Note: APN permutations on Zn and Costas arrays

Authors:
Konstantinos Drakakis;Rod Gow;Gary McGuire
Affiliations:
School of Electrical, Electronic, and Mechanical Engineering, University College Dublin, Belfield, Dublin 4, Ireland and UCD CASL, University College Dublin, Belfield, Dublin 4, Ireland;School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland and UCD CASL, University College Dublin, Belfield, Dublin 4, Ireland;School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland and UCD CASL, University College Dublin, Belfield, Dublin 4, Ireland
Venue:
Discrete Applied Mathematics
Year:
2009

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Abstract

We study PN and APN functions over the integers modulo n. We give some construction techniques based on Costas arrays, which allow us to construct APN permutations on Z"p"-"1 where p is a prime. Although PN permutations do not exist, one set of our functions is very close to being a set of PN permutations.