Working (in one script)

#!/usr/bin/perl

use strict;
use warnings;
use Crypt::OpenSSL::RSA;
use Crypt::OpenSSL::Random;
use Data::Dumper;

my $password = 'test123';

sub encrypt_password {
  my $privkey  = shift;
  my $password = shift;

  #Crypt::OpenSSL::Random::random_seed('test');
  #Crypt::OpenSSL::RSA->import_random_seed();
  my $crypt = Crypt::OpenSSL::RSA->new_private_key($privkey);
  $crypt->use_pkcs1_padding;

  return $crypt->private_encrypt($password);
}

my $encrypted = encrypt_password('PRIVATEKEY-HERE', $password);
print Dumper($encrypted);

sub decrypt_password {
  my $pubkey   = shift;
  my $password = shift;

  #Crypt::OpenSSL::Random::random_seed('test');
  #Crypt::OpenSSL::RSA->import_random_seed();
  my $crypt = Crypt::OpenSSL::RSA->new_public_key($pubkey);

  return $crypt->public_decrypt($password);
}

print Dumper(decrypt_password('PUBLICKEY-HERE', $encrypted));