A comparative Study to calculate the Runs Property in the encryption systems

Abstract

Cryptographic applications demand much more of a pseudo-random-sequence generator than do most other applications. Cryptographic randomness does not mean just statistical randomness, although that is part of it. For a sequence to be cryptographically secure pseudo-random, it must be unpredictable.The random sequences should satisfy the basic randomness postulates; one of them is the run postulate (sequences of the same bit). These sequences should have about the same number of ones and zeros, about half the runs should be of length one, one quarter of length two, one eighth of length three, and so on.The distribution of run lengths for zeros and ones should be the same. These properties can be measured deterministicallyand then compared to statistical expectations using a chi-square test.In this paper the Run Criterion, is calculated, it can be calculated for any key generator before it be implemented or constructed (software or hardware).The cryptosystems: Linear, Product and Brüer are chosen as study cases.