Spectral domain analysis of correlation immune and resilient Boolean functions

被引：41

作者：

Carlet, C ^{[1
]}

Sarkar, P

机构：

[1] Univ Paris 08, F-93526 St Denis 02, France

[2] Inst Natl Rech Informat & Automat, Project CODES, F-78153 Le Chesnay, France

[3] Univ Waterloo, Dept Combinator & Optimizat, Ctr Appl Cryptog Res, Waterloo, ON N2L 3G1, Canada

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2002年 / 8卷 / 01期

关键词：

Boolean function; correlation immunity; resiliency; nonlinearity; algebraic degree; stream ciphers;

D O I：

10.1006/ffta.2001.0332

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We use a general property of Fourier transform to obtain direct proofs of recent divisibility results on the Walsh transform of correlation immune and resilient functions. Improved upper bounds on the nonlinearity of these functions are obtained from the divisibility results. We deduce further information on correlation immune and resilient functions. In particular, we obtain a necessary condition on the algebraic normal form of correlation immune functions attaining the maximum possible nonlinearity. (C) 2002 Elsevier Science.

引用

页码：120 / 130

页数：11

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