Public-key Cryptography: Theory and Practice

4.1. Introduction

Public-key cryptographic systems are based on the apparent intractability of solving certain computational problems. However, there is very little evidence (if any) to corroborate the fact that algorithmic solutions to these problems are really very difficult. In spite of intensive studies over a long period, mathematicians and cryptologists have not come up with good algorithms, and it is their failures that justify the attempts to go on building secure cryptographic protocols based on these problems. The inherent assumption is that it would be infeasible for an opponent having practical amounts of computing resources to break these cryptosystems in a reasonable amount of time. Of course, the fear remains that someone may ...