul(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
, const BIGNUM
*p
, BN_CTX
*ctx
)
444 const int max
= BN_num_bits(p
) + 1;
449 if ((arr
= (int *)OPENSSL_malloc(sizeof(int) * max
)) == NULL
) goto err
;
450 ret
= BN_GF2m_poly2arr(p
, arr
, max
);
451 if (!ret
|| ret
> max
)
453 BNerr(BN_F_BN_GF2M_MOD_MUL
,BN_R_INVALID_LENGTH
);
456 ret
= BN_GF2m_mod_mul_arr(r
, a
, b
, arr
, ctx
);
459 if (arr
) OPENSSL_free(arr
);
464 /* Square a, reduce the result mod p, and store it in a. r could be a. */
465 int BN_GF2m_mod_sqr_arr(BIGNUM
*r
, const BIGNUM
*a
, const int p
[], BN_CTX
*ctx
)
472 if ((s
= BN_CTX_get(ctx
)) == NULL
) return 0;
473 if (!bn_wexpand(s
, 2 * a
->top
)) goto err
;
475 for (i
= a
->top
- 1; i
>= 0; i
--)
477 s
->d
[2*i
+1] = SQR1(a
->d
[i
]);
478 s
->d
[2*i
] = SQR0(a
->d
[i
]);
483 if (!BN_GF2m_mod_arr(r
, s
, p
)) goto err
;
491 /* Square a, reduce the result mod p, and store it in a. r could be a.
493 * This function calls down to the BN_GF2m_mod_sqr_arr implementation; this wrapper
494 * function is only provided for convenience; for best performance, use the
495 * BN_GF2m_mod_sqr_arr function.
497 int BN_GF2m_mod_sqr(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
, BN_CTX
*ctx
)
500 const int max
= BN_num_bits(p
) + 1;
505 if ((arr
= (int *)OPENSSL_malloc(sizeof(int) * max
)) == NULL
) goto err
;
506 ret
= BN_GF2m_poly2arr(p
, arr
, max
);
507 if (!ret
|| ret
> max
)
509 BNerr(BN_F_BN_GF2M_MOD_SQR
,BN_R_INVALID_LENGTH
);
512 ret
= BN_GF2m_mod_sqr_arr(r
, a
, arr
, ctx
);
515 if (arr
) OPENSSL_free(arr
);
520 /* Invert a, reduce modulo p, and store the result in r. r could be a.
521 * Uses Modified Almost Inverse Algorithm (Algorithm 10) from
522 * Hankerson, D., Hernandez, J.L., and Menezes, A. "Software Implementation
523 * of Elliptic Curve Cryptography Over Binary Fields".
525 int BN_GF2m_mod_inv(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
, BN_CTX
*ctx
)
527 BIGNUM
*b
, *c
= NULL
, *u
= NULL
, *v
= NULL
, *tmp
;
535 if ((b
= BN_CTX_get(ctx
))==NULL
) goto err
;
536 if ((c
= BN_CTX_get(ctx
))==NULL
) goto err
;
537 if ((u
= BN_CTX_get(ctx
))==NULL
) goto err
;
538 if ((v
= BN_CTX_get(ctx
))==NULL
) goto err
;
540 if (!BN_GF2m_mod(u
, a
, p
)) goto err
;
541 if (BN_is_zero(u
)) goto err
;
543 if (!BN_copy(v
, p
)) goto err
;
545 if (!BN_one(b
)) goto err
;
549 while (!BN_is_odd(u
))
551 if (BN_is_zero(u
)) goto err
;
552 if (!BN_rshift1(u
, u
)) goto err
;
555 if (!BN_GF2m_add(b
, b
, p
)) goto err
;
557 if (!BN_rshift1(b
, b
)) goto err
;
560 if (BN_abs_is_word(u
, 1)) break;
562 if (BN_num_bits(u
) < BN_num_bits(v
))
564 tmp
= u
; u
= v
; v
= tmp
;
565 tmp
= b
; b
= c
; c
= tmp
;
568 if (!BN_GF2m_add(u
, u
, v
)) goto err
;
569 if (!BN_GF2m_add(b
, b
, c
)) goto err
;
573 int i
, ubits
= BN_num_bits(u
),
574 vbits
= BN_num_bits(v
), /* v is copy of p */
576 BN_ULONG
*udp
,*bdp
,*vdp
,*cdp
;
578 bn_wexpand(u
,top
); udp
= u
->d
;
579 for (i
=u
->top
;i
<top
;i
++) udp
[i
] = 0;
581 bn_wexpand(b
,top
); bdp
= b
->d
;
583 for (i
=1;i
<top
;i
++) bdp
[i
] = 0;
585 bn_wexpand(c
,top
); cdp
= c
->d
;
586 for (i
=0;i
<top
;i
++) cdp
[i
] = 0;
588 vdp
= v
->d
; /* It pays off to "cache" *->d pointers, because
589 * it allows optimizer to be more aggressive.
