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Asymptotic Nonlinearity of Boolean Functions

Author： Rodier François  

Publisher： Springer Publishing Company

ISSN： 0925-1022

Source： Designs, Codes and Cryptography, Vol.40, Iss.1, 2006-07, pp. : 59-70

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

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Abstract

Boolean functions on the space are not only important in the theory of error-correcting codes, but also in cryptography. In these two cases, the nonlinearity of these functions is a main concept. Carlet, Olejár and Stanek gave an asymptotic lower bound for the nonlinearity of most of them, and I gave an asymptotic upper bound which was strictly larger. In this article, I improve the bounds and get an exact limit for the nonlinearity of most of Boolean functions. This article is inspired by a paper of G. Halász about the related problem of real polynomials with random coefficients.

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