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Binary field arithmetic contributed by Sun Microsystems.

Browse Source 
The 'OPENSSL_NO_SUN_DIV' default is still subject to change,
so I didn't bother to finish the CHANGES entry yet.

Submitted by: Douglas Stebila <douglas.stebila@sun.com>, Sheueling Chang <sheueling.chang@sun.com>
(CHANGES entry by Bodo Moeller)
This commit is contained in:
Bodo Möller 2002-08-02 13:03:55 +00:00
parent 16dc1cfb5c
commit 1dc920c8de
6 changed files with 1768 additions and 3 deletions
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52
CHANGES
View File

@ -4,6 +4,58 @@
Changes between 0.9.7 and 0.9.8 [xx XXX 2002]
*) Add binary polynomial arithmetic software in crypto/bn/bn_gf2m.c.
Polynomials are represented as BIGNUMs (where the sign bit is not
used) in the following functions [macros]:
BN_GF2m_add
BN_GF2m_sub [= BN_GF2m_add]
BN_GF2m_mod [wrapper for BN_GF2m_mod_arr]
BN_GF2m_mod_mul [wrapper for BN_GF2m_mod_mul_arr]
BN_GF2m_mod_sqr [wrapper for BN_GF2m_mod_sqr_arr]
BN_GF2m_mod_inv
BN_GF2m_mod_exp [wrapper for BN_GF2m_mod_exp_arr]
BN_GF2m_mod_sqrt [wrapper for BN_GF2m_mod_sqrt_arr]
BN_GF2m_mod_solve_quad [wrapper for BN_GF2m_mod_solve_quad_arr]
BN_GF2m_cmp [= BN_ucmp]
(Note that only the 'mod' functions are actually for fields GF(2^m).
BN_GF2m_add() is misnomer, but this is for the sake of consistency.)
For some functions, an the irreducible polynomial defining a
field can be given as an 'unsigned int[]' with strictly
decreasing elements giving the indices of those bits that are set;
i.e., p[] represents the polynomial
f(t) = t^p[0] + t^p[1] + ... + t^p[k]
where
p[0] > p[1] > ... > p[k] = 0.
This applies to the following functions:
BN_GF2m_mod_arr
BN_GF2m_mod_mul_arr
BN_GF2m_mod_sqr_arr
BN_GF2m_mod_inv_arr [wrapper for BN_GF2m_mod_inv]
BN_GF2m_mod_div_arr [wrapper for BN_GF2m_mod_div]
BN_GF2m_mod_exp_arr
BN_GF2m_mod_sqrt_arr
BN_GF2m_mod_solve_quad_arr
BN_GF2m_poly2arr
BN_GF2m_arr2poly
Conversion can be performed by the following functions:
BN_GF2m_poly2arr
BN_GF2m_arr2poly
bntest.c has additional tests for binary polynomial arithmetic.
Two implementations for BN_GF2m_mod_div() are available (selected
at compile-time). ...
TBD ... OPENSSL_NO_SUN_DIV ... --Bodo
[Sheueling Chang Shantz and Douglas Stebila
(Sun Microsystems Laboratories)]
*) Add more WAP/WTLS elliptic curve OIDs.
[Douglas Stebila <douglas.stebila@sun.com>]

11
crypto/bn/Makefile.ssl
View File

@ -39,12 +39,12 @@ LIB=$(TOP)/libcrypto.a
LIBSRC= bn_add.c bn_div.c bn_exp.c bn_lib.c bn_ctx.c bn_mul.c bn_mod.c \
bn_print.c bn_rand.c bn_shift.c bn_word.c bn_blind.c \
bn_kron.c bn_sqrt.c bn_gcd.c bn_prime.c bn_err.c bn_sqr.c bn_asm.c \
bn_recp.c bn_mont.c bn_mpi.c bn_exp2.c
bn_recp.c bn_mont.c bn_mpi.c bn_exp2.c bn_gf2m.c
LIBOBJ= bn_add.o bn_div.o bn_exp.o bn_lib.o bn_ctx.o bn_mul.o bn_mod.o \
bn_print.o bn_rand.o bn_shift.o bn_word.o bn_blind.o \
bn_kron.o bn_sqrt.o bn_gcd.o bn_prime.o bn_err.o bn_sqr.o $(BN_ASM) \
bn_recp.o bn_mont.o bn_mpi.o bn_exp2.o
bn_recp.o bn_mont.o bn_mpi.o bn_exp2.o bn_gf2m.o
SRC= $(LIBSRC)
@ -194,6 +194,13 @@ bn_asm.o: ../../include/openssl/lhash.h ../../include/openssl/opensslconf.h
bn_asm.o: ../../include/openssl/opensslv.h ../../include/openssl/safestack.h
bn_asm.o: ../../include/openssl/stack.h ../../include/openssl/symhacks.h
bn_asm.o: ../cryptlib.h bn_asm.c bn_lcl.h
bn_gf2m.o: ../../e_os.h ../../include/openssl/bio.h ../../include/openssl/bn.h
bn_gf2m.o: ../../include/openssl/buffer.h ../../include/openssl/crypto.h
bn_gf2m.o: ../../include/openssl/e_os2.h ../../include/openssl/err.h
bn_gf2m.o: ../../include/openssl/lhash.h ../../include/openssl/opensslconf.h
bn_gf2m.o: ../../include/openssl/opensslv.h ../../include/openssl/safestack.h
bn_gf2m.o: ../../include/openssl/stack.h ../../include/openssl/symhacks.h
bn_gf2m.o: ../cryptlib.h bn_gf2m.c bn_lcl.h
bn_blind.o: ../../e_os.h ../../include/openssl/bio.h ../../include/openssl/bn.h
bn_blind.o: ../../include/openssl/buffer.h ../../include/openssl/crypto.h
bn_blind.o: ../../include/openssl/e_os2.h ../../include/openssl/err.h

68
crypto/bn/bn.h
View File

@ -55,6 +55,32 @@
* copied and put under another distribution licence
* [including the GNU Public Licence.]
*/
/* ====================================================================
* Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
*
* Portions of the attached software ("Contribution") are developed by
* SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
*
* The Contribution is licensed pursuant to the Eric Young open source
* license provided above.
*
* In addition, Sun covenants to all licensees who provide a reciprocal
* covenant with respect to their own patents if any, not to sue under
* current and future patent claims necessarily infringed by the making,
* using, practicing, selling, offering for sale and/or otherwise
* disposing of the Contribution as delivered hereunder
* (or portions thereof), provided that such covenant shall not apply:
* 1) for code that a licensee deletes from the Contribution;
* 2) separates from the Contribution; or
* 3) for infringements caused by:
* i) the modification of the Contribution or
* ii) the combination of the Contribution with other software or
* devices where such combination causes the infringement.
*
* The binary polynomial arithmetic software is originally written by
* Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
*
*/
#ifndef HEADER_BN_H
#define HEADER_BN_H
@ -453,6 +479,40 @@ int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
int BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m,
BN_RECP_CTX *recp, BN_CTX *ctx);
/* Functions for arithmetic over binary polynomials represented by BIGNUMs.
*
* The BIGNUM::neg property of BIGNUMs representing binary polynomials is ignored.
*
* Note that input arguments are not const so that their bit arrays can
* be expanded to the appropriate size if needed.
*/
int BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); /* r = a + b */
#define BN_GF2m_sub(r, a, b) BN_GF2m_add(r, a, b)
int BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p); /* r = a mod p */
int BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx); /* r = (a * b) mod p */
int BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx); /* r = (a * a) mod p */
int BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx); /* r = (1 / b) mod p */
int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx); /* r = (a / b) mod p */
int BN_GF2m_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx); /* r = (a ^ b) mod p */
int BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx); /* r = sqrt(a) mod p */
int BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx); /* r^2 + r = a mod p */
#define BN_GF2m_cmp(a, b) BN_ucmp((a), (b))
/* Some functions allow for representation of the irreducible polynomials
* as an unsigned int[], say p. The irreducible f(t) is then of the form:
* t^p[0] + t^p[1] + ... + t^p[k]
* where m = p[0] > p[1] > ... > p[k] = 0.
