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 D n(x+y, xy) x ny n for every x, y ε F q 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 F q. 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.

Additional Metadata
Keywords Ambiguity and Deficiency, APN Functions, Dickson Polynomials, DO-Polynomials, Reversed Dickson Polynomials
Persistent URL dx.doi.org/10.1109/ITW.2011.6089369
Conference 2011 IEEE Information Theory Workshop, ITW 2011
Citation
Panario, D. (Daniel), Sakzad, A. (Amin), Stevens, B, & Wang, Q. (2011). Ambiguity and deficiency of permutations from finite fields. In 2011 IEEE Information Theory Workshop, ITW 2011 (pp. 165–169). doi:10.1109/ITW.2011.6089369