New semifields, PN and APN functions
Document Type
Article
Publication Date
3-2010
Department
Department of Mathematical Sciences
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.
Publication Title
Designs, Codes, and Cryptography
Recommended Citation
Bierbrauer, J.
(2010).
New semifields, PN and APN functions.
Designs, Codes, and Cryptography,
54(3), 189-200.
http://doi.org/10.1007/s10623-009-9318-7
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/4876