*/
int BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const unsigned int p[]); /* r = a mod p */
int BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const unsigned int p[], BN_CTX *ctx); /* r = (a * b) mod p */
int BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const unsigned int p[], BN_CTX *ctx); /* r = (a * a) mod p */
int BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *b, const unsigned int p[], BN_CTX *ctx); /* r = (1 / b) mod p */
int BN_GF2m_mod_div_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const unsigned int p[], BN_CTX *ctx); /* r = (a / b) mod p */
int BN_GF2m_mod_exp_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const unsigned int p[], BN_CTX *ctx); /* r = (a ^ b) mod p */
int BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a, const unsigned int p[], BN_CTX *ctx); /* r = sqrt(a) mod p */
int BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a, const unsigned int p[], BN_CTX *ctx); /* r^2 + r = a mod p */
int BN_GF2m_poly2arr(const BIGNUM *a, unsigned int p[], int max);
int BN_GF2m_arr2poly(const unsigned int p[], BIGNUM *a);
/* library internal functions */
#define bn_expand(a,bits) ((((((bits+BN_BITS2-1))/BN_BITS2)) <= (a)->dmax)?\
@ -510,6 +570,13 @@ void ERR_load_BN_strings(void);
#define BN_F_BN_DIV 107
#define BN_F_BN_EXPAND2 108
#define BN_F_BN_EXPAND_INTERNAL 120
#define BN_F_BN_GF2M_MOD 126
#define BN_F_BN_GF2M_MOD_DIV 123
#define BN_F_BN_GF2M_MOD_EXP 127
#define BN_F_BN_GF2M_MOD_MUL 124
#define BN_F_BN_GF2M_MOD_SOLVE_QUAD 128
#define BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR 129
#define BN_F_BN_GF2M_MOD_SQR 125
#define BN_F_BN_MOD_EXP2_MONT 118
#define BN_F_BN_MOD_EXP_MONT 109
#define BN_F_BN_MOD_EXP_MONT_WORD 117
@ -535,6 +602,7 @@ void ERR_load_BN_strings(void);
#define BN_R_INVALID_LENGTH 106
#define BN_R_INVALID_RANGE 115
#define BN_R_NOT_A_SQUARE 111
#define BN_R_NOT_IMPLEMENTED 116
#define BN_R_NOT_INITIALIZED 107
#define BN_R_NO_INVERSE 108
#define BN_R_P_IS_NOT_PRIME 112

10
crypto/bn/bn_err.c
View File

@ -1,6 +1,6 @@
/* crypto/bn/bn_err.c */
/* ====================================================================
* Copyright (c) 1999 The OpenSSL Project. All rights reserved.
* Copyright (c) 1999-2002 The OpenSSL Project. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
@ -77,6 +77,13 @@ static ERR_STRING_DATA BN_str_functs[]=
{ERR_PACK(0,BN_F_BN_DIV,0), "BN_div"},
{ERR_PACK(0,BN_F_BN_EXPAND2,0), "bn_expand2"},
{ERR_PACK(0,BN_F_BN_EXPAND_INTERNAL,0), "BN_EXPAND_INTERNAL"},
{ERR_PACK(0,BN_F_BN_GF2M_MOD,0), "BN_GF2m_mod"},
{ERR_PACK(0,BN_F_BN_GF2M_MOD_DIV,0), "BN_GF2m_mod_div"},
{ERR_PACK(0,BN_F_BN_GF2M_MOD_EXP,0), "BN_GF2m_mod_exp"},
{ERR_PACK(0,BN_F_BN_GF2M_MOD_MUL,0), "BN_GF2m_mod_mul"},
{ERR_PACK(0,BN_F_BN_GF2M_MOD_SOLVE_QUAD,0), "BN_GF2m_mod_solve_quad"},
{ERR_PACK(0,BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR,0), "BN_GF2m_mod_solve_quad_arr"},
{ERR_PACK(0,BN_F_BN_GF2M_MOD_SQR,0), "BN_GF2m_mod_sqr"},
{ERR_PACK(0,BN_F_BN_MOD_EXP2_MONT,0), "BN_mod_exp2_mont"},
{ERR_PACK(0,BN_F_BN_MOD_EXP_MONT,0), "BN_mod_exp_mont"},
{ERR_PACK(0,BN_F_BN_MOD_EXP_MONT_WORD,0), "BN_mod_exp_mont_word"},
@ -105,6 +112,7 @@ static ERR_STRING_DATA BN_str_reasons[]=
{BN_R_INVALID_LENGTH ,"invalid length"},
{BN_R_INVALID_RANGE ,"invalid range"},
{BN_R_NOT_A_SQUARE ,"not a square"},
{BN_R_NOT_IMPLEMENTED ,"not implemented"},
{BN_R_NOT_INITIALIZED ,"not initialized"},
{BN_R_NO_INVERSE ,"no inverse"},
{BN_R_P_IS_NOT_PRIME ,"p is not prime"},

984
crypto/bn/bn_gf2m.c Normal file
View File

@ -0,0 +1,984 @@
/* crypto/bn/bn_gf2m.c */
/* ====================================================================
* Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
*
* The Elliptic Curve Public-Key Crypto Library (ECC Code) included
* herein is developed by SUN MICROSYSTEMS, INC., and is contributed
* to the OpenSSL project.
*
* The ECC Code is licensed pursuant to the OpenSSL open source
* license provided below.
*
* In addition, Sun covenants to all licensees who provide a reciprocal
* covenant with respect to their own patents if any, not to sue under
* current and future patent claims necessarily infringed by the making,
* using, practicing, selling, offering for sale and/or otherwise
* disposing of the ECC Code as delivered hereunder (or portions thereof),
* provided that such covenant shall not apply:
* 1) for code that a licensee deletes from the ECC Code;
* 2) separates from the ECC Code; or
* 3) for infringements caused by:
* i) the modification of the ECC Code or
* ii) the combination of the ECC Code with other software or
* devices where such combination causes the infringement.
*
* The software is originally written by Sheueling Chang Shantz and
* Douglas Stebila of Sun Microsystems Laboratories.
*
*/
/* ====================================================================
* Copyright (c) 1998-2002 The OpenSSL Project. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in
* the documentation and/or other materials provided with the
* distribution.
*
* 3. All advertising materials mentioning features or use of this
* software must display the following acknowledgment:
* "This product includes software developed by the OpenSSL Project
* for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
*
* 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
* endorse or promote products derived from this software without
* prior written permission. For written permission, please contact
* openssl-core@openssl.org.
*
* 5. Products derived from this software may not be called "OpenSSL"
* nor may "OpenSSL" appear in their names without prior written
* permission of the OpenSSL Project.
*
* 6. Redistributions of any form whatsoever must retain the following
* acknowledgment:
* "This product includes software developed by the OpenSSL Project
* for use in the OpenSSL Toolkit (http://www.openssl.org/)"
*
* THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
* EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
* ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
* STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
* OF THE POSSIBILITY OF SUCH DAMAGE.
* ====================================================================
*
* This product includes cryptographic software written by Eric Young
* (eay@cryptsoft.com). This product includes software written by Tim
* Hudson (tjh@cryptsoft.com).
