NAME

Crypt::OpenSSL::EC - Perl extension for OpenSSL EC (Elliptic Curves) library

SYNOPSIS

   use Crypt::OpenSSL::EC;
   use Crypt::OpenSSL::Bignum::CTX;

   # Use of $ctx is optional in all calls, here we demonstrate its use.
   # If it is provided it will increase performance.
   my $ctx = Crypt::OpenSSL::Bignum::CTX->new();

   my $method = Crypt::OpenSSL::EC::EC_GFp_mont_method();
   my $group = Crypt::OpenSSL::EC::EC_GROUP::new($method);
   Crypt::OpenSSL::EC::EC_GROUP::set_curve_GFp($group, $p, $a, $b, $ctx);
   my $method = Crypt::OpenSSL::EC::EC_GROUP::method_of($group);
   Crypt::OpenSSL::EC::EC_GROUP::copy($tmp, $group);
   Crypt::OpenSSL::EC::EC_GROUP::get_curve_GFp($group, $p, $a, $b, $ctx);

   $Crypt::OpenSSL::EC::trace = 1;
   Crypt::OpenSSL::EC::print_errs();
   my $P = Crypt::OpenSSL::EC::EC_POINT::new($group);


   Crypt::OpenSSL::EC::EC_POINT_set_to_infinity($group, $P);
   my $bool = Crypt::OpenSSL::EC::EC_POINT::is_at_infinity($group, $P);

   my $buf = Crypt::OpenSSL::EC::EC_POINT::point2oct($group, $Q, &Crypt::OpenSSL::EC::POINT_CONVERSION_COMPRESSED, $ctx);
   Crypt::OpenSSL::EC::EC_POINT::oct2point($group, $P, $buf, $ctx);
   Crypt::OpenSSL::EC::EC_POINT::add($group, $P, $P, $Q, $ctx);

   Crypt::OpenSSL::EC::EC_POINT::set_compressed_coordinates_GFp($group, $Q, $x, 1, $ctx));
   my $bool = Crypt::OpenSSL::EC::EC_POINT::is_on_curve($group, $Q, $ctx));
   Crypt::OpenSSL::EC::EC_POINT::copy($R, $P);
   my $result = Crypt::OpenSSL::EC::EC_POINT::cmp($group, $P, $Q, $ctx);
   Crypt::OpenSSL::EC::EC_POINT::set_affine_coordinates_GFp($group, $P, $x, $y, $ctx);
   Crypt::OpenSSL::EC::EC_POINT::get_affine_coordinates_GFp($group, $P, $x, $y, $ctx);
   Crypt::OpenSSL::EC::EC_GROUP::set_generator($group, $P, $z, Crypt::OpenSSL::Bignum->one());
   my $degree = Crypt::OpenSSL::EC::EC_GROUP::get_degree($group)
   my $order = Crypt::OpenSSL::EC::EC_GROUP::get_order($group, $order, $ctx);
   Crypt::OpenSSL::EC::EC_POINT::mul($group, $Q, $order, $P, $n1, $ctx));
   Crypt::OpenSSL::EC::EC_POINT::free($P);
   Crypt::OpenSSL::EC::EC_GROUP::free($group);

DESCRIPTION

This module provides a standard (non-OO) interface to the OpenSSL EC (Elliptic Curve) library. Some OO Calls are supported.

Most of the functions described in openssl/ec.h are supported.

It provides the Crypt::OpenSSL::EC class which defines some high level functions and constants. At also provides 4 other classes for managing EC objects:

Crypt::OpenSSL::EC::EC_GROUP
Crypt::OpenSSL::EC::EC_POINT
Crypt::OpenSSL::EC::EC_KEY
Crypt::OpenSSL::EC::EC_METHOD

All objects created by these 4 classes are implemented as blessed Perl mortal references. This ensures they will be auto-destroyed when the Perl variable becomes unreferenced. ASlo the approproae EC free function wil be called to free the underlying EC object.

Further, it means that many of the functions below can be called using O-O methods. If a method's first argument is the same as the class the method is in, then it can be called O-O style. For example the following 2 calls are equivalent:

my $newgroup = Crypt::OpenSSL::EC::EC_GROUP::dup($group);
my $newgroup = $group->dup();
Crypt::OpenSSL::EC::EC_GFp_simple_method();

Returns the basic GFp ec methods which provides the basis for the optimized methods.

Crypt::OpenSSL::EC::EC_GFp_mont_method();

Returns GFp methods using montgomery multiplication.

