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cd2eebfd
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体验新版 GitCode,发现更多精彩内容 >>
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cd2eebfd
编写于
11月 30, 2000
作者:
B
Bodo Möller
浏览文件
操作
浏览文件
下载
电子邮件补丁
差异文件
BN_sqrt
上级
06676624
变更
8
隐藏空白更改
内联
并排
Showing
8 changed file
with
438 addition
and
21 deletion
+438
-21
crypto/bn/Makefile.ssl
crypto/bn/Makefile.ssl
+2
-2
crypto/bn/bn.h
crypto/bn/bn.h
+8
-1
crypto/bn/bn_err.c
crypto/bn/bn_err.c
+4
-0
crypto/bn/bn_exp.c
crypto/bn/bn_exp.c
+31
-8
crypto/bn/bn_exp2.c
crypto/bn/bn_exp2.c
+8
-2
crypto/bn/bn_kron.c
crypto/bn/bn_kron.c
+0
-2
crypto/bn/bn_sqrt.c
crypto/bn/bn_sqrt.c
+308
-1
crypto/bn/bntest.c
crypto/bn/bntest.c
+77
-5
未找到文件。
crypto/bn/Makefile.ssl
浏览文件 @
cd2eebfd
...
...
@@ -37,12 +37,12 @@ APPS=
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_gcd.c bn_prime.c bn_err.c bn_sqr.c bn_asm.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
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_gcd.o bn_prime.o bn_err.o bn_sqr.o
$(BN_ASM)
\
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
SRC
=
$(LIBSRC)
...
...
crypto/bn/bn.h
浏览文件 @
cd2eebfd
...
...
@@ -238,7 +238,7 @@ typedef struct bignum_st
}
BIGNUM
;
/* Used for temp variables */
#define BN_CTX_NUM
16
#define BN_CTX_NUM
20
#define BN_CTX_NUM_POS 12
typedef
struct
bignum_ctx
{
...
...
@@ -357,6 +357,7 @@ int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m, BN_
int
BN_mod_sub_quick
(
BIGNUM
*
r
,
const
BIGNUM
*
a
,
const
BIGNUM
*
b
,
const
BIGNUM
*
m
);
int
BN_mod_mul
(
BIGNUM
*
r
,
const
BIGNUM
*
a
,
const
BIGNUM
*
b
,
const
BIGNUM
*
m
,
BN_CTX
*
ctx
);
int
BN_mod_sqr
(
BIGNUM
*
r
,
const
BIGNUM
*
a
,
const
BIGNUM
*
m
,
BN_CTX
*
ctx
);
int
BN_mod_lshift1
(
BIGNUM
*
r
,
const
BIGNUM
*
a
,
const
BIGNUM
*
m
,
BN_CTX
*
ctx
);
int
BN_mod_lshift1_quick
(
BIGNUM
*
r
,
const
BIGNUM
*
a
,
const
BIGNUM
*
m
);
int
BN_mod_lshift
(
BIGNUM
*
r
,
const
BIGNUM
*
a
,
int
n
,
const
BIGNUM
*
m
,
BN_CTX
*
ctx
);
...
...
@@ -414,6 +415,8 @@ int BN_gcd(BIGNUM *r,const BIGNUM *a,const BIGNUM *b,BN_CTX *ctx);
int
BN_kronecker
(
const
BIGNUM
*
a
,
const
BIGNUM
*
b
,
BN_CTX
*
ctx
);
/* returns -2 for error */
BIGNUM
*
BN_mod_inverse
(
BIGNUM
*
ret
,
const
BIGNUM
*
a
,
const
BIGNUM
*
n
,
BN_CTX
*
ctx
);
BIGNUM
*
BN_mod_sqrt
(
BIGNUM
*
ret
,
const
BIGNUM
*
a
,
const
BIGNUM
*
n
,
BN_CTX
*
ctx
);
BIGNUM
*
BN_generate_prime
(
BIGNUM
*
ret
,
int
bits
,
int
safe
,
const
BIGNUM
*
add
,
const
BIGNUM
*
rem
,
void
(
*
callback
)(
int
,
int
,
void
*
),
void
*
cb_arg
);
...
...
