Ambiguity and deficiency in costas arrays and APN permutations

Authors:
Daniel Panario;Brett Stevens;Qiang Wang
Affiliations:
School of Mathematics and Statistics, Carleton University, Ottawa, Canada;School of Mathematics and Statistics, Carleton University, Ottawa, Canada;School of Mathematics and Statistics, Carleton University, Ottawa, Canada
Venue:
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Year:
2010

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Abstract

We introduce the concepts of weighted ambiguity and deficiency for a mapping between two finite Abelian groups of the same size. Then we study the optimum lower bounds of these measures for a permutation of ℤn and give a construction of permutations meeting the lower bound by modifying some permutation polynomials over finite fields. These permutations are also APN permutations.