Graph Theoretic Approach to Randomness Test Based on the Overlapping Blocks

Abstract

Cryptographic parameters such as secret keys, should be chosen randomly and at the same time it should not be
 so difficult to reproduced them when necessary. Because of this, pseudorandom bit (or number) generators take the role of true random generators. Outputs of pseudorandom generators, although they are produced through some deterministic process, should be random looking, that is not distinguishable from true random sequences. In other word they should not follow any pattern. In this paper we propose a new approach using graph theory, to determine when to expected a fixed pattern to appear in a random sequence for the fist time. Using these expected values and comparing them with the observed values a randomness test can be defined. In this work patters are traced through the sequence in an overlapping manner.