@@ -517,6 +520,7 @@ void bn_dump1(FILE *o, const char *a, const BN_ULONG *b,int n);
#define BN_F_BN_MOD_INVERSE 110
#define BN_F_BN_MOD_LSHIFT_QUICK 119
#define BN_F_BN_MOD_MUL_RECIPROCAL 111
#define BN_F_BN_MOD_SQRT 121
#define BN_F_BN_MPI2BN 112
#define BN_F_BN_NEW 113
#define BN_F_BN_RAND 114
...
...
@@ -531,8 +535,11 @@ void bn_dump1(FILE *o, const char *a, const BN_ULONG *b,int n);
#define BN_R_EXPAND_ON_STATIC_BIGNUM_DATA 105
#define BN_R_INPUT_NOT_REDUCED 110
#define BN_R_INVALID_LENGTH 106
#define BN_R_NOT_A_SQUARE 111
#define BN_R_NOT_INITIALIZED 107
#define BN_R_NO_INVERSE 108
#define BN_R_P_IS_NOT_PRIME 112
#define BN_R_TOO_MANY_ITERATIONS 113
#define BN_R_TOO_MANY_TEMPORARY_VARIABLES 109
#ifdef __cplusplus
...
...
crypto/bn/bn_err.c
浏览文件 @
cd2eebfd
...
...
@@ -83,6 +83,7 @@ static ERR_STRING_DATA BN_str_functs[]=
{
ERR_PACK
(
0
,
BN_F_BN_MOD_INVERSE
,
0
),
"BN_mod_inverse"
},
{
ERR_PACK
(
0
,
BN_F_BN_MOD_LSHIFT_QUICK
,
0
),
"BN_mod_lshift_quick"
},
{
ERR_PACK
(
0
,
BN_F_BN_MOD_MUL_RECIPROCAL
,
0
),
"BN_mod_mul_reciprocal"
},
{
ERR_PACK
(
0
,
BN_F_BN_MOD_SQRT
,
0
),
"BN_mod_sqrt"
},
{
ERR_PACK
(
0
,
BN_F_BN_MPI2BN
,
0
),
"BN_mpi2bn"
},
{
ERR_PACK
(
0
,
BN_F_BN_NEW
,
0
),
"BN_new"
},
{
ERR_PACK
(
0
,
BN_F_BN_RAND
,
0
),
"BN_rand"
},
...
...
@@ -100,8 +101,11 @@ static ERR_STRING_DATA BN_str_reasons[]=
{
BN_R_EXPAND_ON_STATIC_BIGNUM_DATA
,
"expand on static bignum data"
},
{
BN_R_INPUT_NOT_REDUCED
,
"input not reduced"
},
{
BN_R_INVALID_LENGTH
,
"invalid length"
},
{
BN_R_NOT_A_SQUARE
,
"not a square"
},
{
BN_R_NOT_INITIALIZED
,
"not initialized"
},
{
BN_R_NO_INVERSE
,
"no inverse"
},
{
BN_R_P_IS_NOT_PRIME
,
"p is not prime"
},
{
BN_R_TOO_MANY_ITERATIONS
,
"too many iterations"
},
{
BN_R_TOO_MANY_TEMPORARY_VARIABLES
,
"too many temporary variables"
},
{
0
,
NULL
}
};
...
...
crypto/bn/bn_exp.c
浏览文件 @
cd2eebfd
...
...
@@ -205,6 +205,8 @@ int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
if
(
a
->
top
==
1
&&
!
a
->
neg
)
{
BN_ULONG
A
=
a
->
d
[
0
];
if
(
m
->
top
==
1
)
A
%=
m
->
d
[
0
];
/* make sure that A is reduced */
ret
=
BN_mod_exp_mont_word
(
r
,
A
,
p
,
m
,
ctx
,
NULL
);
}
else
...
...
@@ -235,8 +237,13 @@ int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
if
(
bits
==
0
)
{
BN_one
(
r
);
return
(
1
);
ret
=
BN_one
(
r
);
return
ret
;
}
if
(
BN_is_zero
(
a
))
{
ret
=
BN_zero
(
r
);
return
ret
;
}
BN_CTX_start
(
ctx
);
...
...
