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- W1488367145 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 $$ 2^{n - 1} - 2^{leftlfloor {tfrac{n} {2}} rightrfloor } $$ . 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." @default.
- W1488367145 created "2016-06-24" @default.
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- W1488367145 date "2000-01-01" @default.
- W1488367145 modified "2023-10-05" @default.
- W1488367145 title "Construction of Nonlinear Boolean Functions with Important Cryptographic Properties" @default.
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- W1488367145 doi "https://doi.org/10.1007/3-540-45539-6_35" @default.
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