On the nonlinear key generator design using unit-step and trace functions

Abstract EN

he paper presents a proposed method with an algorithm which has been written in Matlab language for designing a nonlinear key generator, which is denoted by (US-TR), using unit-step function and trace function from Galois field of order 2N (i.e.

GF (2N), (N ≥ 2)) to Galois field of order 2 (GF (2)).

The proposed generator produces a binary sequence of period (2N 1) where N is a composite number, with high degree of complexity and good randomness properties.

The advantage of the new nonlinear generator is the output sequence which has high degree of complexity to increase the security of this generator concerning the designed feature that limit the ability of anti-jammer when it uses as a key in cipher systems or in spread spectrum digital communication system.

This paper has useful properties of the trace function.

Moreover, Illustrative examples are given for determining the output sequence with its complexity of the proposed generator and good results are obtained.