- On Public Key Algorithms based on the Discrete Logarithm Problem
A general introduction on the topic (Cryptography related). I wrote this paper
for my Master's Comprehensive Exam (Spring 2002).
In this paper we introduce public key algorithms based on the discrete logarithm problem. We first define what we mean by a public key cryptosystem and then introduce the Diffie-Hellman key-agreement protocol. We generalize this protocol to arbitrary cyclic groups. From this protocol we derive the ElGamal cryptosystem, which is a public key cryptosystem in the sense of our definition. We furthermore introduce ElGamal signatures. All these algorithms are based on the discrete logarithm problem. We will introduce two algorithms which can be used to calculate discrete logarithms in finite fields. We will see, that the running time of these algorithms is high for large groups (or groups with special properties) and therefore impractical. We will further introduce alternatives to the traditional Z/p* group.