Boolean Functions with Large Distance to All Bijective Monomials: N Odd Case

  • Amr Youssef
  • Guang Gong
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2259)

Abstract

Cryptographic Boolean functions should have large distance to functions with simple algebraic description to avoid cryptanalytic attacks based on successive approximation of the round function such as the interpolation attack. Hyper-bent functions achieve the maximal minimum distance to all the coordinate functions of all bijective monomials. However, this class of functions exists only for functions with even number of inputs. In this paper we provide some constructions for Boolean functions with odd number of inputs that achieve large distance to all the coordinate functions of all bijective monomials.

Key words

Boolean functions hyper-bent functions extended Hadamard transform Legendre sequences nonlinearity 

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Amr Youssef
    • 1
  • Guang Gong
    • 2
  1. 1.Department of Combinatorics & OptimizationCenter for Applied Cryptographic Research, University of WaterlooOntarioCanada
  2. 2.Department of Electrical and Computer EngineeringCenter for Applied Cryptographic Research, University of WaterlooOntarioCanada

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