Cryptology ePrint Archive: Report 2012/033

A note on hyper-bent functions via Dillon-like exponents

Sihem Mesnager and Jean-Pierre Flori

Abstract: This note is devoted to hyper-bent functions with multiple trace terms (including binomial functions) via Dillon-like exponents. We show how the approach developed by Mesnager to extend the Charpin–Gong family and subsequently extended by Wang et al. fits in a much more general setting. To this end, we first explain how the original restriction for Charpin–Gong criterion can be weakened before generalizing the Mesnager approach to arbitrary Dillon-like exponents. Afterward, we tackle the problem of devising infinite families of extension degrees for which a given exponent is valid and apply these results not only to reprove straightforwardly the results of Mesnager and Wang et al., but also to characterize the hyper-bentness of new infinite classes of Boolean functions.

Category / Keywords: foundations / Boolean functions, hyper-bent functions, Walsh–Hadamard transform, exponential sums, Kloosterman sums, Dickson polynomial, finite field permutations, Dillon exponent.

Date: received 21 Jan 2012, last revised 23 Jan 2012

Contact author: flori at enst fr

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Version: 20120129:045118 (All versions of this report)

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