Crypt::OpenSSL::EC::EC_GFp_nist_method();

Returns GFp methods using optimized methods for NIST recommended curves

Crypt::OpenSSL::EC::EC_GF2m_simple_method();

Not available if OPENSSL_NO_EC2M is defined in OpenSSL.

Returns the basic GF2m ec method

Crypt::OpenSSL::EC::EC_GROUP::new($method);

Creates a new EC_GROUP object $method is the method to use

Crypt::OpenSSL::EC::EC_GROUP::set_curve_GFp($group, $p, $a, $b, $ctx);

Sets the parameter of a ec over GFp defined by y^2 = x^3 + a*x + b group EC_GROUP object p BIGNUM with the prime number a BIGNUM with parameter a of the equation b BIGNUM with parameter b of the equation ctx BN_CTX object (optional) return 1 on success and 0 if an error occured

Crypt::OpenSSL::EC::EC_GROUP::method_of($group);

Returns the EC_METHOD of the EC_GROUP object.

Crypt::OpenSSL::EC::EC_METHOD::get_field_type($method)

Returns the field type of the EC_METHOD.

Crypt::OpenSSL::EC::EC_GROUP::copy($dst, $src);

Copies EC_GROUP objects. Note: both EC_GROUPs must use the same EC_METHOD. return newly created EC_GROUP object or NULL in case of an error.

Crypt::OpenSSL::EC::EC_GROUP::dup($src);

Creates a new EC_GROUP object and copies the copies the content form src to the newly created EC_GROUP object. return newly created EC_GROUP object or NULL in case of an error.

Crypt::OpenSSL::EC::EC_GROUP::get_curve_GFp($group, $p, $a, $b, $ctx);

Gets the parameter of the ec over GFp defined by y^2 = x^3 + a*x + b group EC_GROUP object p BIGNUM for the prime number a BIGNUM for parameter a of the equation b BIGNUM for parameter b of the equation ctx BN_CTX object (optional) return 1 on success and 0 if an error occured

Crypt::OpenSSL::EC::EC_GROUP::set_curve_GF2m($group, $p, $a, $b, $ctx);

Not available if OPENSSL_NO_EC2M is defined in OpenSSL.

Sets the parameter of a ec over GF2m defined by y^2 + x*y = x^3 + a*x^2 + b group EC_GROUP object p BIGNUM with the polynomial defining the underlying field a BIGNUM with parameter a of the equation b BIGNUM with parameter b of the equation ctx BN_CTX object (optional) return 1 on success and 0 if an error occured

Crypt::OpenSSL::EC::EC_GROUP::get_curve_GF2m($group, $p, $a, $b, $ctx);

Not available if OPENSSL_NO_EC2M is defined in OpenSSL.

Gets the parameter of the ec over GF2m defined by y^2 + x*y = x^3 + a*x^2 + b group EC_GROUP object p BIGNUM for the polynomial defining the underlying field a BIGNUM for parameter a of the equation b BIGNUM for parameter b of the equation ctx BN_CTX object (optional) return 1 on success and 0 if an error occured

Crypt::OpenSSL::EC::print_errs();
Crypt::OpenSSL::EC::EC_POINT::new($group);

Creates a new EC_POINT object for the specified EC_GROUP group EC_GROUP the underlying EC_GROUP object return newly created EC_POINT object or NULL if an error occurred

Crypt::OpenSSL::EC::EC_POINT::free($point);

Frees a EC_POINT object point EC_POINT object to be freed This should normally not be called from Perl, since EC_POINT objects created by this library are auto-destroyed when they become unreferenced.

Crypt::OpenSSL::EC::EC_POINT::clear_free($point);

Clears and frees a EC_POINT object point EC_POINT object to be cleared and freed This should normally not be called from Perl, since EC_POINT objects created by this library are auto-destroyed when they become unreferenced.

