Background on Public Key Cryptography

Abstract

In this chapter we describe, very briefly, some classical concepts and cryptographic primitives that were the inspiration behind new, “non-commutative”, primitives discussed in our Chapter 4. It is not our goal here to give a comprehensive survey of all or even of the most popular public key cryptographic primitives in use today, but just of those relevant to the main theme of our book, which is using non-commutative groups in cryptography. In particular, we leave out RSA, the most common public key cryptosystem in use today, because its mechanism is based on Euler’s generalization of Fermat’s little theorem, an elementary fact from number theory that does not yet seem to have any analogs in non-commutative group theory.