Estimation of the Frequency Postulate for non-Linear Sequences Generated from Complement Product and Shrinking Generators

Abstract

The Randomness is one of the basic criterions to measure stream cipherEfficiency. The stream cipher generator depends basically on LinearFeedBack Shift Register which is considered as one of the basic units ofStream Cipher Systems. In this paper, the frequency postulate ofRandomness criteria is calculated theoretically for non-linear stream ciphersystems before it be implemented or constructed (software or hardware),this procedure save time and costs. Two non-linear stream ciphergenerators are chosen to apply the theoretical studies; these key generatorsare the Complement Product and Shrinking Generators. The theoreticalproofs of frequency estimation for the two key generators are introduced.