*
*/
#include <assert.h>
#include <limits.h>
#include <stdio.h>
#include "cryptlib.h"
#include "bn_lcl.h"
/* Maximum number of iterations before BN_GF2m_mod_solve_quad_arr should fail. */
#define MAX_ITERATIONS 50
static const BN_ULONG SQR_tb[16] =
{ 0, 1, 4, 5, 16, 17, 20, 21,
64, 65, 68, 69, 80, 81, 84, 85 };
/* Platform-specific macros to accelerate squaring. */
#if defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG)
#define SQR1(w) \
SQR_tb[(w) >> 60 & 0xF] << 56 | SQR_tb[(w) >> 56 & 0xF] << 48 | \
SQR_tb[(w) >> 52 & 0xF] << 40 | SQR_tb[(w) >> 48 & 0xF] << 32 | \
SQR_tb[(w) >> 44 & 0xF] << 24 | SQR_tb[(w) >> 40 & 0xF] << 16 | \
SQR_tb[(w) >> 36 & 0xF] << 8 | SQR_tb[(w) >> 32 & 0xF]
#define SQR0(w) \
SQR_tb[(w) >> 28 & 0xF] << 56 | SQR_tb[(w) >> 24 & 0xF] << 48 | \
SQR_tb[(w) >> 20 & 0xF] << 40 | SQR_tb[(w) >> 16 & 0xF] << 32 | \
SQR_tb[(w) >> 12 & 0xF] << 24 | SQR_tb[(w) >> 8 & 0xF] << 16 | \
SQR_tb[(w) >> 4 & 0xF] << 8 | SQR_tb[(w) & 0xF]
#endif
#ifdef THIRTY_TWO_BIT
#define SQR1(w) \
SQR_tb[(w) >> 28 & 0xF] << 24 | SQR_tb[(w) >> 24 & 0xF] << 16 | \
SQR_tb[(w) >> 20 & 0xF] << 8 | SQR_tb[(w) >> 16 & 0xF]
#define SQR0(w) \
SQR_tb[(w) >> 12 & 0xF] << 24 | SQR_tb[(w) >> 8 & 0xF] << 16 | \
SQR_tb[(w) >> 4 & 0xF] << 8 | SQR_tb[(w) & 0xF]
#endif
#ifdef SIXTEEN_BIT
#define SQR1(w) \
SQR_tb[(w) >> 12 & 0xF] << 8 | SQR_tb[(w) >> 8 & 0xF]
#define SQR0(w) \
SQR_tb[(w) >> 4 & 0xF] << 8 | SQR_tb[(w) & 0xF]
#endif
#ifdef EIGHT_BIT
#define SQR1(w) \
SQR_tb[(w) >> 4 & 0xF]
#define SQR0(w) \
SQR_tb[(w) & 15]
#endif
/* Product of two polynomials a, b each with degree < BN_BITS2 - 1,
* result is a polynomial r with degree < 2 * BN_BITS - 1
* The caller MUST ensure that the variables have the right amount
* of space allocated.
*/
#ifdef EIGHT_BIT
static void bn_GF2m_mul_1x1(BN_ULONG *r1, BN_ULONG *r0, const BN_ULONG a, const BN_ULONG b)
{
register BN_ULONG h, l, s;
BN_ULONG tab[4], top1b = a >> 7;
register BN_ULONG a1, a2;
a1 = a & (0x7F); a2 = a1 << 1;
tab[0] = 0; tab[1] = a1; tab[2] = a2; tab[3] = a1^a2;
s = tab[b & 0x3]; l = s;
s = tab[b >> 2 & 0x3]; l ^= s << 2; h = s >> 6;
s = tab[b >> 4 & 0x3]; l ^= s << 4; h ^= s >> 4;
s = tab[b >> 6 ]; l ^= s << 6; h ^= s >> 2;
/* compensate for the top bit of a */
if (top1b & 01) { l ^= b << 7; h ^= b >> 1; }
*r1 = h; *r0 = l;
}
#endif
#ifdef SIXTEEN_BIT
static void bn_GF2m_mul_1x1(BN_ULONG *r1, BN_ULONG *r0, const BN_ULONG a, const BN_ULONG b)
{
register BN_ULONG h, l, s;
BN_ULONG tab[4], top1b = a >> 15;
register BN_ULONG a1, a2;
a1 = a & (0x7FFF); a2 = a1 << 1;
tab[0] = 0; tab[1] = a1; tab[2] = a2; tab[3] = a1^a2;
s = tab[b & 0x3]; l = s;
s = tab[b >> 2 & 0x3]; l ^= s << 2; h = s >> 14;
s = tab[b >> 4 & 0x3]; l ^= s << 4; h ^= s >> 12;
s = tab[b >> 6 & 0x3]; l ^= s << 6; h ^= s >> 10;
s = tab[b >> 8 & 0x3]; l ^= s << 8; h ^= s >> 8;
s = tab[b >>10 & 0x3]; l ^= s << 10; h ^= s >> 6;
s = tab[b >>12 & 0x3]; l ^= s << 12; h ^= s >> 4;
s = tab[b >>14 ]; l ^= s << 14; h ^= s >> 2;
/* compensate for the top bit of a */
if (top1b & 01) { l ^= b << 15; h ^= b >> 1; }
*r1 = h; *r0 = l;
}
#endif
#ifdef THIRTY_TWO_BIT
static void bn_GF2m_mul_1x1(BN_ULONG *r1, BN_ULONG *r0, const BN_ULONG a, const BN_ULONG b)
{
register BN_ULONG h, l, s;
BN_ULONG tab[8], top2b = a >> 30;
register BN_ULONG a1, a2, a4;
a1 = a & (0x3FFFFFFF); a2 = a1 << 1; a4 = a2 << 1;
tab[0] = 0; tab[1] = a1; tab[2] = a2; tab[3] = a1^a2;
tab[4] = a4; tab[5] = a1^a4; tab[6] = a2^a4; tab[7] = a1^a2^a4;
s = tab[b & 0x7]; l = s;
s = tab[b >> 3 & 0x7]; l ^= s << 3; h = s >> 29;
s = tab[b >> 6 & 0x7]; l ^= s << 6; h ^= s >> 26;
s = tab[b >> 9 & 0x7]; l ^= s << 9; h ^= s >> 23;
s = tab[b >> 12 & 0x7]; l ^= s << 12; h ^= s >> 20;
s = tab[b >> 15 & 0x7]; l ^= s << 15; h ^= s >> 17;
s = tab[b >> 18 & 0x7]; l ^= s << 18; h ^= s >> 14;
s = tab[b >> 21 & 0x7]; l ^= s << 21; h ^= s >> 11;
s = tab[b >> 24 & 0x7]; l ^= s << 24; h ^= s >> 8;
s = tab[b >> 27 & 0x7]; l ^= s << 27; h ^= s >> 5;
s = tab[b >> 30 ]; l ^= s << 30; h ^= s >> 2;
/* compensate for the top two bits of a */
if (top2b & 01) { l ^= b << 30; h ^= b >> 2; }
if (top2b & 02) { l ^= b << 31; h ^= b >> 1; }
*r1 = h; *r0 = l;
}
#endif
#if defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG)
static void bn_GF2m_mul_1x1(BN_ULONG *r1, BN_ULONG *r0, const BN_ULONG a, const BN_ULONG b)
{
register BN_ULONG h, l, s;
BN_ULONG tab[16], top3b = a >> 61;
register BN_ULONG a1, a2, a4, a8;
a1 = a & (0x1FFFFFFFFFFFFFFF); a2 = a1 << 1; a4 = a2 << 1; a8 = a4 << 1;
tab[ 0] = 0; tab[ 1] = a1; tab[ 2] = a2; tab[ 3] = a1^a2;
tab[ 4] = a4; tab[ 5] = a1^a4; tab[ 6] = a2^a4; tab[ 7] = a1^a2^a4;
tab[ 8] = a8; tab[ 9] = a1^a8; tab[10] = a2^a8; tab[11] = a1^a2^a8;
tab[12] = a4^a8; tab[13] = a1^a4^a8; tab[14] = a2^a4^a8; tab[15] = a1^a2^a4^a8;
s = tab[b & 0xF]; l = s;
s = tab[b >> 4 & 0xF]; l ^= s << 4; h = s >> 60;
s = tab[b >> 8 & 0xF]; l ^= s << 8; h ^= s >> 56;
s = tab[b >> 12 & 0xF]; l ^= s << 12; h ^= s >> 52;
s = tab[b >> 16 & 0xF]; l ^= s << 16; h ^= s >> 48;
s = tab[b >> 20 & 0xF]; l ^= s << 20; h ^= s >> 44;
s = tab[b >> 24 & 0xF]; l ^= s << 24; h ^= s >> 40;
s = tab[b >> 28 & 0xF]; l ^= s << 28; h ^= s >> 36;
s = tab[b >> 32 & 0xF]; l ^= s << 32; h ^= s >> 32;
s = tab[b >> 36 & 0xF]; l ^= s << 36; h ^= s >> 28;
s = tab[b >> 40 & 0xF]; l ^= s << 40; h ^= s >> 24;
s = tab[b >> 44 & 0xF]; l ^= s << 44; h ^= s >> 20;
s = tab[b >> 48 & 0xF]; l ^= s << 48; h ^= s >> 16;
s = tab[b >> 52 & 0xF]; l ^= s << 52; h ^= s >> 12;
s = tab[b >> 56 & 0xF]; l ^= s << 56; h ^= s >> 8;
s = tab[b >> 60 ]; l ^= s << 60; h ^= s >> 4;
/* compensate for the top three bits of a */
if (top3b & 01) { l ^= b << 61; h ^= b >> 3; }
if (top3b & 02) { l ^= b << 62; h ^= b >> 2; }
if (top3b & 04) { l ^= b << 63; h ^= b >> 1; }
*r1 = h; *r0 = l;
}
#endif
/* Product of two polynomials a, b each with degree < 2 * BN_BITS2 - 1,
* result is a polynomial r with degree < 4 * BN_BITS2 - 1
* The caller MUST ensure that the variables have the right amount
* of space allocated.
