The Berlekamp-Massey algorithm takes a sequence of elements from a field and finds the shortest linear recurrence (or linear feedback shift register) that can generate the sequence. In this paper we extend the algorithm to the case when the elements of the sequence are integers modulo m, where m is an arbitrary integer with known prime decomposition.

Abstract A new approach to optimize a configurable twodimensional (2-D) linear feedback shift registers (LFSR) for both embedded and random test pattern generation in built-in self-test (BIST) is proposed. This configurable 2-D LFSR based test pattern generator generates: 1) a deterministic sequence of test patterns for random-pattern-resistant faults, and then 2) random patterns for random-pat...

We propose a construction of de Bruijn sequences by the cycle joining method from linear feedback shift registers (LFSRs) with arbitrary characteristic polynomial f(x). We study in detail the cycle structure of the set Ω(f(x)) that contains all sequences produced by a specific LFSR on distinct inputs and provide an efficient way to find a state of each cycle. Our structural results lead to an e...

Many stream ciphers use irregular clocking to introduce nonlinearity to the keystream. We present three distinguishers on irregularly clocked linear feedback shift registers. The general idea used is to find suitable linear combinations of keystream bits, here called samples, that are drawn from a biased distribution. We describe how to place windows around the estimated positions around member...

In this paper we interpret the Berlekamp-Massey algorithm (BMA) for synthesis of linear feedback shift register (LFSR) as an algorithm computing Pade approximants for Laurent series over arbitrary field. This interpretation of the BMA is based on a iterated procedure for computing of the sequence of polynomials orthogonal to some sequence of polynomial spaces with scalar product depending on th...

Maximal-length binary sequences have been known for a long time. They have many interesting properties, one of them is that when taken in blocks of n consecutive positions they form 2 − 1 different codes in a closed circular sequence. This property can be used for measuring absolute angular positions as the circle can be divided in as many parts as different codes can be retrieved. This paper d...

Filter generators are vulnerable to several attacks which have led to well-known design criteria on the Boolean filtering function. However, Rønjom and Cid have observed that a change of the primitive root defining the LFSR leads to several equivalent generators. They usually offer different security levels since they involve filtering functions of the form F (x) where k is coprime to (2 − 1) a...