590 * But we don't have to "cache" p->d, because *p
591 * is declared 'const'... */
594 while (ubits
&& !(udp
[0]&1))
596 BN_ULONG u0
,u1
,b0
,b1
,mask
;
600 mask
= (BN_ULONG
)0-(b0
&1);
602 for (i
=0;i
<top
-1;i
++)
605 udp
[i
] = ((u0
>>1)|(u1
<<(BN_BITS2
-1)))&BN_MASK2
;
607 b1
= bdp
[i
+1]^(p
->d
[i
+1]&mask
);
608 bdp
[i
] = ((b0
>>1)|(b1
<<(BN_BITS2
-1)))&BN_MASK2
;
616 if (ubits
<=BN_BITS2
&& udp
[0]==1) break;
620 i
= ubits
; ubits
= vbits
; vbits
= i
;
621 tmp
= u
; u
= v
; v
= tmp
;
622 tmp
= b
; b
= c
; c
= tmp
;
623 udp
= vdp
; vdp
= v
->d
;
624 bdp
= cdp
; cdp
= c
->d
;
634 int utop
= (ubits
-1)/BN_BITS2
;
636 while ((ul
=udp
[utop
])==0 && utop
) utop
--;
637 ubits
= utop
*BN_BITS2
+ BN_num_bits_word(ul
);
644 if (!BN_copy(r
, b
)) goto err
;
649 #ifdef BN_DEBUG /* BN_CTX_end would complain about the expanded form */
658 /* Invert xx, reduce modulo p, and store the result in r. r could be xx.
660 * This function calls down to the BN_GF2m_mod_inv implementation; this wrapper
661 * function is only provided for convenience; for best performance, use the
662 * BN_GF2m_mod_inv function.
664 int BN_GF2m_mod_inv_arr(BIGNUM
*r
, const BIGNUM
*xx
, const int p
[], BN_CTX
*ctx
)
671 if ((field
= BN_CTX_get(ctx
)) == NULL
) goto err
;
672 if (!BN_GF2m_arr2poly(p
, field
)) goto err
;
674 ret
= BN_GF2m_mod_inv(r
, xx
, field
, ctx
);
683 #ifndef OPENSSL_SUN_GF2M_DIV
684 /* Divide y by x, reduce modulo p, and store the result in r. r could be x
685 * or y, x could equal y.
687 int BN_GF2m_mod_div(BIGNUM
*r
, const BIGNUM
*y
, const BIGNUM
*x
, const BIGNUM
*p
, BN_CTX
*ctx
)
697 xinv
= BN_CTX_get(ctx
);
698 if (xinv
== NULL
) goto err
;
700 if (!BN_GF2m_mod_inv(xinv
, x
, p
, ctx
)) goto err
;
701 if (!BN_GF2m_mod_mul(r
, y
, xinv
, p
, ctx
)) goto err
;
710 /* Divide y by x, reduce modulo p, and store the result in r. r could be x
711 * or y, x could equal y.
712 * Uses algorithm Modular_Division_GF(2^m) from
713 * Chang-Shantz, S. "From Euclid's GCD to Montgomery Multiplication to
716 int BN_GF2m_mod_div(BIGNUM
*r
, const BIGNUM
*y
, const BIGNUM
*x
, const BIGNUM
*p
, BN_CTX
*ctx
)
718 BIGNUM
*a
, *b
, *u
, *v
;
731 if (v
== NULL
) goto err
;
733 /* reduce x and y mod p */
734 if (!BN_GF2m_mod(u
, y
, p
)) goto err
;
735 if (!BN_GF2m_mod(a
, x
, p
)) goto err
;
736 if (!BN_copy(b
, p
)) goto err
;
738 while (!BN_is_odd(a
))
740 if (!BN_rshift1(a
, a
)) goto err
;
741 if (BN_is_odd(u
)) if (!BN_GF2m_add(u
, u
, p
)) goto err
;
742 if (!BN_rshift1(u
, u
)) goto err
;
747 if (BN_GF2m_cmp(b
, a
) > 0)
749 if (!BN_GF2m_add(b
, b
, a
)) goto err
;
750 if (!BN_GF2m_add(v
, v
, u
)) goto err
;
753 if (!BN_rshift1(b
, b
)) goto err
;
754 if (BN_is_odd(v
)) if (!BN_GF2m_add(v
, v
, p
)) goto err
;
755 if (!BN_rshift1(v
, v
)) goto err
;
756 } while (!BN_is_odd(b
));
758 else if (BN_abs_is_word(a
, 1))
762 if (!BN_GF2m_add(a
, a
, b
)) goto err
;
763 if (!BN_GF2m_add(u
, u
, v
)) goto err
;
766 if (!BN_rshift1(a
, a
)) goto err
;
767 if (BN_is_odd(u
)) if (!BN_GF2m_add(u
, u
, p
)) goto err
;
768 if (!BN_rshift1(u
, u
)) goto err
;
769 } while (!BN_is_odd(a
));
773 if (!BN_copy(r
, u
)) goto err
;
783 /* Divide yy by xx, reduce modulo p, and store the result in r. r could be xx
784 * or yy, xx could equal yy.
