Cryptology ePrint Archive: Report 2005/089

Cryptographer's Toolkit for Construction of $8$-Bit Bent Functions

Hans Dobbertin and Gregor Leander

Abstract: Boolean functions form basic building blocks in various cryptographic algorithms. They are used for instance as filters in stream ciphers. Maximally non-linear (necessarily non-balanced) Boolean functions with an even number of variables are called bent functions. Bent functions can be modified to get balanced highly non-linear Boolean functions.

Recently the first author has demonstrated how bent functions can be studied in a recursive framework of certain integer-valued functions. Based on this new approach we describe the practical systematic construction of $8$-bit bent functions. We outline also how to compute the number of all $8$-bit bent functions.

Category / Keywords: bent functions, highly nonlinear Boolean functions