```
package Crypt::OpenSSL::Bignum;
use 5.005;
use strict;
use Carp;
use vars qw( $VERSION @ISA );
use base qw(DynaLoader);
$VERSION = '0.09';
bootstrap Crypt::OpenSSL::Bignum $VERSION;
1;
__END__
=head1 NAME
Crypt::OpenSSL::Bignum - OpenSSL's multiprecision integer arithmetic
=head1 SYNOPSIS
use Crypt::OpenSSL::Bignum;
my $bn = Crypt::OpenSSL::Bignum->new_from_decimal( "1000" );
# or
my $bn = Crypt::OpenSSL::Bignum->new_from_word( 1000 );
# or
my $bn = Crypt::OpenSSL::Bignum->new_from_hex("3e8"); # no leading 0x
# or
my $bn = Crypt::OpenSSL::Bignum->new_from_bin(pack( "C*", 3, 232 ))
use Crypt::OpenSSL::Bignum::CTX;
sub print_factorial
{
my( $n ) = @_;
my $fac = Crypt::OpenSSL::Bignum->one();
my $ctx = Crypt::OpenSSL::Bignum::CTX->new();
foreach my $i (1 .. $n)
{
$fac->mul( Crypt::OpenSSL::Bignum->new_from_word( $i ), $ctx, $fac );
}
print "$n factorial is ", $fac->to_decimal(), "\n";
}
=head1 DESCRIPTION
Crypt::OpenSSL::Bignum provides access to OpenSSL multiprecision
integer arithmetic libraries. Presently, many though not all of the
arithmetic operations that OpenSSL provides are exposed to perl. In
addition, this module can be used to provide access to bignum values
produced by other OpenSSL modules, such as key parameters from
Crypt::OpenSSL::RSA.
I<NOTE>: Many of the methods in this package can croak, so use eval, or
Error.pm's try/catch mechanism to capture errors.
=head1 Constructors
=over
=item new_from_decimal
my $bn = Crypt::OpenSSL::Bignum->new_from_decimal($decimal_string);
Create a new Crypt::OpenSSL::Bignum object whose value is specified by
the given decimal representation.
=item new_from_hex
my $bn = Crypt::OpenSSL::Bignum->new_from_hex($hex_string); #no leading '0x'
Create a new Crypt::OpenSSL::Bignum object whose value is specified by
the given hexidecimal representation.
=item new_from_word
my $bn = Crypt::OpenSSL::Bignum->new_from_word($unsigned_integer);
Create a new Crypt::OpenSSL::Bignum object whose value will be the
word given. Note that numbers represented by objects created using
this method are necessarily between 0 and 2^32 - 1.
=item new_from_bin
my $bn = Crypt::OpenSSL::Bignum->new_from_bin($bin_buffer);
Create a new Crypt::OpenSSL::Bignum object whose value is specified by
the given packed binary string (created by L</to_bin>). Note that objects
created using this method are necessarily nonnegative.
=item new
my $bn = Crypt::OpenSSL::Bignum->new;
Returns a new Crypt::OpenSSL::Bignum object representing 0
=item zero
my $bn = Crypt::OpenSSL::Bignum->zero;
Returns a new Crypt::OpenSSL::Bignum object representing 0 (same as new)
=item one
my $bn = Crypt::OpenSSL::Bignum->one;
Returns a new Crypt::OpenSSL::Bignum object representing 1
=item rand
my $bn = Crypt::OpenSSL::Bignum->rand($bits, $top, $bottom)
# $bits, $top, $bottom are integers
generates a cryptographically strong pseudo-random number of bits bits in
length and stores it in rnd. If top is -1, the most significant bit of the
random number can be zero. If top is 0, it is set to 1, and if top is 1, the
two most significant bits of the number will be set to 1, so that the product
of two such random numbers will always have 2*bits length. If bottom is true,
the number will be odd.
=item pseudo_rand
my $bn = Crypt::OpenSSL::Bignum->pseudo_rand($bits, $top, $bottom)
# $bits, $top, $bottom are integers
does the same, but pseudo-random numbers generated by this function are not
necessarily unpredictable. They can be used for non-cryptographic purposes and
for certain purposes in cryptographic protocols, but usually not for key
generation etc.
