Crypt::OpenSSL::Bignum − OpenSSL’s multiprecision integer arithmetic

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";

}

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.

*NOTE*
: Many of the methods in this package can croak, so use
eval, or Error.pm’s try/catch mechanism to capture
errors.

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.

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.

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.

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 "to_bin"). Note that objects created using this method are necessarily nonnegative.

new |
my $bn = Crypt::OpenSSL::Bignum−>new; |

Returns a new Crypt::OpenSSL::Bignum object representing 0

zero

my $bn = Crypt::OpenSSL::Bignum−>zero;

Returns a new Crypt::OpenSSL::Bignum object representing 0 (same as new)

one |
my $bn = Crypt::OpenSSL::Bignum−>one; |

Returns a new Crypt::OpenSSL::Bignum object representing 1

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.

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.

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.

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.

to_decimal

my $decimal_string = $self−>to_decimal;

Return a decimal string representation of this object.

to_hex

my $hex_string = $self−>to_hex;

Return a hexidecimal string representation of this object.

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.

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.

is_zero

my $bool = $self−>is_zero;

Returns true of this object represents 0.

is_one

my $bool = $self−>is_one;

Returns true of this object represents 1.

is_odd

my $bool = $self−>is_odd;

Returns true of this object represents an odd number.

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.

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.

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.

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.

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.

sqr |
my $new_bn_object = $self−>sqr($ctx); |

# new object is created $self is not modified

This method returns the square ("$self ** 2") of Crypt::OpenSSL::Bignum object.

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.

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.

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 "($self * $bn_b) % $bn_mod", using the third argument, a Crypt::OpenSSL::Bignum::CTX object, as a scratchpad.

mod_inverse

my $new_bn_object =
$self−>mod_inverse($bn_n, $ctx);

# new object is created $self is not modified

Computes the inverse of $self modulo $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.

gcd |
my $new_bn_object = $self−>gcd($bn_b, $ctx); |

# new object is created $self is not modified

Computes the greatest common divisor of $self and $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.

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 $self and $bn_b (Crypt::OpenSSL::Bignum objects).

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 $self and $bn_b (Crypt::OpenSSL::Bignum objects).

equals

my $result =
$self−>equals($bn_b);

#returns:

# 1 if self == bn_b

# 0 otherwise

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 "floor(log2(w)) + 1".

num_bytes

my $bytes = $self−>num_bytes;

Returns the size of binary represenatation in bytes.

rshift

my $new_bn_object =
$self−>rshift($n);

# new object is created $self is not modified

Shifts a right by $n (integer) bits and places the result into a newly created Crypt::OpenSSL::Bignum object.

lshift

my $new_bn_object =
$self−>lshift($n);

# new object is created $self is not modified

Shifts a left by $n (integer) bits and places the result into a newly created Crypt::OpenSSL::Bignum object.

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.

copy

my $new_bn_object = $self−>copy;

Returns a copy of this object.

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.

Ian Robertson, iroberts@cpan.org

<https://www.openssl.org/docs/crypto/bn.html>