@@ -355,8 +362,13 @@ int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
bits
=
BN_num_bits
(
p
);
if
(
bits
==
0
)
{
BN_one
(
rr
);
return
(
1
);
ret
=
BN_one
(
rr
);
return
ret
;
}
if
(
BN_is_zero
(
a
))
{
ret
=
BN_zero
(
rr
);
return
ret
;
}
BN_CTX_start
(
ctx
);
d
=
BN_CTX_get
(
ctx
);
...
...
@@ -500,9 +512,15 @@ int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
bits
=
BN_num_bits
(
p
);
if
(
bits
==
0
)
{
BN_one
(
rr
);
return
(
1
)
;
ret
=
BN_one
(
rr
);
return
ret
;
}
if
(
a
==
0
)
{
ret
=
BN_zero
(
rr
);
return
ret
;
}
BN_CTX_start
(
ctx
);
d
=
BN_CTX_get
(
ctx
);
r
=
BN_CTX_get
(
ctx
);
...
...
@@ -611,8 +629,13 @@ int BN_mod_exp_simple(BIGNUM *r,
if
(
bits
==
0
)
{
BN_one
(
r
);
return
(
1
);
ret
=
BN_one
(
r
);
return
ret
;
}
if
(
BN_is_zero
(
a
))
{
ret
=
BN_one
(
r
);
return
ret
;
}
BN_CTX_start
(
ctx
);
...
...
crypto/bn/bn_exp2.c
浏览文件 @
cd2eebfd
...
...
@@ -141,9 +141,15 @@ int BN_mod_exp2_mont(BIGNUM *rr, const BIGNUM *a1, const BIGNUM *p1,
bits2
=
BN_num_bits
(
p2
);
if
((
bits1
==
0
)
&&
(
bits2
==
0
))
{
BN_one
(
rr
);
return
(
1
)
;
ret
=
BN_one
(
rr
);
return
ret
;
}
if
(
BN_is_zero
(
a1
)
||
BN_is_zero
(
a2
))
{
ret
=
BN_zero
(
rr
);
return
ret
;
}
bits
=
(
bits1
>
bits2
)
?
bits1
:
bits2
;
BN_CTX_start
(
ctx
);
...
...
crypto/bn/bn_kron.c
浏览文件 @
cd2eebfd
/* totally untested */
/* crypto/bn/bn_kron.c */
/* ====================================================================
* Copyright (c) 1998-2000 The OpenSSL Project. All rights reserved.
...
...
crypto/bn/bn_sqrt.c
浏览文件 @
cd2eebfd
XXX
/* crypto/bn/bn_mod.c */
/* Written by Lenka Fibikova <fibikova@exp-math.uni-essen.de>
* and Bodo Moeller for the OpenSSL project. */
/* ====================================================================
* Copyright (c) 1998-2000 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 "cryptlib.h"
#include "bn_lcl.h"
BIGNUM
*
BN_mod_sqrt
(
BIGNUM
*
in
,
const
BIGNUM
*
a
,
const
BIGNUM
*
p
,
BN_CTX
*
ctx
)
/* Returns 'ret' such that
* ret^2 == a (mod p),
* using the Tonelli/Shanks algorithm (cf. Henri Cohen, "A Course
* in Algebraic Computational Number Theory", algorithm 1.5.1).
* 'p' must be prime!
*/
{
BIGNUM
*
ret
=
in
;
int
err
=
1
;
int
r
;
BIGNUM
*
b
,
*
q
,
*
t
,
*
x
,
*
y
;
int
e
,
i
,
j
;
if
(
!
BN_is_odd
(
p
)
||
BN_abs_is_word
(
p
,
1
))
{
if
(
BN_abs_is_word
(
p
,
2
))
{
if
(
ret
==
NULL
)
ret
=
BN_new
();
if
(
ret
==
NULL
)
goto
end
;
if
(
!
