Permutation Resemblance

Li An Chen; Robert S. Coulter

doi:10.1109/TIT.2023.3292598

Permutation Resemblance

Li An Chen
, Robert S. Coulter

Mathematics Department

Boise State University

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

1 Scopus citations

Abstract

Motivated by the problem of constructing bijective maps with low differential uniformity, we introduce the notion of permutation resemblance of a function, which looks to measure the distance a given map is from being a permutation. We prove several results concerning permutation resemblance and show how it can be used to produce low differentially uniform bijections. We also study the permutation resemblance of planar functions, which over fields of odd characteristic are known not to be bijections and to have the optimal differential uniformity.

Original language	English
Pages (from-to)	6711-6718
Number of pages	8
Journal	IEEE Transactions on Information Theory
Volume	69
Issue number	10
DOIs	https://doi.org/10.1109/TIT.2023.3292598
State	Published - 1 Oct 2023

Keywords

differential uniformity
finite fields
image sets
Permutation resemblance
planar functions

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10.1109/TIT.2023.3292598

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abstract = "Motivated by the problem of constructing bijective maps with low differential uniformity, we introduce the notion of permutation resemblance of a function, which looks to measure the distance a given map is from being a permutation. We prove several results concerning permutation resemblance and show how it can be used to produce low differentially uniform bijections. We also study the permutation resemblance of planar functions, which over fields of odd characteristic are known not to be bijections and to have the optimal differential uniformity.",

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AB - Motivated by the problem of constructing bijective maps with low differential uniformity, we introduce the notion of permutation resemblance of a function, which looks to measure the distance a given map is from being a permutation. We prove several results concerning permutation resemblance and show how it can be used to produce low differentially uniform bijections. We also study the permutation resemblance of planar functions, which over fields of odd characteristic are known not to be bijections and to have the optimal differential uniformity.

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KW - finite fields

KW - image sets

KW - Permutation resemblance

KW - planar functions

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Permutation Resemblance

Abstract

Keywords

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