Some facets of complexity theory and cryptography

Abstract

In this tutorial, selected topics of cryptology and of computational complexity theory are presented. We give a brief overview of the history and the foundations of classical cryptography, and then move on to modern public-key cryptography. Particular attention is paid to cryptographic protocols and the problem of constructing key components of protocols such as one-way functions. A function is one-way if it is easy to compute, but hard to invert. We discuss the notion of one-way functions both in a cryptographic and in a complexity-theoretic setting. We also consider interactive proof systems and present some interesting zero-knowledge protocols. In a zero-knowledge protocol, one party can convince the other party of knowing some secret information without disclosing any bit of this information. Motivated by these protocols, we survey some complexity-theoretic results on interactive proof systems and related complexity classes.