I want you to build a procedures that allow you to perform an Elliptic Curve Diffie-Hellman exchange to establish a shared secret. Use a NIST approved curve.
For each chunk of public information sent, generate an RSA Digital Signature.
Validate the RSA digital signature of the packets you receive.
Once you have a shared key encrypt a message using AES in GCM mode
Here is an online site you can use to validate your ECDH parameters:
[login to view URL]~tjw/jsbn/[login to view URL]