Crypt::OpenSSL::EC::EC_POINT::copy($dst, $src);

Copies EC_POINT object dst destination EC_POINT object src source EC_POINT object return 1 on success and 0 if an error occured

Crypt::OpenSSL::EC::EC_POINT::dup($src, $group);

Creates a new EC_POINT object and copies the content of the supplied EC_POINT src source EC_POINT object group underlying the EC_GROUP object return newly created EC_POINT object or NULL if an error occurred

Crypt::OpenSSL::EC::EC_POINT::set_to_infinity($group, $point);

Sets a point to infinity (neutral element) group underlying EC_GROUP object point EC_POINT to set to infinity return 1 on success and 0 if an error occured

Crypt::OpenSSL::EC::EC_POINT::get_Jprojective_coordinates_GFp($group, $p, $x, $y, $z, $ctx);

Gets the jacobian projective coordinates of a EC_POINT over GFp group underlying EC_GROUP object p EC_POINT object x BIGNUM for the x-coordinate y BIGNUM for the y-coordinate z BIGNUM for the z-coordinate ctx BN_CTX object (optional) return 1 on success and 0 if an error occured

Crypt::OpenSSL::EC::EC_POINT::set_affine_coordinates_GFp($group, $p, $x, $y, $ctx);

Sets the affine coordinates of a EC_POINT over GFp group underlying EC_GROUP object p EC_POINT object x BIGNUM with the x-coordinate y BIGNUM with the y-coordinate ctx BN_CTX object (optional) return 1 on success and 0 if an error occured

Crypt::OpenSSL::EC::EC_POINT::get_affine_coordinates_GFp($group, $p, $x, $y, $ctx);

Gets the affine coordinates of a EC_POINT over GFp group underlying EC_GROUP object p EC_POINT object x BIGNUM for the x-coordinate y BIGNUM for the y-coordinate ctx BN_CTX object (optional) return 1 on success and 0 if an error occured

Crypt::OpenSSL::EC::EC_POINT::set_compressed_coordinates_GFp($group, $p, $x, $y_bit, $ctx);

Sets the x9.62 compressed coordinates of a EC_POINT over GFp group underlying EC_GROUP object p EC_POINT object x BIGNUM with x-coordinate y_bit integer with the y-Bit (either 0 or 1) ctx BN_CTX object (optional) return 1 on success and 0 if an error occured

Crypt::OpenSSL::EC::EC_POINT::set_affine_coordinates_GF2m($group, $p, $x, $y, $ctx);

Not available if OPENSSL_NO_EC2M is defined in OpenSSL.

Sets the affine coordinates of a EC_POINT over GF2m group underlying EC_GROUP object p EC_POINT object x BIGNUM with the x-coordinate y BIGNUM with the y-coordinate ctx BN_CTX object (optional) return 1 on success and 0 if an error occured

Crypt::OpenSSL::EC::EC_POINT::get_affine_coordinates_GF2m($group, $p, $x, $y, $ctx);

Not available if OPENSSL_NO_EC2M is defined in OpenSSL.

Gets the affine coordinates of a EC_POINT over GF2m group underlying EC_GROUP object p EC_POINT object x BIGNUM for the x-coordinate y BIGNUM for the y-coordinate ctx BN_CTX object (optional) return 1 on success and 0 if an error occured

Crypt::OpenSSL::EC::EC_POINT::set_compressed_coordinates_GF2m($group, $p, $x, $y_bit, $ctx);

Not available if OPENSSL_NO_EC2M is defined in OpenSSL.

Sets the x9.62 compressed coordinates of a EC_POINT over GF2m group underlying EC_GROUP object p EC_POINT object x BIGNUM with x-coordinate y_bit integer with the y-Bit (either 0 or 1) ctx BN_CTX object (optional) \return 1 on success and 0 if an error occured

Crypt::OpenSSL::EC::EC_POINT::is_at_infinity($group, $p);

Checks whether the point is the neutral element of the group group the underlying EC_GROUP object p EC_POINT object return 1 if the point is the neutral element and 0 otherwise

Crypt::OpenSSL::EC::EC_POINT::point2oct($group, $p, $form, $ctx);

Encodes a EC_POINT object to a octet string group underlying EC_GROUP object p EC_POINT object form point conversion form ctx BN_CTX object (optional) return the encoded EC point

Crypt::OpenSSL::EC::EC_POINT::oct2point($group, $p, $buf, $ctx);

Decodes a EC_POINT from a octet string group underlying EC_GROUP object p EC_POINT object buf buffer with the encoded ec point ctx BN_CTX object (optional) return 1 on success and 0 if an error occured