BN_set_word
(
ret
,
BN_is_bit_set
(
a
,
0
)))
{
BN_free
(
ret
);
return
NULL
;
}
return
ret
;
}
BNerr
(
BN_F_BN_MOD_SQRT
,
BN_R_P_IS_NOT_PRIME
);
return
(
NULL
);
}
#if 0 /* if BN_mod_sqrt is used with correct input, this just wastes time */
r = BN_kronecker(a, p, ctx);
if (r < -1) return NULL;
if (r == -1)
{
BNerr(BN_F_BN_MOD_SQRT, BN_R_NOT_A_SQUARE);
return(NULL);
}
#endif
BN_CTX_start
(
ctx
);
b
=
BN_CTX_get
(
ctx
);
q
=
BN_CTX_get
(
ctx
);
t
=
BN_CTX_get
(
ctx
);
x
=
BN_CTX_get
(
ctx
);
y
=
BN_CTX_get
(
ctx
);
if
(
y
==
NULL
)
goto
end
;
if
(
ret
==
NULL
)
ret
=
BN_new
();
if
(
ret
==
NULL
)
goto
end
;
/* now write |p| - 1 as 2^e*q where q is odd */
e
=
1
;
while
(
!
BN_is_bit_set
(
p
,
e
))
e
++
;
if
(
!
BN_rshift
(
q
,
p
,
e
))
goto
end
;
q
->
neg
=
0
;
if
(
e
==
1
)
{
/* The easy case: (p-1)/2 is odd, so 2 has an inverse
* modulo (p-1)/2, and square roots can be computed
* directly by modular exponentiation.
* We have
* 2 * (p+1)/4 == 1 (mod (p-1)/2),
* so we can use exponent (p+1)/4, i.e. (q+1)/2.
*/
if
(
!
BN_add_word
(
q
,
1
))
goto
end
;
if
(
!
BN_rshift1
(
q
,
q
))
goto
end
;
if
(
!
BN_mod_exp
(
ret
,
a
,
q
,
p
,
ctx
))
goto
end
;
err
=
0
;
goto
end
;
}
/* e > 1, so we really have to use the Tonelli/Shanks algorithm.
* First, find some y that is not a square. */
i
=
1
;
do
{
/* For efficiency, try small numbers first;
* if this fails, try random numbers.
*/
if
(
i
<
20
)
{
if
(
!
BN_set_word
(
y
,
i
))
goto
end
;
}
else
{
if
(
!
BN_pseudo_rand
(
y
,
BN_num_bits
(
p
),
0
,
0
))
goto
end
;
if
(
BN_ucmp
(
y
,
p
)
>=
0
)
{
if
(
!
(
p
->
neg
?
BN_add
:
BN_sub
)(
y
,
y
,
p
))
goto
end
;
}
/* now 0 <= y < |p| */
if
(
BN_is_zero
(
y
))
if
(
!
BN_set_word
(
y
,
i
))
goto
end
;
}
r
=
BN_kronecker
(
y
,
p
,
ctx
);
if
(
r
<
-
1
)
goto
end
;
if
(
r
==
0
)
{
/* m divides p */
BNerr
(
BN_F_BN_MOD_SQRT
,
BN_R_P_IS_NOT_PRIME
);
goto
end
;
}
}
while
(
r
==
1
&&
i
++
<
80
);
if
(
r
!=
-
1
)
{
/* Many rounds and still no non-square -- this is more likely
* a bug than just bad luck.
* Even if p is not prime, we should have found some y
* such that r == -1.
*/
BNerr
(
BN_F_BN_MOD_SQRT
,
BN_R_TOO_MANY_ITERATIONS
);
goto
end
;
}
/* Now that we have some non-square, we can find an element
* of order 2^e by computing its q'th power. */
if
(
!
BN_mod_exp
(
y
,
y
,
q
,
p
,
ctx
))
goto
end
;
if
(
BN_is_one
(
y
))
{
BNerr
(
BN_F_BN_MOD_SQRT
,
BN_R_P_IS_NOT_PRIME
);
goto
end
;
}
/* Now we know that (if p is indeed prime) there is an integer
* k, 0 <= k < 2^e, such that
*
* a^q * y^k == 1 (mod p).
*
* As a^q is a square and y is not, k must be even.
* q+1 is even, too, so there is an element
*
* X := a^((q+1)/2) * y^(k/2),
*
* and it satisfies
*
* X^2 = a^q * a * y^k
* = a,
*
* so it is the square root that we are looking for.
