Dynamic LFSRs as an alternative to LFSRs in extended fields - A comparative study

Linear feedback shift registers (LFSRs) with dynamic feedback (DLFSRs) and LFSRs defined over extended fields i.e., over GF(2n), constitute building blocks of many pseudorandom sequence generators used in stream ciphers. In this work, the advantages and disadvantages of using DLSFR instead of LFSR in GF(2n) are analyzed. The work is based on the possibility of obtaining a DLFSR in GF(2) equivalent to an LFSR in GF(2n), given that both structures present equivalent binary models formed by interleaved sequences. Likewise, the possibility of using DLFSR on binary vectors is proposed in order to take advantage of the word lengths of current processors

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

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

On the inherent intractability of certain coding problems

The fact that the general decoding problem for linear codes and the general problem of finding the weights of a linear code are both NP-complete is shown. This strongly suggests, but does not rigorously imply, that no algorithm for either of these problems which runs in polynomial time exists