*/
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)
{
BN_ULONG m1, m0;
/* r[3] = h1, r[2] = h0; r[1] = l1; r[0] = l0 */
bn_GF2m_mul_1x1(r+3, r+2, a1, b1);
bn_GF2m_mul_1x1(r+1, r, a0, b0);
bn_GF2m_mul_1x1(&m1, &m0, a0 ^ a1, b0 ^ b1);
/* Correction on m1 ^= l1 ^ h1; m0 ^= l0 ^ h0; */
r[2] ^= m1 ^ r[1] ^ r[3]; /* h0 ^= m1 ^ l1 ^ h1; */
r[1] = r[3] ^ r[2] ^ r[0] ^ m1 ^ m0; /* l1 ^= l0 ^ h0 ^ m0; */
}
/* Add polynomials a and b and store result in r; r could be a or b, a and b
* could be equal; r is the bitwise XOR of a and b.
*/
int BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b)
{
int i;
const BIGNUM *at, *bt;
if (a->top < b->top) { at = b; bt = a; }
else { at = a; bt = b; }
bn_expand2(r, at->top);
for (i = 0; i < bt->top; i++)
{
r->d[i] = at->d[i] ^ bt->d[i];
}
for (; i < at->top; i++)
{
r->d[i] = at->d[i];
}
r->top = at->top;
bn_fix_top(r);
return 1;
}
/* Some functions allow for representation of the irreducible polynomials
* as an int[], say p. The irreducible f(t) is then of the form:
* t^p[0] + t^p[1] + ... + t^p[k]
* where m = p[0] > p[1] > ... > p[k] = 0.
*/
/* Performs modular reduction of a and store result in r. r could be a. */
int BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const unsigned int p[])
{
int j, k;
int n, dN, d0, d1;
BN_ULONG zz, *z;
/* Since the algorithm does reduction in place, if a == r, copy the
* contents of a into r so we can do reduction in r.
*/
if ((a != NULL) && (a->d != r->d))
{
if (!bn_wexpand(r, a->top)) return 0;
for (j = 0; j < a->top; j++)
{
r->d[j] = a->d[j];
}
r->top = a->top;
}
z = r->d;
/* start reduction */
dN = p[0] / BN_BITS2;
for (j = r->top - 1; j > dN;)
{
zz = z[j];
if (z[j] == 0) { j--; continue; }
z[j] = 0;
for (k = 1; p[k] > 0; k++)
{
/* reducing component t^p[k] */
n = p[0] - p[k];
d0 = n % BN_BITS2; d1 = BN_BITS2 - d0;
n /= BN_BITS2;
z[j-n] ^= (zz>>d0);
if (d0) z[j-n-1] ^= (zz<<d1);
}
/* reducing component t^0 */
n = dN;
d0 = p[0] % BN_BITS2;
d1 = BN_BITS2 - d0;
z[j-n] ^= (zz >> d0);
if (d0) z[j-n-1] ^= (zz << d1);
}
/* final round of reduction */
while (j == dN)
{
d0 = p[0] % BN_BITS2;
zz = z[dN] >> d0;
if (zz == 0) break;
d1 = BN_BITS2 - d0;
if (d0) z[dN] = (z[dN] << d1) >> d1; /* clear up the top d1 bits */
z[0] ^= zz; /* reduction t^0 component */
for (k = 1; p[k] > 0; k++)
{
/* reducing component t^p[k]*/
n = p[k] / BN_BITS2;
d0 = p[k] % BN_BITS2;
d1 = BN_BITS2 - d0;
z[n] ^= (zz << d0);
if (d0) z[n+1] ^= (zz >> d1);
}
}
bn_fix_top(r);
return 1;
}
/* Performs modular reduction of a by p and store result in r. r could be a.
*
* This function calls down to the BN_GF2m_mod_arr implementation; this wrapper
* function is only provided for convenience; for best performance, use the
* BN_GF2m_mod_arr function.
*/
int BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p)
{
const int max = BN_num_bits(p);
unsigned int *arr=NULL, ret = 0;
if ((arr = (unsigned int *)OPENSSL_malloc(sizeof(unsigned int) * max)) == NULL) goto err;
if (BN_GF2m_poly2arr(p, arr, max) > max)
{
BNerr(BN_F_BN_GF2M_MOD,BN_R_INVALID_LENGTH);
goto err;
}
ret = BN_GF2m_mod_arr(r, a, arr);
err:
if (arr) OPENSSL_free(arr);
return ret;
}
/* Compute the product of two polynomials a and b, reduce modulo p, and store
* the result in r. r could be a or b; a could be b.
*/
int BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const unsigned int p[], BN_CTX *ctx)
{
int zlen, i, j, k, ret = 0;
BIGNUM *s;
BN_ULONG x1, x0, y1, y0, zz[4];
if (a == b)
{
return BN_GF2m_mod_sqr_arr(r, a, p, ctx);
}
BN_CTX_start(ctx);
if ((s = BN_CTX_get(ctx)) == NULL) goto err;
zlen = a->top + b->top;
if (!bn_wexpand(s, zlen)) goto err;
s->top = zlen;
for (i = 0; i < zlen; i++) s->d[i] = 0;
for (j = 0; j < b->top; j += 2)
{
y0 = b->d[j];
y1 = ((j+1) == b->top) ? 0 : b->d[j+1];
for (i = 0; i < a->top; i += 2)
{
x0 = a->d[i];
x1 = ((i+1) == a->top) ? 0 : a->d[i+1];
bn_GF2m_mul_2x2(zz, x1, x0, y1, y0);
for (k = 0; k < 4; k++) s->d[i+j+k] ^= zz[k];
}
}
bn_fix_top(s);
BN_GF2m_mod_arr(r, s, p);
ret = 1;
err:
BN_CTX_end(ctx);
return ret;
}
/* Compute the product of two polynomials a and b, reduce modulo p, and store
* the result in r. r could be a or b; a could equal b.
*
* This function calls down to the BN_GF2m_mod_mul_arr implementation; this wrapper
* function is only provided for convenience; for best performance, use the
* BN_GF2m_mod_mul_arr function.
*/
int BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx)
{
const int max = BN_num_bits(p);
unsigned int *arr=NULL, ret = 0;
if ((arr = (unsigned int *)OPENSSL_malloc(sizeof(unsigned int) * max)) == NULL) goto err;
if (BN_GF2m_poly2arr(p, arr, max) > max)
{
BNerr(BN_F_BN_GF2M_MOD_MUL,BN_R_INVALID_LENGTH);
goto err;
}
ret = BN_GF2m_mod_mul_arr(r, a, b, arr, ctx);
err:
if (arr) OPENSSL_free(arr);
return ret;
}
/* Square a, reduce the result mod p, and store it in a. r could be a. */
int BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const unsigned int p[], BN_CTX *ctx)
{
int i, ret = 0;
BIGNUM *s;
BN_CTX_start(ctx);
if ((s = BN_CTX_get(ctx)) == NULL) return 0;
if (!bn_wexpand(s, 2 * a->top)) goto err;
for (i = a->top - 1; i >= 0; i--)
{
s->d[2*i+1] = SQR1(a->d[i]);
s->d[2*i ] = SQR0(a->d[i]);
}
s->top = 2 * a->top;
bn_fix_top(s);
if (!BN_GF2m_mod_arr(r, s, p)) goto err;
ret = 1;
err:
BN_CTX_end(ctx);
return ret;
}
/* Square a, reduce the result mod p, and store it in a. r could be a.
*
* This function calls down to the BN_GF2m_mod_sqr_arr implementation; this wrapper
* function is only provided for convenience; for best performance, use the
* BN_GF2m_mod_sqr_arr function.
