Identity Schemes

Abstract

This chapter is for mathematicians, specifically number theory enthusiasts. It presents several identity schemes with which Alice and Bob, and sometimes Cathy and Denise, can prove to each other that both have a secret group key previously received from a trusted host by secure means. We need to be really sneaky; not only is the secret never revealed, but an interceptor cannot cryptanalyze it by overhearing the protocol interchange, even if overhearing the exchange many times. In the sneakiest schemes, Bob and the girls do not even know the secret group key itself; these schemes are called zero-knowledge proofs.