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

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