Key minimal authentication systems for unconditional secrecy

Abstract

This paper is concerned with cryptosystems offering unconditional secrecy. For those perfect secrecy systems which involve using key just once, the theory is well established since Shannon’s works; however, this is not the case for those systems which involve using a key several times. This paper intends to take a rigorous approach to the definition of such systems. We use the basic model for a security code developped by Simmons, initially for unconditional authentication. We consider the definition of perfect L-fold secrecy given by Stinson and used by De Soete and others. We consider other definitions: Ordered Perfect L-fold secrety and Massey's Perfect L-fold secrecy, and attempt to classify them. Lower bounds are given for the number of keys in such perfect systems, and characterisation of systems meeting these lower bounds are obtained. The last part of the paper is concerned with discussing examples of key minimal systems providing unconditional secrecy.