Strict avalanche criterion over finite fields

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...

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Bibliographic Details
Main Authors:	Li Yuan, Cusick T. W.
Format:	Article
Language:	English
Published:	De Gruyter 2007-01-01
Series:	Journal of Mathematical Cryptology
Subjects:	fourier transform, cryptography, boolean functions, algebraic normal form, strict avalanche criterion, resilience, bent functions, permutation polynomials, finite field, quadratic residue, legendre symbol
Online Access:	https://doi.org/10.1515/JMC.2007.005

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spelling	doaj-db9049f3082f4be4a4c8a14bc5d5cfbc2021-09-06T19:39:35ZengDe GruyterJournal of Mathematical Cryptology1862-29761862-29842007-01-0111657810.1515/JMC.2007.005Strict avalanche criterion over finite fieldsLi Yuan0Cusick T. W.11 Department of Mathematical Science, Alcorn State University, Alcorn State, MS 39096, USA. yuanli7983@gmail.com2 SUNY Department of Mathematics, 244 Mathematics Building, Buffalo, NY 14260, USA. cusick@buffalo.eduBoolean 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.https://doi.org/10.1515/JMC.2007.005fourier transform,cryptography,boolean functions,algebraic normal form,strict avalanche criterion,resilience,bent functions,permutation polynomials,finite field,quadratic residue,legendre symbol
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Li Yuan Cusick T. W.
spellingShingle	Li Yuan Cusick T. W. Strict avalanche criterion over finite fields Journal of Mathematical Cryptology fourier transform, cryptography, boolean functions, algebraic normal form, strict avalanche criterion, resilience, bent functions, permutation polynomials, finite field, quadratic residue, legendre symbol
author_facet	Li Yuan Cusick T. W.
author_sort	Li Yuan
title	Strict avalanche criterion over finite fields
title_short	Strict avalanche criterion over finite fields
title_full	Strict avalanche criterion over finite fields
title_fullStr	Strict avalanche criterion over finite fields
title_full_unstemmed	Strict avalanche criterion over finite fields
title_sort	strict avalanche criterion over finite fields
publisher	De Gruyter
series	Journal of Mathematical Cryptology
issn	1862-2976 1862-2984
publishDate	2007-01-01
description	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.
topic	fourier transform, cryptography, boolean functions, algebraic normal form, strict avalanche criterion, resilience, bent functions, permutation polynomials, finite field, quadratic residue, legendre symbol
url	https://doi.org/10.1515/JMC.2007.005
work_keys_str_mv	AT liyuan strictavalanchecriterionoverfinitefields AT cusicktw strictavalanchecriterionoverfinitefields
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Strict avalanche criterion over finite fields

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