Crypt::OpenSSL::EC::EC_POINT::point2bn($group, $p, $form, $bn, $ctx);
Crypt::OpenSSL::EC::EC_POINT::bn2point($group, $bn, $p, $ctx);
Crypt::OpenSSL::EC::EC_POINT::point2hex($group, $p, $form, $bn, $ctx);
Crypt::OpenSSL::EC::EC_POINT::hex2point($group, $bn, $p, $ctx);
Crypt::OpenSSL::EC::EC_POINT::add($group, $r, $a, $b, $ctx);
 Computes the sum of two EC_POINT 
  group  underlying EC_GROUP object
  r      EC_POINT object for the result (r = a + b)
  a      EC_POINT object with the first summand
  b      EC_POINT object with the second summand
  ctx    BN_CTX object (optional)
  return 1 on success and 0 if an error occured
Crypt::OpenSSL::EC::EC_POINT::dbl($group, $r, $a, $ctx);

Computes the double of a EC_POINT group underlying EC_GROUP object r EC_POINT object for the result (r = 2 * a) a EC_POINT object ctx BN_CTX object (optional) return 1 on success and 0 if an error occured

Crypt::OpenSSL::EC::EC_POINT::invert($group, $a, $ctx);

Computes the inverse of a EC_POINT group underlying EC_GROUP object a EC_POINT object to be inverted (it's used for the result as well) ctx BN_CTX object (optional) return 1 on success and 0 if an error occured

Crypt::OpenSSL::EC::EC_POINT::is_on_curve($group, $point, $ctx));

Checks whether the point is on the curve group underlying EC_GROUP object point EC_POINT object to check ctx BN_CTX object (optional) return 1 if point if on the curve and 0 otherwise

Crypt::OpenSSL::EC::EC_POINT::cmp($group, $a, $b, $ctx);

Compares two EC_POINTs group underlying EC_GROUP object a first EC_POINT object b second EC_POINT object ctx BN_CTX object (optional) return 0 if both points are equal and a value != 0 otherwise

Crypt::OpenSSL::EC::EC_POINT::make_affine($group, $point, $ct);
Crypt::OpenSSL::EC::EC_POINTs::make_affine

Not Implemented

Crypt::OpenSSL::EC::EC_POINTs::mul

Not Implemented

Crypt::OpenSSL::EC::EC_GROUP::set_generator($group, $generator, $order, $cofactor);

Sets the generator and it's order/cofactor of a EC_GROUP object. group EC_GROUP object generator EC_POINT object with the generator. order the order of the group generated by the generator. cofactor the index of the sub-group generated by the generator in the group of all points on the elliptic curve. return 1 on success and 0 if an error occured

Crypt::OpenSSL::EC::EC_GROUP::get0_generator($group);

Returns the generator of a EC_GROUP object.

  group  EC_GROUP object

return the currently used generator (possibly NULL).

Crypt::OpenSSL::EC::EC_GROUP::get_degree($group)

Returns the number of bits needed to represent a field element group EC_GROUP object return number of bits needed to represent a field element

Crypt::OpenSSL::EC::EC_GROUP::check($group, $ctx);

Checks whether the parameter in the EC_GROUP define a valid ec group group EC_GROUP object ctx BN_CTX object (optional) return 1 if group is a valid ec group and 0 otherwise

Crypt::OpenSSL::EC::EC_GROUP::check_discriminant($group, $ctx);

Checks whether the discriminant of the elliptic curve is zero or not group EC_GROUP object ctx BN_CTX object (optional) return 1 if the discriminant is not zero and 0 otherwise

Crypt::OpenSSL::EC:: EC_GROUP::cmp($a, $b, $ctx);

Compares two EC_GROUP objects a first EC_GROUP object b second EC_GROUP object ctx BN_CTX object (optional) return 0 if both groups are equal and 1 otherwise

Crypt::OpenSSL::EC::EC::EC_GROUP::new_curve_GFp($p, $a, $b, $ctx);

Creates a new EC_GROUP object with the specified parameters defined over GFp (defined by the equation y^2 = x^3 + a*x + b) p BIGNUM with the prime number a BIGNUM with the parameter a of the equation b BIGNUM with the parameter b of the equation ctx BN_CTX object (optional) return newly created EC_GROUP object with the specified parameters

Crypt::OpenSSL::EC::EC_GROUP::new_curve_GF2m($p, $a, $b, $ctx);

Not available if OPENSSL_NO_EC2M is defined in OpenSSL.

