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.