*/
/* t := (q-1)/2 (note that q is odd) */
if
(
!
BN_rshift1
(
t
,
q
))
goto
end
;
/* x := a^((q-1)/2) */
if
(
BN_is_zero
(
t
))
/* special case: p = 2^e + 1 */
{
if
(
!
BN_nnmod
(
t
,
a
,
p
,
ctx
))
goto
end
;
if
(
BN_is_zero
(
t
))
{
/* special case: a == 0 (mod p) */
if
(
!
BN_zero
(
ret
))
goto
end
;
err
=
0
;
goto
end
;
}
else
if
(
!
BN_one
(
x
))
goto
end
;
}
else
{
if
(
!
BN_mod_exp
(
x
,
a
,
t
,
p
,
ctx
))
goto
end
;
if
(
BN_is_zero
(
x
))
{
/* special case: a == 0 (mod p) */
if
(
!
BN_zero
(
ret
))
goto
end
;
err
=
0
;
goto
end
;
}
}
/* b := a*x^2 (= a^q) */
if
(
!
BN_mod_sqr
(
b
,
x
,
p
,
ctx
))
goto
end
;
if
(
!
BN_mod_mul
(
b
,
b
,
a
,
p
,
ctx
))
goto
end
;
/* x := a*x (= a^((q+1)/2)) */
if
(
!
BN_mod_mul
(
x
,
x
,
a
,
p
,
ctx
))
goto
end
;
while
(
1
)
{
/* Now b is a^q * y^k for some even k (0 <= k < 2^E
* where E refers to the original value of e, which we
* don't keep in a variable), and x is a^((q+1)/2) * y^(k/2).
*
* We have a*b = x^2,
* y^2^(e-1) = -1,
* b^2^(e-1) = 1.
*/
if
(
BN_is_one
(
b
))
{
if
(
!
BN_copy
(
ret
,
x
))
goto
end
;
err
=
0
;
goto
end
;
}
/* find smallest i such that b^(2^i) = 1 */
i
=
1
;
if
(
!
BN_mod_sqr
(
t
,
b
,
p
,
ctx
))
goto
end
;
while
(
!
BN_is_one
(
t
))
{
i
++
;
if
(
i
==
e
)
{
BNerr
(
BN_F_BN_MOD_SQRT
,
BN_R_NOT_A_SQUARE
);
goto
end
;
}
if
(
!
BN_mod_mul
(
t
,
t
,
t
,
p
,
ctx
))
goto
end
;
}
/* t := y^2^(e - i - 1) */
if
(
!
BN_copy
(
t
,
y
))
goto
end
;
for
(
j
=
e
-
i
-
1
;
j
>
0
;
j
--
)
{
if
(
!
BN_mod_sqr
(
t
,
t
,
p
,
ctx
))
goto
end
;
}
if
(
!
BN_mod_mul
(
y
,
t
,
t
,
p
,
ctx
))
goto
end
;
if
(
!
BN_mod_mul
(
x
,
x
,
t
,
p
,
ctx
))
goto
end
;
if
(
!
BN_mod_mul
(
b
,
b
,
y
,
p
,
ctx
))
goto
end
;
e
=
i
;
}
end:
if
(
err
)
{
if
(
ret
!=
NULL
&&
ret
!=
in
)
{
BN_clear_free
(
ret
);
}
ret
=
NULL
;
}
BN_CTX_end
(
ctx
);
return
ret
;
}
crypto/bn/bntest.c
浏览文件 @
cd2eebfd
...
...
@@ -92,6 +92,7 @@ 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_kron
(
BIO
*
bp
,
BN_CTX
*
ctx
);
int
test_sqrt
(
BIO
*
bp
,
BN_CTX
*
ctx
);
int
rand_neg
(
void
);
static
int
results
=
0
;
...
...
@@ -233,6 +234,10 @@ int main(int argc, char *argv[])
if
(
!
test_kron
(
out
,
ctx
))
goto
err
;
BIO_flush
(
out
);
message
(
out
,
"BN_mod_sqrt"
);
if
(
!
test_sqrt
(
out
,
ctx
))
goto
err
;
BIO_flush
(
out
);
BN_CTX_free
(
ctx
);
BIO_free
(
out
);
...