*/
int BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
{
const int max = BN_num_bits(p);
unsigned int *arr=NULL, ret = 0;
if ((arr = (unsigned int *)OPENSSL_malloc(sizeof(unsigned int) * max)) == NULL) goto err;
if (BN_GF2m_poly2arr(p, arr, max) > max)
{
BNerr(BN_F_BN_GF2M_MOD_SQR,BN_R_INVALID_LENGTH);
goto err;
}
ret = BN_GF2m_mod_sqr_arr(r, a, arr, ctx);
err:
if (arr) OPENSSL_free(arr);
return ret;
}
/* Invert a, reduce modulo p, and store the result in r. r could be a.
* Uses Modified Almost Inverse Algorithm (Algorithm 10) from
* Hankerson, D., Hernandez, J.L., and Menezes, A. "Software Implementation
* of Elliptic Curve Cryptography Over Binary Fields".
*/
int BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
{
BIGNUM *b, *c, *u, *v, *tmp;
int ret = 0;
BN_CTX_start(ctx);
b = BN_CTX_get(ctx);
c = BN_CTX_get(ctx);
u = BN_CTX_get(ctx);
v = BN_CTX_get(ctx);
if (v == NULL) goto err;
if (!BN_one(b)) goto err;
if (!BN_zero(c)) goto err;
if (!BN_GF2m_mod(u, a, p)) goto err;
if (!BN_copy(v, p)) goto err;
u->neg = 0; /* Need to set u->neg = 0 because BN_is_one(u) checks
* the neg flag of the bignum.
*/
if (BN_is_zero(u)) goto err;
while (1)
{
while (!BN_is_odd(u))
{
if (!BN_rshift1(u, u)) goto err;
if (BN_is_odd(b))
{
if (!BN_GF2m_add(b, b, p)) goto err;
}
if (!BN_rshift1(b, b)) goto err;
}
if (BN_is_one(u)) break;
if (BN_num_bits(u) < BN_num_bits(v))
{
tmp = u; u = v; v = tmp;
tmp = b; b = c; c = tmp;
}
if (!BN_GF2m_add(u, u, v)) goto err;
if (!BN_GF2m_add(b, b, c)) goto err;
}
if (!BN_copy(r, b)) goto err;
ret = 1;
err:
BN_CTX_end(ctx);
return ret;
}
/* Invert xx, reduce modulo p, and store the result in r. r could be xx.
*
* This function calls down to the BN_GF2m_mod_inv implementation; this wrapper
* function is only provided for convenience; for best performance, use the
* BN_GF2m_mod_inv function.
*/
int BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *xx, const unsigned int p[], BN_CTX *ctx)
{
BIGNUM *field;
int ret = 0;
BN_CTX_start(ctx);
if ((field = BN_CTX_get(ctx)) == NULL) goto err;
if (!BN_GF2m_arr2poly(p, field)) goto err;
ret = BN_GF2m_mod_inv(r, xx, field, ctx);
err:
BN_CTX_end(ctx);
return ret;
}
#ifdef OPENSSL_NO_SUN_DIV
/* Divide y by x, reduce modulo p, and store the result in r. r could be x
* or y, x could equal y.
*/
int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *y, const BIGNUM *x, const BIGNUM *p, BN_CTX *ctx)
{
BIGNUM *xinv = NULL;
int ret = 0;
BN_CTX_start(ctx);
xinv = BN_CTX_get(ctx);
if (xinv == NULL) goto err;
if (!BN_GF2m_mod_inv(xinv, x, p, ctx)) goto err;
if (!BN_GF2m_mod_mul(r, y, xinv, p, ctx)) goto err;
ret = 1;
err:
BN_CTX_end(ctx);
return ret;
}
#else
/* Divide y by x, reduce modulo p, and store the result in r. r could be x
* or y, x could equal y.
* Uses algorithm Modular_Division_GF(2^m) from
* Chang-Shantz, S. "From Euclid's GCD to Montgomery Multiplication to
* the Great Divide".
*/
int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *y, const BIGNUM *x, const BIGNUM *p, BN_CTX *ctx)
{
BIGNUM *a, *b, *u, *v;
int ret = 0;
BN_CTX_start(ctx);
a = BN_CTX_get(ctx);
b = BN_CTX_get(ctx);
u = BN_CTX_get(ctx);
v = BN_CTX_get(ctx);
if (v == NULL) goto err;
/* reduce x and y mod p */
if (!BN_GF2m_mod(u, y, p)) goto err;
if (!BN_GF2m_mod(a, x, p)) goto err;
if (!BN_copy(b, p)) goto err;
if (!BN_zero(v)) goto err;
a->neg = 0; /* Need to set a->neg = 0 because BN_is_one(a) checks
* the neg flag of the bignum.
*/
while (!BN_is_odd(a))
{
if (!BN_rshift1(a, a)) goto err;
if (BN_is_odd(u)) if (!BN_GF2m_add(u, u, p)) goto err;
if (!BN_rshift1(u, u)) goto err;
}
do
{
if (BN_GF2m_cmp(b, a) > 0)
{
if (!BN_GF2m_add(b, b, a)) goto err;
if (!BN_GF2m_add(v, v, u)) goto err;
do
{
if (!BN_rshift1(b, b)) goto err;
if (BN_is_odd(v)) if (!BN_GF2m_add(v, v, p)) goto err;
if (!BN_rshift1(v, v)) goto err;
} while (!BN_is_odd(b));
}
else if (BN_is_one(a))
break;
else
{
if (!BN_GF2m_add(a, a, b)) goto err;
if (!BN_GF2m_add(u, u, v)) goto err;
do
{
if (!BN_rshift1(a, a)) goto err;
if (BN_is_odd(u)) if (!BN_GF2m_add(u, u, p)) goto err;
if (!BN_rshift1(u, u)) goto err;
} while (!BN_is_odd(a));
}
} while (1);
if (!BN_copy(r, u)) goto err;
ret = 1;
err:
BN_CTX_end(ctx);
return ret;
}
#endif
/* Divide yy by xx, reduce modulo p, and store the result in r. r could be xx
* or yy, xx could equal yy.
*
* This function calls down to the BN_GF2m_mod_div implementation; this wrapper
* function is only provided for convenience; for best performance, use the
* BN_GF2m_mod_div function.
*/
int BN_GF2m_mod_div_arr(BIGNUM *r, const BIGNUM *yy, const BIGNUM *xx, const unsigned int p[], BN_CTX *ctx)
{
BIGNUM *field;
int ret = 0;
BN_CTX_start(ctx);
if ((field = BN_CTX_get(ctx)) == NULL) goto err;
if (!BN_GF2m_arr2poly(p, field)) goto err;
ret = BN_GF2m_mod_div(r, yy, xx, field, ctx);
err:
BN_CTX_end(ctx);
return ret;
}
/* Compute the bth power of a, reduce modulo p, and store
* the result in r. r could be a.
* Uses simple square-and-multiply algorithm A.5.1 from IEEE P1363.
*/
int BN_GF2m_mod_exp_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const unsigned int p[], BN_CTX *ctx)
{
int ret = 0, i, n;
BIGNUM *u;
if (BN_is_zero(b))
{
return(BN_one(r));
}
BN_CTX_start(ctx);
if ((u = BN_CTX_get(ctx)) == NULL) goto err;
if (!BN_GF2m_mod_arr(u, a, p)) goto err;
n = BN_num_bits(b) - 1;
for (i = n - 1; i >= 0; i--)
{
if (!BN_GF2m_mod_sqr_arr(u, u, p, ctx)) goto err;
if (BN_is_bit_set(b, i))
{
if (!BN_GF2m_mod_mul_arr(u, u, a, p, ctx)) goto err;
}
}
if (!BN_copy(r, u)) goto err;
ret = 1;
err:
BN_CTX_end(ctx);
return ret;
}
/* Compute the bth power of a, reduce modulo p, and store
* the result in r. r could be a.
*
* This function calls down to the BN_GF2m_mod_exp_arr implementation; this wrapper
* function is only provided for convenience; for best performance, use the
* BN_GF2m_mod_exp_arr function.
*/
int BN_GF2m_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx)
{
const int max = BN_num_bits(p);
unsigned int *arr=NULL, ret = 0;
if ((arr = (unsigned int *)OPENSSL_malloc(sizeof(unsigned int) * max)) == NULL) goto err;
if (BN_GF2m_poly2arr(p, arr, max) > max)
{
BNerr(BN_F_BN_GF2M_MOD_EXP,BN_R_INVALID_LENGTH);
goto err;
}
ret = BN_GF2m_mod_exp_arr(r, a, b, arr, ctx);
err:
if (arr) OPENSSL_free(arr);
return ret;
}
/* Compute the square root of a, reduce modulo p, and store
* the result in r. r could be a.
