Title

New semifields, PN and APN functions

Document Type

Article

Publication Date

3-1-2010

Abstract

We describe a method of proving that certain functions f : F → F defined on a finite field F are either PN-functions (in odd characteristic) or APN-functions (in characteristic 2). This method is illustrated by giving short proofs of the APN-respectively the PN-property for various families of functions. The main new contribution is the construction of a family of PN-functions and their corresponding commutative semifields of dimension 4s in arbitrary odd characteristic. It is shown that a subfamily of order p 4s for odd s > 1 is not isotopic to previously known examples. © 2009 Springer Science+Business Media, LLC.

Publication Title

Designs, Codes, and Cryptography

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