PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Robert Vaughan.

Title:Ambiguity and deficiency of permutations
Seminar:Algebra and Number Theory Seminar
Speaker:David Thomson, Carleton University, Ottawa and Penn State University
Abstract:
The difference map of a function f between finitegroups is given by D_{f,a}(x) = f(x+a) - f(x). For cryptographic purposes, permutation functions whose difference maps are nearly injective are preferred. The ambiguity and deficiency of a function was recently introduced by Panario, et al (2011) to give a fine measure of the injectivity of the difference maps of candidate functions for symmetric key ciphers. In this talk, we discuss some of the motivations of considering the ambiguity and deficiency, as well as introducing some of their basic properties. We will focus our attention primarily on permutation functions defined over finite Abelian groups. We give lower-bounds on both measures and show that permutations which achieve optimal ambiguity and deficiency also achieve high non-linearity. We will also prove some differential properties of a subset of an important class of polynomials, namely the Dembowski-Ostrom polynomials.

Room Reservation Information

Room Number:MB106
Date:09 / 20 / 2012
Time:11:15am - 12:05pm