Combinatorics Seminar: Dr. Li-An Chen (Boise State University)

Permutation resemblance Consider a function f on a finite group G. How close is f from being a bijection on G? A standard way to measure this is to look at the number of distinct images |f(G)|. In this talk, we introduce the notion of permutation resemblance, which provides a more nuanced measure to the bijectivity of a function on a finite group. We introduce an integer programming approach to compute the permutation resemblance. Moreover, we show that this notion and approach can be applied to the problem of constructing bijections with good resistance against differential cryptanalysis. This is joint work with Robert S. Coulter