Cyclic/non-cyclic groups and their applications in credit card/ smart card security

Question

Can someone point me to resources on "Cyclic/non-cyclic groups and their applications in credit card/ smart card security"

What I have right now is some things on

1. Diffie-Hellman Key exchange protocol
2. El Gamal Public Key encryption
3. RSA Public Key Encryption

I would like to know if I am on the right track and any help would be appreciated.