* Uses exponentiation as in algorithm A.4.1 from IEEE P1363.
*/
int BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a, const unsigned int p[], BN_CTX *ctx)
{
int ret = 0;
BIGNUM *u;
BN_CTX_start(ctx);
if ((u = BN_CTX_get(ctx)) == NULL) goto err;
if (!BN_zero(u)) goto err;
if (!BN_set_bit(u, p[0] - 1)) goto err;
ret = BN_GF2m_mod_exp_arr(r, a, u, p, ctx);
err:
BN_CTX_end(ctx);
return ret;
}
/* Compute the square root of a, reduce modulo p, and store
* the result in r. r could be a.
*
* This function calls down to the BN_GF2m_mod_sqrt_arr implementation; this wrapper
* function is only provided for convenience; for best performance, use the
* BN_GF2m_mod_sqrt_arr function.
*/
int BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
{
const int max = BN_num_bits(p);
unsigned int *arr=NULL, ret = 0;
if ((arr = (unsigned int *)OPENSSL_malloc(sizeof(unsigned int) * max)) == NULL) goto err;
if (BN_GF2m_poly2arr(p, arr, max) > max)
{
BNerr(BN_F_BN_GF2M_MOD_EXP,BN_R_INVALID_LENGTH);
goto err;
}
ret = BN_GF2m_mod_sqrt_arr(r, a, arr, ctx);
err:
if (arr) OPENSSL_free(arr);
return ret;
}
/* Find r such that r^2 + r = a mod p. r could be a. If no r exists returns 0.
* Uses algorithms A.4.7 and A.4.6 from IEEE P1363.
*/
int BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a_, const unsigned int p[], BN_CTX *ctx)
{
int ret = 0, i, count = 0;
BIGNUM *a, *z, *rho, *w, *w2, *tmp;
BN_CTX_start(ctx);
a = BN_CTX_get(ctx);
z = BN_CTX_get(ctx);
w = BN_CTX_get(ctx);
if (w == NULL) goto err;
if (!BN_GF2m_mod_arr(a, a_, p)) goto err;
if (BN_is_zero(a))
{
ret = BN_zero(r);
goto err;
}
if (p[0] & 0x1) /* m is odd */
{
/* compute half-trace of a */
if (!BN_copy(z, a)) goto err;
for (i = 1; i <= (p[0] - 1) / 2; i++)
{
if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx)) goto err;
if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx)) goto err;
if (!BN_GF2m_add(z, z, a)) goto err;
}
}
else /* m is even */
{
rho = BN_CTX_get(ctx);
w2 = BN_CTX_get(ctx);
tmp = BN_CTX_get(ctx);
if (tmp == NULL) goto err;
do
{
if (!BN_rand(rho, p[0], 0, 0)) goto err;
if (!BN_GF2m_mod_arr(rho, rho, p)) goto err;
if (!BN_zero(z)) goto err;
if (!BN_copy(w, rho)) goto err;
for (i = 1; i <= p[0] - 1; i++)
{
if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx)) goto err;
if (!BN_GF2m_mod_sqr_arr(w2, w, p, ctx)) goto err;
if (!BN_GF2m_mod_mul_arr(tmp, w2, a, p, ctx)) goto err;
if (!BN_GF2m_add(z, z, tmp)) goto err;
if (!BN_GF2m_add(w, w2, rho)) goto err;
}
count++;
} while (BN_is_zero(w) && (count < MAX_ITERATIONS));
if (BN_is_zero(w))
{
BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR,BN_R_TOO_MANY_ITERATIONS);
goto err;
}
}
if (!BN_GF2m_mod_sqr_arr(w, z, p, ctx)) goto err;
if (!BN_GF2m_add(w, z, w)) goto err;
if (BN_GF2m_cmp(w, a)) goto err;
if (!BN_copy(r, z)) goto err;
ret = 1;
err:
BN_CTX_end(ctx);
return ret;
}
/* Find r such that r^2 + r = a mod p. r could be a. If no r exists returns 0.
*
* This function calls down to the BN_GF2m_mod_solve_quad_arr implementation; this wrapper
* function is only provided for convenience; for best performance, use the
* BN_GF2m_mod_solve_quad_arr function.
*/
int BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
{
const int max = BN_num_bits(p);
unsigned int *arr=NULL, ret = 0;
if ((arr = (unsigned int *)OPENSSL_malloc(sizeof(unsigned int) * max)) == NULL) goto err;
if (BN_GF2m_poly2arr(p, arr, max) > max)
{
BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD,BN_R_INVALID_LENGTH);
goto err;
}
ret = BN_GF2m_mod_solve_quad_arr(r, a, arr, ctx);
err:
if (arr) OPENSSL_free(arr);
return ret;
}
/* Convert the bit-string representation of a polynomial a into an array
* of integers corresponding to the bits with non-zero coefficient.
* Up to max elements of the array will be filled. Return value is total
* number of coefficients that would be extracted if array was large enough.
*/
int BN_GF2m_poly2arr(const BIGNUM *a, unsigned int p[], int max)
{
int i, j, k;
BN_ULONG mask;
for (k = 0; k < max; k++) p[k] = 0;
k = 0;
for (i = a->top - 1; i >= 0; i--)
{
mask = BN_TBIT;
for (j = BN_BITS2 - 1; j >= 0; j--)
{
if (a->d[i] & mask)
{
if (k < max) p[k] = BN_BITS2 * i + j;
k++;
}
mask >>= 1;
}
}
return k;
}
/* Convert the coefficient array representation of a polynomial to a
* bit-string. The array must be terminated by 0.
*/
int BN_GF2m_arr2poly(const unsigned int p[], BIGNUM *a)
{
int i;
BN_zero(a);
for (i = 0; p[i] > 0; i++)
{
BN_set_bit(a, p[i]);
}
BN_set_bit(a, 0);
return 1;
}

646
crypto/bn/bntest.c
View File

@ -55,6 +55,32 @@
* copied and put under another distribution licence
* [including the GNU Public Licence.]
*/
/* ====================================================================
* Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
*
* Portions of the attached software ("Contribution") are developed by
* SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
*
* The Contribution is licensed pursuant to the Eric Young open source
* license provided above.
*
* In addition, Sun covenants to all licensees who provide a reciprocal
* covenant with respect to their own patents if any, not to sue under
* current and future patent claims necessarily infringed by the making,
* using, practicing, selling, offering for sale and/or otherwise
* disposing of the Contribution as delivered hereunder
* (or portions thereof), provided that such covenant shall not apply:
* 1) for code that a licensee deletes from the Contribution;
* 2) separates from the Contribution; or
* 3) for infringements caused by:
* i) the modification of the Contribution or
* ii) the combination of the Contribution with other software or
* devices where such combination causes the infringement.
