A deterministic encryption scheme (as opposed to a probabilistic encryption scheme) is a cryptosystem which always produces the same ciphertext for a given plaintext and key, even over separate executions of the encryption algorithm. Examples of deterministic encryption algorithms include the RSA cryptosystem (without encryption padding)

The documentation for Crypt::RSA specifically says:

[..] there exists a scheme called Simple RSA[16] that provides security without padding. However, Crypt::RSA doesn't implement this scheme yet.

Is there a CPAN module that implements deterministic asymmetric encryption?

$ perl -l
use strict;
use warnings;

use Log::Log4perl;
use Crypt::RSA;

my $rsa = new Crypt::RSA;
my ($public, $private) = $rsa->keygen(
  Identity  => 'Lord Macbeth <macbeth@glamis.com>',
  Size      => 1024,
  Password  => 'A day so foul & fair',
  Verbosity => 0,
) or die $rsa->errstr();

my $secret = q{Thanks for all the fish};

my $ciphertext1 =
  $rsa->encrypt(Message => $secret, Key => $public, Armour => 1,)
  || die $rsa->errstr();
my $ciphertext2 =
  $rsa->encrypt(Message => $secret, Key => $public, Armour => 1,)
  || die $rsa->errstr();

$ciphertext1 eq $ciphertext2 ? print q{deterministic} : print q{not de
+terministic};

__END__

not deterministic
$
[download]

Update: What would the consequences be if I disregarded the advise in the documentation:

In any event, Crypt::RSA::Primitives (without padding) should never be used directly.

my $prim = new Crypt::RSA::Primitives;
my $ctxt1 = $prim->core_encrypt (Key => $public, Plaintext => $pan); 
my $ctxt2 = $prim->core_encrypt (Key => $public, Plaintext => $pan); 
$ctxt1 eq $ctxt2 ? print q{deterministic} : print q{not deterministic}
+;
[download]

Prints "deterministic".