Creates a new EC_GROUP object with the specified parameters defined over GF2m (defined by the equation y^2 + x*y = x^3 + a*x^2 + b) p BIGNUM with the polynomial defining the underlying field a BIGNUM with the parameter a of the equation b BIGNUM with the parameter b of the equation ctx BN_CTX object (optional) return newly created EC_GROUP object with the specified parameters

Crypt::OpenSSL::EC::EC_GROUP::new_by_curve_name($nid);

Creates a EC_GROUP object with a curve specified by a NID nid NID of the OID of the curve name return newly created EC_GROUP object with specified curve or NULL if an error occurred

Crypt::OpenSSL::EC::EC_get_builtin_curves($r, $nitems);

EC_builtin_curves(EC_builtin_curve *r, size_t size) returns number of all available curves or zero if a error occurred. In case r ist not zero nitems EC_builtin_curve structures are filled with the data of the first nitems internal groups

Crypt::OpenSSL::EC::EC_GROUP::get_order($group, $order, $ctx);

Gets the order of a EC_GROUP

  group  EC_GROUP object
  order  BIGNUM to which the order is copied
  ctx    BN_CTX object (optional)
  return 1 on success and 0 if an error occured
Crypt::OpenSSL::EC::EC_GROUP::get_cofactor($group, $cofactopr, $ctx)

Gets the cofactor of a EC_GROUP

  group     EC_GROUP object
  cofactor  BIGNUM to which the cofactor is copied
  ctx       BN_CTX object (optional)
  return 1 on success and 0 if an error occured
Crypt::OpenSSL::EC::EC_GROUP::set_curve_name($group, $nid);

Sets the name of a EC_GROUP object group EC_GROUP object nid NID of the curve name OID

Crypt::OpenSSL::EC::EC_GROUP::get_curve_name($group);

Returns the curve name of a EC_GROUP object group EC_GROUP object return NID of the curve name OID or 0 if not set.

Crypt::OpenSSL::EC::EC_GROUP::set_asn1_flag($group, $flag);

Sets the ASN flag for the group

Crypt::OpenSSL::EC::EC_GROUP::get_asn1_flag($group);

Returns the ASN flag for the group

Crypt::OpenSSL::EC::EC_GROUP::set_point_conversion_form($group, $form);

Sets the point conversion form.

Crypt::OpenSSL::EC::EC_GROUP::get_point_conversion_form($group);

Retuns the point conversion for for the group

Crypt::OpenSSL::EC::EC_GROUP::get0_seed($group);

Returns the 0 seed

Crypt::OpenSSL::EC::EC_GROUP::get_seed_len($group);

Returns the seed length

Crypt::OpenSSL::EC::EC_GROUP::set_seed($group, $seed);

Sets the group seed

Crypt::OpenSSL::EC::EC_POINT::mul($group, $r, $n, $q, $m, $ctx));

Computes r = generator * n + q * m group underlying EC_GROUP object r EC_POINT object for the result n BIGNUM with the multiplier for the group generator (optional) q EC_POINT object with the first factor of the second summand m BIGNUM with the second factor of the second summand ctx BN_CTX object (optional) return 1 on success and 0 if an error occured

Crypt::OpenSSL::EC::EC_GROUP::precompute_mult($group, $ctx);

Stores multiples of generator for faster point multiplication group EC_GROUP object ctx BN_CTX object (optional) return 1 on success and 0 if an error occured

Crypt::OpenSSL::EC::EC_GROUP::have_precompute_mult($group);

Reports whether a precomputation has been done group EC_GROUP object return 1 if a pre-computation has been done and 0 otherwise

Crypt::OpenSSL::EC::EC_GROUP::get_basis_type($group);

EC_GROUP_get_basis_type() returns the NID of the basis type used to represent the field elements

Crypt::OpenSSL::EC::EC_GROUP::get_trinomial_basis($group, $k);

Not available if OPENSSL_NO_EC2M is defined in OpenSSL.

Crypt::OpenSSL::EC:: EC_GROUP::get_pentanomial_basis($group, $k1, $k2, $k3);

Not available if OPENSSL_NO_EC2M is defined in OpenSSL.

Crypt::OpenSSL::EC::EC_GROUP::free($group);

Frees a EC_GROUP object. This should normally not be called from Perl, since EC_GROUP objects created by this library are auto-destroyed when they become unreferenced.

Crypt::OpenSSL::EC::EC_GROUP::clear_free($group);

Clears and frees a EC_GROUP object This should normally not be called from Perl, since EC_GROUP objects created by this library are auto-destroyed when they become unreferenced.

Crypt::OpenSSL::EC::EC_KEY::new(); Creates a new EC_KEY object. return EC_KEY object or NULL if an error occurred.
Crypt::OpenSSL::EC::EC_KEY::new_by_curve_name($nid);

Creates a new EC_KEY object using a named curve as underlying EC_GROUP object. nid NID of the named curve. return EC_KEY object or NULL if an error occurred.

