Partitioning CCZ classes into EA classes

Kathy Horadam; Russell East

doi:10.3934/amc.2012.6.95

Article Contents

2012, Volume 6, Issue 1: 95-106. Doi: 10.3934/amc.2012.6.95

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Partitioning CCZ classes into EA classes

Kathy Horadam^1, and
Russell East^1,

1.
RMIT University, G.P.O. Box 2476, Melbourne, VIC 3001

Received: January 2011

Revised: September 2011

Published: February 2012

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Abstract

EA equivalence classes and the coarser CCZ equivalence classes of functions over $GF(p^n)$ each preserve measures of nonlinearity desirable in cryptographic functions. We identify very precisely the condition on a linear permutation defining a CCZ isomorphism between functions which ensures that the CCZ isomorphism can be rewritten as EA isomorphism. We introduce new algebraic invariants $n(f)$ of the EA isomorphism class of $f$ and $s(f)$ of the CCZ isomorphism class of $f$, with $n(f) < s(f)$, and relate them to the differential uniformity of $f$. We formulate three questions about partitioning CCZ classes into EA classes and relate these to a conjecture of Edel's about quadratic APN functions.

Keywords:

Mathematics Subject Classification: Primary: 94A60; Secondary: 05B10, 20K35.

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