University of Delaware
Discrete Mathematics Seminar

On ambiguity and deficiency of functions over finite fields.
David Thomson
Carleton University and Penn State
Tuesday, October 23, 2012
Ewing Hall 336 4.00 - 5.00 pm

ABSTRACT: The ambiguity and deficiency of functions between finite groups were recently introduced as finer measures of a function's resistance to differential cryptanalysis than the commonly-considered differential uniformity. Functions with minimal ambiguity and deficiency are the well-known perfect non-linear (or planar) functions. In this talk, we give motivation for introducing ambiguity and deficiency and present some theoretical results on ambiguities and deficiencies. We also study the ambiguity and deficiency of some Dembowski-Ostrom permutation polynomials over finite fields. At the end, we will give some promising avenues for future research.