Crypt::OpenSSL::EC::EC_KEY::free($key);

Frees a EC_KEY object. key EC_KEY object to be freed. This should normally not be called from Perl, since EC_KEY objects created by this library are auto-destroyed when they become unreferenced.

Crypt::OpenSSL::EC::EC_KEY::copy($dst, $src);

Copies a EC_KEY object. dst destination EC_KEY object src src EC_KEY object return dst or NULL if an error occurred.

Crypt::OpenSSL::EC::EC_KEY::dup($src);

Creates a new EC_KEY object and copies the content from src to it. src the source EC_KEY object return newly created EC_KEY object or NULL if an error occurred.

Crypt::OpenSSL::EC::EC_KEY::up_ref($key);

Increases the internal reference count of a EC_KEY object. key EC_KEY object return 1 on success and 0 if an error occurred.

Crypt::OpenSSL::EC::EC_KEY::get0_group($key);

Returns the EC_GROUP object of a EC_KEY object key EC_KEY object \return the EC_GROUP object (possibly NULL).

Crypt::OpenSSL::EC::EC_KEY::set_group($key, $group);

Sets the EC_GROUP of a EC_KEY object. key EC_KEY object group EC_GROUP to use in the EC_KEY object (note: the EC_KEY object will use an own copy of the EC_GROUP). return 1 on success and 0 if an error occurred.

Crypt::OpenSSL::EC::EC_KEY::set_private_key($key, $prv);

Sets the private key of a EC_KEY object. key EC_KEY object prv BIGNUM with the private key (note: the EC_KEY object will use an own copy of the BIGNUM). return 1 on success and 0 if an error occurred.

Crypt::OpenSSL::EC::EC_KEY::get0_public_key($key);

Returns the public key of a EC_KEY object. key the EC_KEY object return a EC_POINT object with the public key (possibly NULL)

Crypt::OpenSSL::EC::EC_KEY::set_public_key($key, $pub);

Sets the public key of a EC_KEY object. key EC_KEY object pub EC_POINT object with the public key (note: the EC_KEY object will use an own copy of the EC_POINT object). return 1 on success and 0 if an error occurred.

Crypt::OpenSSL::EC::EC_KEY::get_enc_flags($key);
Crypt::OpenSSL::EC::EC_KEY::set_enc_flags($key, $flags);
Crypt::OpenSSL::EC::EC_KEY::get_conv_form($key)
Crypt::OpenSSL::EC::EC_KEY::set_conv_form($key, $form);
Crypt::OpenSSL::EC::EC_KEY::get_key_method_data

Not Implemented

Crypt::OpenSSL::EC::EC_KEY::insert_key_method_data

Not Implemented

Crypt::OpenSSL::EC::EC_KEY::set_asn1_flag($key, $flag);
Crypt::OpenSSL::EC::EC_KEY::precompute_mult($key, $ctx);

Creates a table of pre-computed multiples of the generator to further EC_KEY operations. key EC_KEY object ctx BN_CTX object (optional) return 1 on success and 0 if an error occurred.

Crypt::OpenSSL::EC::EC_KEY::generate_key($key);

Creates a new ec private (and optional a new public) key. key EC_KEY object return 1 on success and 0 if an error occurred.

Crypt::OpenSSL::EC::EC_KEY::check_key($key);

Verifies that a private and/or public key is valid. key the EC_KEY object return 1 on success and 0 otherwise.

EXPORT

None by default.