*
* The binary polynomial arithmetic software is originally written by
* Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
*
*/
#include <stdio.h>
#include <stdlib.h>
@ -91,6 +117,15 @@ int test_mod(BIO *bp,BN_CTX *ctx);
int test_mod_mul(BIO *bp,BN_CTX *ctx);
int test_mod_exp(BIO *bp,BN_CTX *ctx);
int test_exp(BIO *bp,BN_CTX *ctx);
int test_gf2m_add(BIO *bp);
int test_gf2m_mod(BIO *bp);
int test_gf2m_mod_mul(BIO *bp,BN_CTX *ctx);
int test_gf2m_mod_sqr(BIO *bp,BN_CTX *ctx);
int test_gf2m_mod_inv(BIO *bp,BN_CTX *ctx);
int test_gf2m_mod_div(BIO *bp,BN_CTX *ctx);
int test_gf2m_mod_exp(BIO *bp,BN_CTX *ctx);
int test_gf2m_mod_sqrt(BIO *bp,BN_CTX *ctx);
int test_gf2m_mod_solve_quad(BIO *bp,BN_CTX *ctx);
int test_kron(BIO *bp,BN_CTX *ctx);
int test_sqrt(BIO *bp,BN_CTX *ctx);
int rand_neg(void);
@ -226,6 +261,42 @@ int main(int argc, char *argv[])
if (!test_exp(out,ctx)) goto err;
BIO_flush(out);
message(out,"BN_GF2m_add");
if (!test_gf2m_add(out)) goto err;
BIO_flush(out);
message(out,"BN_GF2m_mod");
if (!test_gf2m_mod(out)) goto err;
BIO_flush(out);
message(out,"BN_GF2m_mod_mul");
if (!test_gf2m_mod_mul(out,ctx)) goto err;
BIO_flush(out);
message(out,"BN_GF2m_mod_sqr");
if (!test_gf2m_mod_sqr(out,ctx)) goto err;
BIO_flush(out);
message(out,"BN_GF2m_mod_inv");
if (!test_gf2m_mod_inv(out,ctx)) goto err;
BIO_flush(out);
message(out,"BN_GF2m_mod_div");
if (!test_gf2m_mod_div(out,ctx)) goto err;
BIO_flush(out);
message(out,"BN_GF2m_mod_exp");
if (!test_gf2m_mod_exp(out,ctx)) goto err;
BIO_flush(out);
message(out,"BN_GF2m_mod_sqrt");
if (!test_gf2m_mod_sqrt(out,ctx)) goto err;
BIO_flush(out);
message(out,"BN_GF2m_mod_solve_quad");
if (!test_gf2m_mod_solve_quad(out,ctx)) goto err;
BIO_flush(out);
message(out,"BN_kronecker");
if (!test_kron(out,ctx)) goto err;
BIO_flush(out);
@ -872,6 +943,581 @@ int test_exp(BIO *bp, BN_CTX *ctx)
return(1);
}
int test_gf2m_add(BIO *bp)
{
BIGNUM a,b,c;
int i, ret = 0;
BN_init(&a);
BN_init(&b);
BN_init(&c);
for (i=0; i<num0; i++)
{
BN_rand(&a,512,0,0);
BN_copy(&b, BN_value_one());
a.neg=rand_neg();
b.neg=rand_neg();
BN_GF2m_add(&c,&a,&b);
#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
if (bp != NULL)
{
if (!results)
{
BN_print(bp,&a);
BIO_puts(bp," ^ ");
BN_print(bp,&b);
BIO_puts(bp," = ");
}
BN_print(bp,&c);
BIO_puts(bp,"\n");
}
#endif
/* Test that two added values have the correct parity. */
if((BN_is_odd(&a) && BN_is_odd(&c)) || (!BN_is_odd(&a) && !BN_is_odd(&c)))
{
fprintf(stderr,"GF(2^m) addition test (a) failed!\n");
goto err;
}
BN_GF2m_add(&c,&c,&c);
/* Test that c + c = 0. */
if(!BN_is_zero(&c))
{
fprintf(stderr,"GF(2^m) addition test (b) failed!\n");
goto err;
}
}
ret = 1;
err:
BN_free(&a);
BN_free(&b);
BN_free(&c);
return ret;
}
int test_gf2m_mod(BIO *bp)
{
BIGNUM *a,*b[2],*c,*d,*e;
int i, j, ret = 0;
unsigned int p0[] = {163,7,6,3,0};
unsigned int p1[] = {193,15,0};
a=BN_new();
b[0]=BN_new();
b[1]=BN_new();
c=BN_new();
d=BN_new();
e=BN_new();
BN_GF2m_arr2poly(p0, b[0]);
BN_GF2m_arr2poly(p1, b[1]);
for (i=0; i<num0; i++)
{
BN_bntest_rand(a, 1024, 0, 0);
for (j=0; j < 2; j++)
{
BN_GF2m_mod(c, a, b[j]);
#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
if (bp != NULL)
{
if (!results)
{
BN_print(bp,a);
BIO_puts(bp," % ");
BN_print(bp,b[j]);
BIO_puts(bp," - ");
BN_print(bp,c);
BIO_puts(bp,"\n");
}
}
#endif
BN_GF2m_add(d, a, c);
BN_GF2m_mod(e, d, b[j]);
/* Test that a + (a mod p) mod p == 0. */
if(!BN_is_zero(e))
{
fprintf(stderr,"GF(2^m) modulo test failed!\n");
goto err;
}
}
}
ret = 1;
err:
BN_free(a);
BN_free(b[0]);
BN_free(b[1]);
BN_free(c);
BN_free(d);
BN_free(e);
return ret;
}
int test_gf2m_mod_mul(BIO *bp,BN_CTX *ctx)
{
BIGNUM *a,*b[2],*c,*d,*e,*f,*g,*h;
int i, j, ret = 0;
unsigned int p0[] = {163,7,6,3,0};
unsigned int p1[] = {193,15,0};
a=BN_new();
b[0]=BN_new();
b[1]=BN_new();
c=BN_new();
d=BN_new();
e=BN_new();
f=BN_new();
g=BN_new();
h=BN_new();
BN_GF2m_arr2poly(p0, b[0]);
BN_GF2m_arr2poly(p1, b[1]);
for (i=0; i<num0; i++)
{
BN_bntest_rand(a, 1024, 0, 0);
BN_bntest_rand(c, 1024, 0, 0);
BN_bntest_rand(d, 1024, 0, 0);
for (j=0; j < 2; j++)
{
BN_GF2m_mod_mul(e, a, c, b[j], ctx);
#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
if (bp != NULL)
{
if (!results)
{
BN_print(bp,a);
BIO_puts(bp," * ");
BN_print(bp,c);
BIO_puts(bp," % ");
BN_print(bp,b[j]);
BIO_puts(bp," - ");
BN_print(bp,e);
BIO_puts(bp,"\n");
}
}
#endif
BN_GF2m_add(f, a, d);
BN_GF2m_mod_mul(g, f, c, b[j], ctx);
BN_GF2m_mod_mul(h, d, c, b[j], ctx);
BN_GF2m_add(f, e, g);
BN_GF2m_add(f, f, h);
/* Test that (a+d)*c = a*c + d*c. */
if(!BN_is_zero(f))
{
fprintf(stderr,"GF(2^m) modular multiplication test failed!\n");
goto err;
}
}
}
ret = 1;
err:
BN_free(a);
BN_free(b[0]);
BN_free(b[1]);
BN_free(c);
BN_free(d);
BN_free(e);
BN_free(f);
BN_free(g);
BN_free(h);
return ret;
}
int test_gf2m_mod_sqr(BIO *bp,BN_CTX *ctx)
{
BIGNUM *a,*b[2],*c,*d;
int i, j, ret = 0;
unsigned int p0[] = {163,7,6,3,0};
unsigned int p1[] = {193,15,0};
a=BN_new();
b[0]=BN_new();
b[1]=BN_new();
c=BN_new();
d=BN_new();
BN_GF2m_arr2poly(p0, b[0]);
BN_GF2m_arr2poly(p1, b[1]);
for (i=0; i<num0; i++)
{
BN_bntest_rand(a, 1024, 0, 0);
for (j=0; j < 2; j++)
{
BN_GF2m_mod_sqr(c, a, b[j], ctx);
BN_copy(d, a);
BN_GF2m_mod_mul(d, a, d, b[j], ctx);
#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
if (bp != NULL)
{
if (!results)
{
BN_print(bp,a);
BIO_puts(bp," ^ 2 % ");
BN_print(bp,b[j]);
BIO_puts(bp, " = ");
BN_print(bp,c);
BIO_puts(bp,"; a * a = ");
BN_print(bp,d);
BIO_puts(bp,"\n");
}
}
#endif
BN_GF2m_add(d, c, d);
/* Test that a*a = a^2. */
if(!BN_is_zero(d))
{
fprintf(stderr,"GF(2^m) modular squaring test failed!\n");
goto err;
}
}
}
ret = 1;
err:
BN_free(a);
BN_free(b[0]);
