We study the linear complexity of sequences over the prime field Fd introduced by Sidel’nikov. For several classes of period length we can show that these sequences have a large linear complexity.… (More)

We introduce a generalization of Sidel’nikov sequences for arbitrary finite fields. We show that several classes of Sidel’nikov sequences over arbitrary finite fields exhibit a large linear… (More)

k = k1 + k2p+ . . .+ krp , 0 ≤ k1, k2, . . . , kr < p , for 0 ≤ k ≤ q − 1. Let γ be a primitive element of Fq. The discrete logarithm (or index) of a nonzero element ξ ∈ Fq to the base γ, denoted… (More)

The two-prime generator of order 2 has several desirable randomness properties if the two primes are chosen properly. In particular, Ding deduced exact formulas for the (periodic) autocorrelation and… (More)

Motivated by the concepts of Sidel’nikov sequences and two-prime generator (or Jacobi sequences) we introduce and analyze some new binary sequences called two-prime Sidel’nikov sequences. In the… (More)

A high linear complexity profile is a desirable feature of sequences used for cryptographical purposes. For a given binary sequence we estimate its linear complexity profile in terms of the… (More)