### A Mathematical Approach for Computing the Linear Equivalence of a Periodic Key-Stream Sequence Using Fourier Transform

*Baghdad Science Journal*

2011, Volume 8, Issue 3, Pages 849-859

2011, Volume 8, Issue 3, Pages 849-859

#### Abstract

A mathematical method with a new algorithm with the aid of Matlab language is proposed to compute the linear equivalence (or the recursion length) of the pseudo-random key-stream periodic sequences using Fourier transform. The proposed method enables the computation of the linear equivalence to determine the degree of the complexity of any binary or real periodic sequences produced from linear or nonlinear key-stream generators. The procedure can be used with comparatively greater computational ease and efficiency. The results of this algorithm are compared with Berlekamp-Massey (BM) method and good results are obtained where the results of the Fourier transform are more accurate than those of (BM) method for computing the linear equivalence (L) of the sequence of period (p) when (L) is greater than (p/2). Several examples are given for conciliated the accuracy of the results of this proposed method.

#### Keywords

Fourier transform, Linear equivalence, Periodic key-stream sequence, Berlekamp-Massey method.#### Metrics