...
@@ -940,11 +945,6 @@ int test_kron(BIO *bp, BN_CTX *ctx)
if
(
!
BN_generate_prime
(
b
,
512
,
0
,
NULL
,
NULL
,
genprime_cb
,
NULL
))
goto
err
;
putc
(
'\n'
,
stderr
);
if
(
1
!=
BN_is_prime
(
b
,
10
,
NULL
,
ctx
,
NULL
))
{
fprintf
(
stderr
,
"BN_is_prime failed
\n
"
);
goto
err
;
}
for
(
i
=
0
;
i
<
num0
;
i
++
)
{
...
...
@@ -998,6 +998,78 @@ int test_kron(BIO *bp, BN_CTX *ctx)
return
ret
;
}
int
test_sqrt
(
BIO
*
bp
,
BN_CTX
*
ctx
)
{
BIGNUM
*
a
,
*
p
,
*
r
;
int
i
,
j
;
int
ret
=
0
;
a
=
BN_new
();
p
=
BN_new
();
r
=
BN_new
();
if
(
a
==
NULL
||
p
==
NULL
||
r
==
NULL
)
goto
err
;
for
(
i
=
0
;
i
<
16
;
i
++
)
{
if
(
i
<
8
)
{
unsigned
primes
[
8
]
=
{
2
,
3
,
7
,
11
,
13
,
17
,
19
};
if
(
!
BN_set_word
(
p
,
primes
[
i
]))
goto
err
;
}
else
{
if
(
!
BN_set_word
(
a
,
32
))
goto
err
;
if
(
!
BN_set_word
(
r
,
2
*
i
+
1
))
goto
err
;
if
(
!
BN_generate_prime
(
p
,
256
,
0
,
a
,
r
,
genprime_cb
,
NULL
))
goto
err
;
putc
(
'\n'
,
stderr
);
}
for
(
j
=
0
;
j
<
num2
;
j
++
)
{
/* construct 'a' such that it is a square modulo p,
* but in general not a proper square and not reduced modulo p */
if
(
!
BN_rand
(
r
,
256
,
0
,
3
))
goto
err
;
if
(
!
BN_nnmod
(
r
,
r
,
p
,
ctx
))
goto
err
;
if
(
!
BN_mod_sqr
(
r
,
r
,
p
,
ctx
))
goto
err
;
if
(
!
BN_rand
(
a
,
256
,
0
,
3
))
goto
err
;
if
(
!
BN_nnmod
(
a
,
a
,
p
,
ctx
))
goto
err
;
if
(
!
BN_mod_sqr
(
a
,
a
,
p
,
ctx
))
goto
err
;
if
(
!
BN_mul
(
a
,
a
,
r
,
ctx
))
goto
err
;
if
(
!
BN_mod_sqrt
(
r
,
a
,
p
,
ctx
))
goto
err
;
if
(
!
BN_mod_sqr
(
r
,
r
,
p
,
ctx
))
goto
err
;
if
(
!
BN_nnmod
(
a
,
a
,
p
,
ctx
))
goto
err
;
if
(
BN_cmp
(
a
,
r
)
!=
0
)
{
fprintf
(
stderr
,
"BN_mod_sqrt failed: a = "
);
BN_print_fp
(
stderr
,
a
);
fprintf
(
stderr
,
", r = "
);
BN_print_fp
(
stderr
,
r
);
fprintf
(
stderr
,
", p = "
);
BN_print_fp
(
stderr
,
p
);
fprintf
(
stderr
,
"
\n
"
);
goto
err
;
}
putc
(
'.'
,
stderr
);
fflush
(
stderr
);
}
putc
(
'\n'
,
stderr
);
fflush
(
stderr
);
}
ret
=
1
;
err:
if
(
a
!=
NULL
)
BN_free
(
a
);
if
(
p
!=
NULL
)
BN_free
(
p
);
if
(
r
!=
NULL
)
BN_free
(
r
);
return
ret
;
}
int
test_lshift
(
BIO
*
bp
,
BN_CTX
*
ctx
,
BIGNUM
*
a_
)
{
BIGNUM
*
a
,
*
b
,
*
c
,
*
d
;
...
...
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