Some open problems in cryptography

Abstract

In the past, cryptography has been mainly concerned with the problem of private communication between two parties. A number of ciphers exist which solve this problem more or less satisfactorily. One common factor behind these ciphers is the use of certain secret keys. With the advent of commercial data networks, there is a need for many pairs of users to communicate in privacy. The classical method of distributing secret keys (over a secure channel) to each user pair becomes very expensive and alternative means have to be explored. This paper describes a method which does not require prior exchange of secret keys for private communication over a public network. The cryptanalytic complexity of breaking this system is related to the complexity of solving a certain zero-one integer programming problem.