786 * This function calls down to the BN_GF2m_mod_div implementation; this wrapper
787 * function is only provided for convenience; for best performance, use the
788 * BN_GF2m_mod_div function.
790 int BN_GF2m_mod_div_arr(BIGNUM
*r
, const BIGNUM
*yy
, const BIGNUM
*xx
, const int p
[], BN_CTX
*ctx
)
799 if ((field
= BN_CTX_get(ctx
)) == NULL
) goto err
;
800 if (!BN_GF2m_arr2poly(p
, field
)) goto err
;
802 ret
= BN_GF2m_mod_div(r
, yy
, xx
, field
, ctx
);
811 /* Compute the bth power of a, reduce modulo p, and store
812 * the result in r. r could be a.
813 * Uses simple square-and-multiply algorithm A.5.1 from IEEE P1363.
815 int BN_GF2m_mod_exp_arr(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
, const int p
[], BN_CTX
*ctx
)
826 if (BN_abs_is_word(b
, 1))
827 return (BN_copy(r
, a
) != NULL
);
830 if ((u
= BN_CTX_get(ctx
)) == NULL
) goto err
;
832 if (!BN_GF2m_mod_arr(u
, a
, p
)) goto err
;
834 n
= BN_num_bits(b
) - 1;
835 for (i
= n
- 1; i
>= 0; i
--)
837 if (!BN_GF2m_mod_sqr_arr(u
, u
, p
, ctx
)) goto err
;
838 if (BN_is_bit_set(b
, i
))
840 if (!BN_GF2m_mod_mul_arr(u
, u
, a
, p
, ctx
)) goto err
;
843 if (!BN_copy(r
, u
)) goto err
;
851 /* Compute the bth power of a, reduce modulo p, and store
852 * the result in r. r could be a.
854 * This function calls down to the BN_GF2m_mod_exp_arr implementation; this wrapper
855 * function is only provided for convenience; for best performance, use the
856 * BN_GF2m_mod_exp_arr function.
858 int BN_GF2m_mod_exp(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
, const BIGNUM
*p
, BN_CTX
*ctx
)
861 const int max
= BN_num_bits(p
) + 1;
866 if ((arr
= (int *)OPENSSL_malloc(sizeof(int) * max
)) == NULL
) goto err
;
867 ret
= BN_GF2m_poly2arr(p
, arr
, max
);
868 if (!ret
|| ret
> max
)
870 BNerr(BN_F_BN_GF2M_MOD_EXP
,BN_R_INVALID_LENGTH
);
873 ret
= BN_GF2m_mod_exp_arr(r
, a
, b
, arr
, ctx
);
876 if (arr
) OPENSSL_free(arr
);
880 /* Compute the square root of a, reduce modulo p, and store
881 * the result in r. r could be a.
882 * Uses exponentiation as in algorithm A.4.1 from IEEE P1363.
884 int BN_GF2m_mod_sqrt_arr(BIGNUM
*r
, const BIGNUM
*a
, const int p
[], BN_CTX
*ctx
)
893 /* reduction mod 1 => return 0 */
899 if ((u
= BN_CTX_get(ctx
)) == NULL
) goto err
;
901 if (!BN_set_bit(u
, p
[0] - 1)) goto err
;
902 ret
= BN_GF2m_mod_exp_arr(r
, a
, u
, p
, ctx
);
910 /* Compute the square root of a, reduce modulo p, and store
911 * the result in r. r could be a.
913 * This function calls down to the BN_GF2m_mod_sqrt_arr implementation; this wrapper
914 * function is only provided for convenience; for best performance, use the
915 * BN_GF2m_mod_sqrt_arr function.
917 int BN_GF2m_mod_sqrt(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
, BN_CTX
*ctx
)
920 const int max
= BN_num_bits(p
) + 1;
924 if ((arr
= (int *)OPENSSL_malloc(sizeof(int) * max
)) == NULL
) goto err
;
925 ret
= BN_GF2m_poly2arr(p
, arr
, max
);
926 if (!ret
|| ret
> max
)
928 BNerr(BN_F_BN_GF2M_MOD_SQRT
,BN_R_INVALID_LENGTH
);
931 ret
= BN_GF2m_mod_sqrt_arr(r
, a
, arr
, ctx
);
934 if (arr
) OPENSSL_free(arr
);
938 /* Find r such that r^2 + r = a mod p. r could be a. If no r exists returns 0.