BN_free(b[1]);
BN_free(c);
BN_free(d);
return ret;
}
int test_gf2m_mod_inv(BIO *bp,BN_CTX *ctx)
{
BIGNUM *a,*b[2],*c,*d;
int i, j, ret = 0;
unsigned int p0[] = {163,7,6,3,0};
unsigned int p1[] = {193,15,0};
a=BN_new();
b[0]=BN_new();
b[1]=BN_new();
c=BN_new();
d=BN_new();
BN_GF2m_arr2poly(p0, b[0]);
BN_GF2m_arr2poly(p1, b[1]);
for (i=0; i<num0; i++)
{
BN_bntest_rand(a, 512, 0, 0);
for (j=0; j < 2; j++)
{
BN_GF2m_mod_inv(c, a, b[j], ctx);
BN_GF2m_mod_mul(d, a, c, b[j], ctx);
#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
if (bp != NULL)
{
if (!results)
{
BN_print(bp,a);
BIO_puts(bp, " * ");
BN_print(bp,c);
BIO_puts(bp," - 1 % ");
BN_print(bp,b[j]);
BIO_puts(bp,"\n");
}
}
#endif
/* Test that ((1/a)*a) = 1. */
if(!BN_is_one(d))
{
fprintf(stderr,"GF(2^m) modular inversion test failed!\n");
goto err;
}
}
}
ret = 1;
err:
BN_free(a);
BN_free(b[0]);
BN_free(b[1]);
BN_free(c);
BN_free(d);
return ret;
}
int test_gf2m_mod_div(BIO *bp,BN_CTX *ctx)
{
BIGNUM *a,*b[2],*c,*d,*e,*f;
int i, j, ret = 0;
unsigned int p0[] = {163,7,6,3,0};
unsigned int p1[] = {193,15,0};
a=BN_new();
b[0]=BN_new();
b[1]=BN_new();
c=BN_new();
d=BN_new();
e=BN_new();
f=BN_new();
BN_GF2m_arr2poly(p0, b[0]);
BN_GF2m_arr2poly(p1, b[1]);
for (i=0; i<num0; i++)
{
BN_bntest_rand(a, 512, 0, 0);
BN_bntest_rand(c, 512, 0, 0);
for (j=0; j < 2; j++)
{
BN_GF2m_mod_div(d, a, c, b[j], ctx);
BN_GF2m_mod_mul(e, d, c, b[j], ctx);
BN_GF2m_mod_div(f, a, e, b[j], ctx);
#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
if (bp != NULL)
{
if (!results)
{
BN_print(bp,a);
BIO_puts(bp, " = ");
BN_print(bp,c);
BIO_puts(bp," * ");
BN_print(bp,d);
BIO_puts(bp, " % ");
BN_print(bp,b[j]);
BIO_puts(bp,"\n");
}
}
#endif
/* Test that ((a/c)*c)/a = 1. */
if(!BN_is_one(f))
{
fprintf(stderr,"GF(2^m) modular division test failed!\n");
goto err;
}
}
}
ret = 1;
err:
BN_free(a);
BN_free(b[0]);
BN_free(b[1]);
BN_free(c);
BN_free(d);
BN_free(e);
BN_free(f);
return ret;
}
int test_gf2m_mod_exp(BIO *bp,BN_CTX *ctx)
{
BIGNUM *a,*b[2],*c,*d,*e,*f;
int i, j, ret = 0;
unsigned int p0[] = {163,7,6,3,0};
unsigned int p1[] = {193,15,0};
a=BN_new();
b[0]=BN_new();
b[1]=BN_new();
c=BN_new();
d=BN_new();
e=BN_new();
f=BN_new();
BN_GF2m_arr2poly(p0, b[0]);
BN_GF2m_arr2poly(p1, b[1]);
for (i=0; i<num0; i++)
{
BN_bntest_rand(a, 512, 0, 0);
BN_bntest_rand(c, 512, 0, 0);
BN_bntest_rand(d, 512, 0, 0);
for (j=0; j < 2; j++)
{
BN_GF2m_mod_exp(e, a, c, b[j], ctx);
BN_GF2m_mod_exp(f, a, d, b[j], ctx);
BN_GF2m_mod_mul(e, e, f, b[j], ctx);
BN_add(f, c, d);
BN_GF2m_mod_exp(f, a, f, b[j], ctx);
#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
if (bp != NULL)
{
if (!results)
{
BN_print(bp,a);
BIO_puts(bp, " ^ (");
BN_print(bp,c);
BIO_puts(bp," + ");
BN_print(bp,d);
BIO_puts(bp, ") = ");
BN_print(bp,e);
BIO_puts(bp, "; - ");
BN_print(bp,f);
BIO_puts(bp, " % ");
BN_print(bp,b[j]);
BIO_puts(bp,"\n");
}
}
#endif
BN_GF2m_add(f, e, f);
/* Test that a^(c+d)=a^c*a^d. */
if(!BN_is_zero(f))
{
fprintf(stderr,"GF(2^m) modular exponentiation test failed!\n");
goto err;
}
}
}
ret = 1;
err:
BN_free(a);
BN_free(b[0]);
BN_free(b[1]);
BN_free(c);
BN_free(d);
BN_free(e);
BN_free(f);
return ret;
}
int test_gf2m_mod_sqrt(BIO *bp,BN_CTX *ctx)
{
BIGNUM *a,*b[2],*c,*d,*e,*f;
int i, j, ret = 0;
unsigned int p0[] = {163,7,6,3,0};
unsigned int p1[] = {193,15,0};
a=BN_new();
b[0]=BN_new();
b[1]=BN_new();
c=BN_new();
d=BN_new();
e=BN_new();
f=BN_new();
BN_GF2m_arr2poly(p0, b[0]);
BN_GF2m_arr2poly(p1, b[1]);
for (i=0; i<num0; i++)
{
BN_bntest_rand(a, 512, 0, 0);
for (j=0; j < 2; j++)
{
BN_GF2m_mod(c, a, b[j]);
BN_GF2m_mod_sqrt(d, a, b[j], ctx);
BN_GF2m_mod_sqr(e, d, b[j], ctx);
#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
if (bp != NULL)
{
if (!results)
{
BN_print(bp,d);
BIO_puts(bp, " ^ 2 - ");
BN_print(bp,a);
BIO_puts(bp,"\n");
}
}
#endif
BN_GF2m_add(f, c, e);
/* Test that d^2 = a, where d = sqrt(a). */
if(!BN_is_zero(f))
{
fprintf(stderr,"GF(2^m) modular square root test failed!\n");
goto err;
}
}
}
ret = 1;
err:
BN_free(a);
BN_free(b[0]);
BN_free(b[1]);
BN_free(c);
BN_free(d);
BN_free(e);
BN_free(f);
return ret;
}
int test_gf2m_mod_solve_quad(BIO *bp,BN_CTX *ctx)
{
BIGNUM *a,*b[2],*c,*d,*e;
int i, j, s = 0, t, ret = 0;
unsigned int p0[] = {163,7,6,3,0};
unsigned int p1[] = {193,15,0};
a=BN_new();
b[0]=BN_new();
b[1]=BN_new();
c=BN_new();
d=BN_new();
e=BN_new();
BN_GF2m_arr2poly(p0, b[0]);
BN_GF2m_arr2poly(p1, b[1]);
for (i=0; i<num0; i++)
{
BN_bntest_rand(a, 512, 0, 0);
for (j=0; j < 2; j++)
{
t = BN_GF2m_mod_solve_quad(c, a, b[j], ctx);
if (t)
{
s++;
BN_GF2m_mod_sqr(d, c, b[j], ctx);
BN_GF2m_add(d, c, d);
BN_GF2m_mod(e, a, b[j]);
#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
if (bp != NULL)
{
if (!results)
{
BN_print(bp,c);
BIO_puts(bp, " is root of z^2 + z = ");
BN_print(bp,a);
BIO_puts(bp, " % ");
BN_print(bp,b[j]);
BIO_puts(bp, "\n");
}
}
#endif
BN_GF2m_add(e, e, d);
/* Test that solution of quadratic c satisfies c^2 + c = a. */
if(!BN_is_zero(e))
{
fprintf(stderr,"GF(2^m) modular solve quadratic test failed!\n");
goto err;
}
}
else
{
#if 0 /* make test uses ouput in bc but bc can't handle GF(2^m) arithmetic */
if (bp != NULL)
{
if (!results)
{
BIO_puts(bp, "There are no roots of z^2 + z = ");
BN_print(bp,a);
BIO_puts(bp, " % ");
BN_print(bp,b[j]);
BIO_puts(bp, "\n");
}
}
#endif
}
}
}
if (s == 0)
{
fprintf(stderr,"All %i tests of GF(2^m) modular solve quadratic resulted in no roots;\n", num0);
fprintf(stderr,"this is very unlikely and probably indicates an error.\n");
goto err;
}
ret = 1;
err:
BN_free(a);
BN_free(b[0]);
BN_free(b[1]);
BN_free(c);
BN_free(d);
BN_free(e);
return ret;
}
static void genprime_cb(int p, int n, void *arg)
{
char c='*';