=item rand_range
my $bn = Crypt::OpenSSL::Bignum->rand_range($bn_range)
generates a cryptographically strong pseudo-random number rnd in the range 0
<lt>= rnd < range. BN_pseudo_rand_range() does the same, but is based on
BN_pseudo_rand(), and hence numbers generated by it are not necessarily
unpredictable.
=item bless_pointer
my $bn = Crypt::OpenSSL::Bignum->bless_pointer($BIGNUM_ptr)
Given a pointer to a OpenSSL BIGNUM object in memory, construct and
return Crypt::OpenSSL::Bignum object around this. Note that the
underlying BIGNUM object will be destroyed (via BN_clear_free(3ssl))
when the returned Crypt::OpenSSL::Bignum object is no longer
referenced, so the pointer passed to this method should only be
referenced via the returned perl object after calling bless_pointer.
This method is intended only for use by XSUB writers writing code that
interfaces with OpenSSL library methods, and who wish to be able to
return a BIGNUM structure to perl as a Crypt::OpenSSL::Bignum object.
=back
=head1 Instance Methods
=over
=item to_decimal
my $decimal_string = $self->to_decimal;
Return a decimal string representation of this object.
=item to_hex
my $hex_string = $self->to_hex;
Return a hexidecimal string representation of this object.
=item to_bin
my $bin_buffer = $self->to_bin;
Return a packed binary string representation of this object. Note
that sign is ignored, so that to bin called on a
Crypt::OpenSSL::Bignum object representing a negative number returns
the same value as it would called on an object representing that
number's absolute value.
=item get_word
my $unsigned_int = $self->get_word;
Return a scalar integer representation of this object, if it can be
represented as an unsigned long.
=item is_zero
my $bool = $self->is_zero;
Returns true of this object represents 0.
=item is_one
my $bool = $self->is_one;
Returns true of this object represents 1.
=item is_odd
my $bool = $self->is_odd;
Returns true of this object represents an odd number.
=item add
my $new_bn_object = $self->add($bn_b); # $new_bn_object = $self + $bn_b
# or
$self->add($bn_b, $result_bn); # $result_bn = $self + $bn_b
This method returns the sum of this object and the first argument. If
only one argument is passed, a new Crypt::OpenSSL::Bignum object is
created for the return value; otherwise, the value of second argument
is set to the result and returned.
=item sub
my $new_bn_object = $self->sub($bn_b); # $new_bn_object = $self - $bn_b
# or
$self->sub($bn_b, $result_bn); # $result_bn = $self - $bn_b
This method returns the difference of this object and the first
argument. If only one argument is passed, a new
Crypt::OpenSSL::Bignum object is created for the return value;
otherwise, the value of second argument is set to the result and
returned.
=item mul
my $new_bn_object = $self->mul($bn_b, $ctx); # $new_bn_object = $self * $bn_b
# or
$self->mul($bn_b, $ctx, $result_bn); # $result_bn = $self * $bn_b
This method returns the product of this object and the first argument,
using the second argument, a Crypt::OpenSSL::Bignum::CTX object, as a
scratchpad. If only two arguments are passed, a new
Crypt::OpenSSL::Bignum object is created for the return value;
otherwise, the value of third argument is set to the result and
returned.
=item div
my ($quotient, $remainder) = $self->div($bn_b, $ctx);
# or
$self->div($bn_b, $ctx, $quotient, $remainder);
This method returns a list consisting of quotient and the remainder
obtained by dividing this object by the first argument, using the
second argument, a Crypt::OpenSSL::Bignum::CTX object, as a
scratchpad. If only two arguments are passed, new
Crypt::OpenSSL::Bignum objects are created for both return values. If
a third argument is passed, otherwise, the value of third argument is
set to the quotient. If a fourth argument is passed, the value of the
fourth argument is set to the remainder.
=item mod
my $remainder = $self->mod($bn_b, $ctx);
# or
$self->mod($bn_b, $ctx, $remainder);
This method returns the remainder obtained by dividing this object by
the first argument, a Crypt::OpenSSL::Bignum::CTX object, as a
scratchpad. Crypt::OpenSSL::Bignum object is created for the return
value. If a third argument is passed, the value of third argument is
set to the remainder.
=item sqr
my $new_bn_object = $self->sqr($ctx);
# new object is created $self is not modified
This method returns the square (C<$self ** 2>) of Crypt::OpenSSL::Bignum object.
