Abstract
This paper addresses the problem of obtaining new construction methods for cryptographically significant Boolean functions. We show that for each positive integer m, there are infinitely many integers n (both odd and even), such that it is possible to construct n-variable, m-resilient functions having nonlinearity greater than \( 2^{n - 1} - 2^{\left\lfloor {\tfrac{n} {2}} \right\rfloor } \). Also we obtain better results than all published works on the construction of n-variable, m-resilient functions, including cases where the constructed functions have the maximum possible algebraic degree n − m − 1. Next we modify the Patterson-Wiedemann functions to construct balanced Boolean functions on n-variables having nonlinearity strictly greater than \( 2^{n - 1} - 2^{\tfrac{{n - 1}} {2}} \) for all odd n ≥ 15. In addition, we consider the properties strict avalanche criteria and propagation characteristics which are important for design of S-boxes in block ciphers and construct such functions with very high nonlinearity and algebraic degree.
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Sarkar, P., Maitra, S. (2000). Construction of Nonlinear Boolean Functions with Important Cryptographic Properties. In: Preneel, B. (eds) Advances in Cryptology — EUROCRYPT 2000. EUROCRYPT 2000. Lecture Notes in Computer Science, vol 1807. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45539-6_35
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DOI: https://doi.org/10.1007/3-540-45539-6_35
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