Cryptology ePrint Archive: Report 2016/767

A conjecture about Gauss sums and bentness of binomial Boolean functions

Jean-Pierre Flori

Abstract: In this note, the polar decomposition of binary fields of even extension degree is used to reduce the evaluation of the Walsh transform of binomial Boolean functions to that of Gauss sums. In the case of extensions of degree four times an odd number, an explicit formula involving a Kloosterman sum is conjectured, proved with further restrictions, and supported by extensive experimental data in the general case. In particular, the validity of this formula is shown to be equivalent to a simple and efficient characterization for bentness previously conjectured by Mesnager.

Category / Keywords: foundations / boolean functions

Original Publication (with minor differences): WAIFI 2016

Date: received 9 Aug 2016, last revised 9 Aug 2016

Contact author: jean-pierre flori at ssi gouv fr

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Version: 20160812:172103 (All versions of this report)

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