=item exp
my $new_bn_object = $self->exp($bn_exp, $ctx);
# new object is created $self is not modified
This method returns the product of this object exponentiated by the
first argument (Crypt::OpenSSL::Bignum object), using the second argument, a
Crypt::OpenSSL::Bignum::CTX object, as a scratchpad.
=item mod_exp
my $new_bn_object = $self->exp_mod($bn_exp, $bn_mod, $ctx);
# new object is created $self is not modified
This method returns the product of this object exponentiated by the
first argument (Crypt::OpenSSL::Bignum object), modulo the second
argument (also Crypt::OpenSSL::Bignum object), using the third argument,
a Crypt::OpenSSL::Bignum::CTX object, as a scratchpad.
=item mod_mul
my $new_bn_object = $self->mod_mul($bn_b, $bn_mod, $ctx);
# new object is created $self is not modified
This method returns C<($self * $bn_b) % $bn_mod>, using the third argument,
a Crypt::OpenSSL::Bignum::CTX object, as a scratchpad.
=item mod_inverse
my $new_bn_object = $self->mod_inverse($bn_n, $ctx);
# new object is created $self is not modified
Computes the inverse of C<$self> modulo C<$bn_n> and returns the result in
a new Crypt::OpenSSL::Bignum object, using the second argument,
a Crypt::OpenSSL::Bignum::CTX object, as a scratchpad.
=item gcd
my $new_bn_object = $self->gcd($bn_b, $ctx);
# new object is created $self is not modified
Computes the greatest common divisor of C<$self> and C<$bn_b> and returns the result in
a new Crypt::OpenSSL::Bignum object, using the second argument,
a Crypt::OpenSSL::Bignum::CTX object, as a scratchpad.
=item cmp
my $result = $self->cmp($bn_b);
#returns:
# -1 if self < bn_b
# 0 if self == bn_b
# 1 if self > bn_b
Comparison of values C<$self> and C<$bn_b> (Crypt::OpenSSL::Bignum objects).
=item ucmp
my $result = $self->ucmp($bn_b);
#returns:
# -1 if |self| < |bn_b|
# 0 if |self| == |bn_b|
# 1 if |self| > |bn_b|
Comparison using the absolute values of C<$self> and C<$bn_b> (Crypt::OpenSSL::Bignum objects).
=item equals
my $result = $self->equals($bn_b);
#returns:
# 1 if self == bn_b
# 0 otherwise
=item num_bits
my $bits = $self->num_bits;
Returns the number of significant bits in a word. If we take 0x00000432 as an
example, it returns 11, not 16, not 32. Basically, except for a zero, it
returns C<floor(log2(w)) + 1>.
=item num_bytes
my $bytes = $self->num_bytes;
Returns the size of binary represenatation in bytes.
=item rshift
my $new_bn_object = $self->rshift($n);
# new object is created $self is not modified
Shifts a right by C<$n> (integer) bits and places the result into a newly created Crypt::OpenSSL::Bignum object.
=item lshift
my $new_bn_object = $self->lshift($n);
# new object is created $self is not modified
Shifts a left by C<$n> (integer) bits and places the result into a newly created Crypt::OpenSSL::Bignum object.
=item swap
my $bn_a = Crypt::OpenSSL::Bignum->new_from_decimal("1234567890001");
my $bn_b = Crypt::OpenSSL::Bignum->new_from_decimal("1234567890002");
$bn_a->swap($bn_b);
# or
$bn_b->swap($bn_a);
Exchanges the values of two Crypt::OpenSSL::Bignum objects.
=item copy
my $new_bn_object = $self->copy;
Returns a copy of this object.
=item pointer_copy
my $cloned_BIGNUM_ptr = $self->pointer_copy($BIGNUM_ptr);
This method is intended only for use by XSUB writers wanting to have
access to the underlying BIGNUM structure referenced by a
Crypt::OpenSSL::Bignum perl object so that they can pass them to other
routines in the OpenSSL library. It returns a perl scalar whose IV
can be cast to a BIGNUM* value. This can then be passed to an XSUB
which can work with the BIGNUM directly. Note that the BIGNUM object
pointed to will be a copy of the BIGNUM object wrapped by the
instance; it is thus the responsibility of the client to free space
allocated by this BIGNUM object if and when it is done with it. See
also bless_pointer.
=back
=head1 AUTHOR
Ian Robertson, iroberts@cpan.org
=head1 SEE ALSO
L<https://www.openssl.org/docs/crypto/bn.html>
=cut
```