Exportable constants

  EC_F_COMPUTE_WNAF
  EC_F_D2I_ECPARAMETERS
  EC_F_D2I_ECPKPARAMETERS
  EC_F_D2I_ECPRIVATEKEY
  EC_F_DO_EC_KEY_PRINT
  EC_F_ECKEY_PARAM2TYPE
  EC_F_ECKEY_PARAM_DECODE
  EC_F_ECKEY_PRIV_DECODE
  EC_F_ECKEY_PRIV_ENCODE
  EC_F_ECKEY_PUB_DECODE
  EC_F_ECKEY_PUB_ENCODE
  EC_F_ECKEY_TYPE2PARAM
  EC_F_ECPARAMETERS_PRINT
  EC_F_ECPARAMETERS_PRINT_FP
  EC_F_ECPKPARAMETERS_PRINT
  EC_F_ECPKPARAMETERS_PRINT_FP
  EC_F_ECP_NIST_MOD_192
  EC_F_ECP_NIST_MOD_224
  EC_F_ECP_NIST_MOD_256
  EC_F_ECP_NIST_MOD_521
  EC_F_EC_ASN1_GROUP2CURVE
  EC_F_EC_ASN1_GROUP2FIELDID
  EC_F_EC_ASN1_GROUP2PARAMETERS
  EC_F_EC_ASN1_GROUP2PKPARAMETERS
  EC_F_EC_ASN1_PARAMETERS2GROUP
  EC_F_EC_ASN1_PKPARAMETERS2GROUP
  EC_F_EC_EX_DATA_SET_DATA
  EC_F_EC_GF2M_MONTGOMERY_POINT_MULTIPLY
  EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT
  EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE
  EC_F_EC_GF2M_SIMPLE_OCT2POINT
  EC_F_EC_GF2M_SIMPLE_POINT2OCT
  EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES
  EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES
  EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES
  EC_F_EC_GFP_MONT_FIELD_DECODE
  EC_F_EC_GFP_MONT_FIELD_ENCODE
  EC_F_EC_GFP_MONT_FIELD_MUL
  EC_F_EC_GFP_MONT_FIELD_SET_TO_ONE
  EC_F_EC_GFP_MONT_FIELD_SQR
  EC_F_EC_GFP_MONT_GROUP_SET_CURVE
  EC_F_EC_GFP_MONT_GROUP_SET_CURVE_GFP
  EC_F_EC_GFP_NIST_FIELD_MUL
  EC_F_EC_GFP_NIST_FIELD_SQR
  EC_F_EC_GFP_NIST_GROUP_SET_CURVE
  EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT
  EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE
  EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE_GFP
  EC_F_EC_GFP_SIMPLE_GROUP_SET_GENERATOR
  EC_F_EC_GFP_SIMPLE_MAKE_AFFINE
  EC_F_EC_GFP_SIMPLE_OCT2POINT
  EC_F_EC_GFP_SIMPLE_POINT2OCT
  EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE
  EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES
  EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES_GFP
  EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES
  EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES_GFP
  EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES
  EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES_GFP
  EC_F_EC_GROUP_CHECK
  EC_F_EC_GROUP_CHECK_DISCRIMINANT
  EC_F_EC_GROUP_COPY
  EC_F_EC_GROUP_GET0_GENERATOR
  EC_F_EC_GROUP_GET_COFACTOR
  EC_F_EC_GROUP_GET_CURVE_GF2M
  EC_F_EC_GROUP_GET_CURVE_GFP
  EC_F_EC_GROUP_GET_DEGREE
  EC_F_EC_GROUP_GET_ORDER
  EC_F_EC_GROUP_GET_PENTANOMIAL_BASIS
  EC_F_EC_GROUP_GET_TRINOMIAL_BASIS
  EC_F_EC_GROUP_NEW
  EC_F_EC_GROUP_NEW_BY_CURVE_NAME
  EC_F_EC_GROUP_NEW_FROM_DATA
  EC_F_EC_GROUP_PRECOMPUTE_MULT
  EC_F_EC_GROUP_SET_CURVE_GF2M
  EC_F_EC_GROUP_SET_CURVE_GFP
  EC_F_EC_GROUP_SET_EXTRA_DATA
  EC_F_EC_GROUP_SET_GENERATOR
  EC_F_EC_KEY_CHECK_KEY
  EC_F_EC_KEY_COPY
  EC_F_EC_KEY_GENERATE_KEY
  EC_F_EC_KEY_NEW
