International Association for Cryptologic Research

International Association
for Cryptologic Research

IACR News item: 07 July 2014

Chunming Tang, Yanfeng Q
ePrint Report ePrint Report
Hyper-bent functions as a subclass of bent functions attract much interest and it is elusive to completely characterize hyper-bent functions. Most of known hyper-bent functions are Boolean functions with Dillon exponents and they are often characterized by special values of Kloosterman sums.

In this paper, we present a method for characterizing hyper-bent functions

with Dillon exponents. A class of hyper-bent functions with Dillon exponents

over $\\mathbb{F}_{2^{2m}}$ can be characterized by

a Boolean function over $\\mathbb{F}_{2^m}$, whose Walsh spectrum takes the same value twice.

Further, we show several classes of

hyper-bent functions with Dillon exponents characterized by

Kloosterman sum identities and the Walsh

spectra of some common Boolean functions.

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