Boolean Functions Suitable for Strong Cipher Systems

Abstract

Cryptography is one of the important areas in computer science. For strong cipher systems Boolean functions and s-boxes with required cryptographic properties need to be developed. Many attacks on cipher systems consist of approximating the component Boolean functions and the component s-boxes. Many unitary transforms are useful in analyzing the strength of these Boolean functions and the S-boxes against the approximation. A fast and efficient system was implemented to calculate Walsh Hadamard Transform and Nega Hadamard Transform which was further used to calculate non-linearity and PAR values. This system was further extended to calculate the HN transform set and related PAR values. A fast method to calculate the HN transform set is incorporated in the PAR calculation system and results are analyzed. An s-box is chosen and its PAR values are compared with standard s-boxes and results are analyzed. A new method incorporating the Hill Climbing heuristic is also implemented to analyze the use of Nega Hadamard Transform in finding Boolean functions with better non-linearity and results were found to be improved.