Strict avalanche criterion over finite fields

Yuan Li; T. W. Cusick

doi:10.1515/JMC.2007.005

Strict avalanche criterion over finite fields

Yuan Li
, T. W. Cusick

Mathematics

Alcorn State University

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	65-78
Number of pages	14
Journal	Journal of Mathematical Cryptology
Volume	1
Issue number	1
DOIs	https://doi.org/10.1515/JMC.2007.005
State	Published - Jan 2007

Keywords

Algebraic normal form
Bent functions
Boolean functions
Cryptography
Finite field
Fourier transform
Legendre symbol
Permutation polynomials
Quadratic residue
Resilience
Strict avalanche criterion

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abstract = "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.",

keywords = "Algebraic normal form, Bent functions, Boolean functions, Cryptography, Finite field, Fourier transform, Legendre symbol, Permutation polynomials, Quadratic residue, Resilience, Strict avalanche criterion",

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KW - Algebraic normal form

KW - Bent functions

KW - Boolean functions

KW - Cryptography

KW - Finite field

KW - Fourier transform

KW - Legendre symbol

KW - Permutation polynomials

KW - Quadratic residue

KW - Resilience

KW - Strict avalanche criterion

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JO - Journal of Mathematical Cryptology

JF - Journal of Mathematical Cryptology

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ER -

Strict avalanche criterion over finite fields

Abstract

Keywords

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