Differential spectrum of some power functions in odd prime characteristic

Abstract

Upper bound on triangle(f) of the power function x(pk+1/2) in F-pn (Helleseth et al. (1999) 17]) is not tight, for example p = 5, n = 3, and k = 2, which is the motivation of this work. In this paper, for an odd prime p, the differential spectrum of the power function x(pk+1/2) in F-pn is calculated. For an odd prime p such that p equivalent to 3 mod 4 and odd n with m vertical bar n, the differential spectrum of the power function in F-pn is also derived. We also find some new power function x(pn+1/pm+1+pn-1/2) in F-pn is also derived. We also find some new power functions which are differentially 4 and 6-uniform. (C) 2013 Elsevier Inc. All rights