Issue a session ID based on MD5 Digest. Pass the session ID as one of the parameters, unencrypted. Use the session ID to encrypt, pass around and decrypt the data. This way you get symmetrical encryption (not public-key encryption).

I would review Chapter 5 of Secure Programming Cookbook (even though it's for C/C++, not directly Perl) and just copy-paste something from there, since the encryption-decryption routine will be server-side anyway.