A New Tool for Assurance of Perfect Nonlinearity

Authors:
Nuray At;Stephen D. Cohen
Affiliations:
Department of Informatics, University of Bergen, Bergen, Norway 5020;Department of Mathematics, University of Glasgow, Glasgow, Scotland G12 8QW
Venue:
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
Year:
2008

Citing 5
Cited 1

Finite fields

Finite fields
Planar Functions and Planes of Lenz-Barlotti Class II

Designs, Codes and Cryptography
Highly nonlinear mappings

Journal of Complexity - Special issue on coding and cryptography
A family of skew Hadamard difference sets

Journal of Combinatorial Theory Series A
New families of almost perfect nonlinear power mappings

IEEE Transactions on Information Theory

Switching construction of planar functions on finite fields

WAIFI'10 Proceedings of the Third international conference on Arithmetic of finite fields

Quantified Score

Hi-index	0.00

Visualization

Abstract

Let f(x) be a mapping f: GF(pn) 茂戮驴GF(pn), where pis prime and GF(pn) is the finite field with pnelements. A mapping fis called differentially k-uniform if kis the maximum number of solutions x茂戮驴 GF(pn) of f(x+ a) 茂戮驴 f(x) = b, where a, b茂戮驴 GF(pn) and a茂戮驴 0. A 1-uniform mapping is called perfect nonlinear (PN). In this paper, we propose an approach for assurance of perfect nonlinearity which involves simply checking a trace condition.