  EC_F_EC_KEY_PRINT
  EC_F_EC_KEY_PRINT_FP
  EC_F_EC_POINTS_MAKE_AFFINE
  EC_F_EC_POINT_ADD
  EC_F_EC_POINT_CMP
  EC_F_EC_POINT_COPY
  EC_F_EC_POINT_DBL
  EC_F_EC_POINT_GET_AFFINE_COORDINATES_GF2Mg
  EC_F_EC_POINT_GET_AFFINE_COORDINATES_GFP
  EC_F_EC_POINT_GET_JPROJECTIVE_COORDINATES_GFP
  EC_F_EC_POINT_INVERT
  EC_F_EC_POINT_IS_AT_INFINITY
  EC_F_EC_POINT_IS_ON_CURVE
  EC_F_EC_POINT_MAKE_AFFINE
  EC_F_EC_POINT_MUL
  EC_F_EC_POINT_NEW
  EC_F_EC_POINT_OCT2POINT
  EC_F_EC_POINT_POINT2OCT
  EC_F_EC_POINT_SET_AFFINE_COORDINATES_GF2M
  EC_F_EC_POINT_SET_AFFINE_COORDINATES_GFP
  EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GF2M
  EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GFP
  EC_F_EC_POINT_SET_JPROJECTIVE_COORDINATES_GFP
  EC_F_EC_POINT_SET_TO_INFINITY
  EC_F_EC_PRE_COMP_DUP
  EC_F_EC_PRE_COMP_NEW
  EC_F_EC_WNAF_MUL
  EC_F_EC_WNAF_PRECOMPUTE_MULT
  EC_F_I2D_ECPARAMETERS
  EC_F_I2D_ECPKPARAMETERS
  EC_F_I2D_ECPRIVATEKEY
  EC_F_I2O_ECPUBLICKEY
  EC_F_O2I_ECPUBLICKEY
  EC_F_OLD_EC_PRIV_DECODE
  EC_F_PKEY_EC_CTRL
  EC_F_PKEY_EC_CTRL_STR
  EC_F_PKEY_EC_DERIVE
  EC_F_PKEY_EC_KEYGEN
  EC_F_PKEY_EC_PARAMGEN
  EC_F_PKEY_EC_SIGN
  EC_PKEY_NO_PARAMETERS
  EC_PKEY_NO_PUBKEY
  EC_R_ASN1_ERROR
  EC_R_ASN1_UNKNOWN_FIELD
  EC_R_BUFFER_TOO_SMALL
  EC_R_D2I_ECPKPARAMETERS_FAILURE
  EC_R_DECODE_ERROR
  EC_R_DISCRIMINANT_IS_ZERO
  EC_R_EC_GROUP_NEW_BY_NAME_FAILURE
  EC_R_FIELD_TOO_LARGE
  EC_R_GROUP2PKPARAMETERS_FAILURE
  EC_R_I2D_ECPKPARAMETERS_FAILURE
  EC_R_INCOMPATIBLE_OBJECTS
  EC_R_INVALID_ARGUMENT
  EC_R_INVALID_COMPRESSED_POINT
  EC_R_INVALID_COMPRESSION_BIT
  EC_R_INVALID_CURVE
  EC_R_INVALID_DIGEST_TYPE
  EC_R_INVALID_ENCODING
  EC_R_INVALID_FIELD
  EC_R_INVALID_FORM
  EC_R_INVALID_GROUP_ORDER
  EC_R_INVALID_PENTANOMIAL_BASIS
  EC_R_INVALID_PRIVATE_KEY
  EC_R_INVALID_TRINOMIAL_BASIS
  EC_R_KEYS_NOT_SET
  EC_R_MISSING_PARAMETERS
  EC_R_MISSING_PRIVATE_KEY
  EC_R_NOT_A_NIST_PRIME
  EC_R_NOT_A_SUPPORTED_NIST_PRIME
  EC_R_NOT_IMPLEMENTED
  EC_R_NOT_INITIALIZED
  EC_R_NO_FIELD_MOD
  EC_R_NO_PARAMETERS_SET
  EC_R_PASSED_NULL_PARAMETER
  EC_R_PKPARAMETERS2GROUP_FAILURE
  EC_R_POINT_AT_INFINITY
  EC_R_POINT_IS_NOT_ON_CURVE
  EC_R_SLOT_FULL
  EC_R_UNDEFINED_GENERATOR
  EC_R_UNDEFINED_ORDER
  EC_R_UNKNOWN_GROUP
  EC_R_UNKNOWN_ORDER
  EC_R_UNSUPPORTED_FIELD
  EC_R_WRONG_ORDER
  EVP_PKEY_CTRL_EC_PARAMGEN_CURVE_NID
  OPENSSL_ECC_MAX_FIELD_BITS
  OPENSSL_EC_NAMED_CURVE
  POINT_CONVERSION_COMPRESSED
  POINT_CONVERSION_HYBRID
  POINT_CONVERSION_UNCOMPRESSED

SEE ALSO

Crypt::OpenSSL::Bignum

OpenSSL

AUTHOR

Mike McCauley, <mikem@airspayce.com>

COPYRIGHT AND LICENSE

Copyright (C) 2012 by Mike McCauley

This library is free software; you can redistribute it and/or modify it under the same terms as Perl itself, either Perl version 5.14.2 or, at your option, any later version of Perl 5 you may have available.