Lower bounds on the linear complexity of the discrete logarithm in finite fields

Abstract

Let p be a prime, r a positive integer, q=p/sup r/, and d a divisor of p(q-1). We derive lower bounds on the linear complexity over the residue class ring Z/sub d/ of a (q-periodic) sequence representing the residues modulo d of the discrete logarithm in F/sub q/. Moreover, we investigate a sequence over F/sub q/ representing the values of a certain polynomial over F/sub q/ introduced by Mullen and White (1986) which can be identified with the discrete logarithm in F/sub q/ via p-adic expansions and representations of the elements of F/sub q/ with respect to some fixed basis.