Title :
Ambiguity and deficiency of permutations from finite fields
Author :
Panario, Daniel ; Sakzad, Amin ; Stevens, Brett ; Wang, Qiang
Abstract :
The concepts of ambiguity and deficiency for a given bijection on a finite Abelian group were recently introduced [13]. In this work we investigate the ambiguity and deficiency of some well-known polynomials which satisfy Dn(x+y, xy) = xn+yn for every x, y ϵ Fq and n ϵ N, as well as linearized polynomials and Dembowski-Ostrom polynomials (DO polynomials). For some specific values of n (related to q) these polynomials generate permutations on Fq. We derive explicitly the ambiguity and deficiency of some of them. Numerical results on the ambiguity and deficiency of the others are also provided. Some of these polynomials are almost perfect nonlinear (APN) functions.
Keywords :
nonlinear functions; polynomials; Dembowski-Ostrom polynomials; almost perfect nonlinear function; bijection; finite Abelian; finite fields; linearized polynomials; permutation ambiguity; permutation deficiency; Conferences; Cryptography; Educational institutions; Galois fields; Gold; Information theory; Polynomials; APN Functions; Ambiguity and Deficiency; DO-Polynomials; Dickson Polynomials; Reversed Dickson Polynomials;
Conference_Titel :
Information Theory Workshop (ITW), 2011 IEEE
Conference_Location :
Paraty
Print_ISBN :
978-1-4577-0438-3
DOI :
10.1109/ITW.2011.6089369