939 * Uses algorithms A.4.7 and A.4.6 from IEEE P1363.
941 int BN_GF2m_mod_solve_quad_arr(BIGNUM
*r
, const BIGNUM
*a_
, const int p
[], BN_CTX
*ctx
)
943 int ret
= 0, count
= 0, j
;
944 BIGNUM
*a
, *z
, *rho
, *w
, *w2
, *tmp
;
950 /* reduction mod 1 => return 0 */
959 if (w
== NULL
) goto err
;
961 if (!BN_GF2m_mod_arr(a
, a_
, p
)) goto err
;
970 if (p
[0] & 0x1) /* m is odd */
972 /* compute half-trace of a */
973 if (!BN_copy(z
, a
)) goto err
;
974 for (j
= 1; j
<= (p
[0] - 1) / 2; j
++)
976 if (!BN_GF2m_mod_sqr_arr(z
, z
, p
, ctx
)) goto err
;
977 if (!BN_GF2m_mod_sqr_arr(z
, z
, p
, ctx
)) goto err
;
978 if (!BN_GF2m_add(z
, z
, a
)) goto err
;
984 rho
= BN_CTX_get(ctx
);
985 w2
= BN_CTX_get(ctx
);
986 tmp
= BN_CTX_get(ctx
);
987 if (tmp
== NULL
) goto err
;
990 if (!BN_rand(rho
, p
[0], 0, 0)) goto err
;
991 if (!BN_GF2m_mod_arr(rho
, rho
, p
)) goto err
;
993 if (!BN_copy(w
, rho
)) goto err
;
994 for (j
= 1; j
<= p
[0] - 1; j
++)
996 if (!BN_GF2m_mod_sqr_arr(z
, z
, p
, ctx
)) goto err
;
997 if (!BN_GF2m_mod_sqr_arr(w2
, w
, p
, ctx
)) goto err
;
998 if (!BN_GF2m_mod_mul_arr(tmp
, w2
, a
, p
, ctx
)) goto err
;
999 if (!BN_GF2m_add(z
, z
, tmp
)) goto err
;
1000 if (!BN_GF2m_add(w
, w2
, rho
)) goto err
;
1003 } while (BN_is_zero(w
) && (count
< MAX_ITERATIONS
));
1006 BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR
,BN_R_TOO_MANY_ITERATIONS
);
1011 if (!BN_GF2m_mod_sqr_arr(w
, z
, p
, ctx
)) goto err
;
1012 if (!BN_GF2m_add(w
, z
, w
)) goto err
;
1013 if (BN_GF2m_cmp(w
, a
))
1015 BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR
, BN_R_NO_SOLUTION
);
1019 if (!BN_copy(r
, z
)) goto err
;
1029 /* Find r such that r^2 + r = a mod p. r could be a. If no r exists returns 0.
1031 * This function calls down to the BN_GF2m_mod_solve_quad_arr implementation; this wrapper
1032 * function is only provided for convenience; for best performance, use the
1033 * BN_GF2m_mod_solve_quad_arr function.
1035 int BN_GF2m_mod_solve_quad(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
, BN_CTX
*ctx
)
1038 const int max
= BN_num_bits(p
) + 1;
1042 if ((arr
= (int *)OPENSSL_malloc(sizeof(int) *
1043 max
)) == NULL
) goto err
;
1044 ret
= BN_GF2m_poly2arr(p
, arr
, max
);
1045 if (!ret
|| ret
> max
)
1047 BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD
,BN_R_INVALID_LENGTH
);
1050 ret
= BN_GF2m_mod_solve_quad_arr(r
, a
, arr
, ctx
);
1053 if (arr
) OPENSSL_free(arr
);
1057 /* Convert the bit-string representation of a polynomial
1058 * ( \sum_{i=0}^n a_i * x^i) into an array of integers corresponding
1059 * to the bits with non-zero coefficient. Array is terminated with -1.
1060 * Up to max elements of the array will be filled. Return value is total
1061 * number of array elements that would be filled if array was large enough.
1063 int BN_GF2m_poly2arr(const BIGNUM
*a
, int p
[], int max
)
1071 for (i
= a
->top
- 1; i
>= 0; i
--)
1074 /* skip word if a->d[i] == 0 */
1077 for (j
= BN_BITS2
- 1; j
>= 0; j
--)
1081 if (k
< max
) p
[k
] = BN_BITS2
* i
+ j
;
1096 /* Convert the coefficient array representation of a polynomial to a
1097 * bit-string. The array must be terminated by -1.
1099 int BN_GF2m_arr2poly(const int p
[], BIGNUM
*a
)
1105 for (i
= 0; p
[i
] != -1; i
++)
1107 if (BN_set_bit(a
, p
[i
]) == 0)