Strict avalanche criterion over finite fields

被引：8

作者：

Li, Yuan ^{[1
]}

Cusick, T. W. ^{[2
]}

机构：

[1] Alcorn State Univ, Dept Math Sci, Alcorn State, MS 39096 USA

[2] SUNY Buffalo, Dept Math, Buffalo, NY 14260 USA

来源：

JOURNAL OF MATHEMATICAL CRYPTOLOGY | 2007年 / 1卷 / 01期

关键词：

Fourier transform; cryptography; Boolean functions; algebraic normal form; strict avalanche criterion; resilience; bent functions; permutation polynomials; finite field; quadratic residue; Legendre symbol;

D O I：

10.1515/JMC.2007.005

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Boolean functions which satisfy the Strict Avalanche Criterion (SAC) play an important role in the art of information security. In this paper, we extend the concept of SAC to finite fields GF(p). A necessary and sufficient condition is given by using spectral analysis. Also, based on an interesting permutation polynomial theorem, we prove various facts about (n - 1)-th order SAC functions on GF(p). We also construct many such functions.

引用

页码：65 / 78

页数：14

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