On Binary de Bruijn Sequences from LFSRs with Arbitrary Characteristic Polynomials

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 $\Omega(f(x))$ that contains all sequences produced by a specific LFSR on distinct inputs and provide a fast way to find a state of each cycle. This leads to an efficient algorithm to find all conjugate pairs between any two cycles, yielding the adjacency graph. The approach is practical to generate a large class of de Bruijn sequences up to order $n \approx 20$. Many previously proposed constructions of de Bruijn sequences are shown to be special cases of our construction

Modelling Nonlinear Sequence Generators in terms of Linear Cellular Automata

In this work, a wide family of LFSR-based sequence generators, the so-called Clock-Controlled Shrinking Generators (CCSGs), has been analyzed and identified with a subset of linear Cellular Automata (CA). In fact, a pair of linear models describing the behavior of the CCSGs can be derived. The algorithm that converts a given CCSG into a CA-based linear model is very simple and can be applied to CCSGs in a range of practical interest. The linearity of these cellular models can be advantageously used in two different ways: (a) for the analysis and/or cryptanalysis of the CCSGs and (b) for the reconstruction of the output sequence obtained from this kind of generators.Comment: 15 pages, 0 figure

The Cycle Structure of LFSR with Arbitrary Characteristic Polynomial over Finite Fields

We determine the cycle structure of linear feedback shift register with arbitrary monic characteristic polynomial over any finite field. For each cycle, a method to find a state and a new way to represent the state are proposed.Comment: An extended abstract containing preliminary results was presented at SETA 201

A transformation sequencing approach to pseudorandom number generation

This paper presents a new approach to designing pseudorandom number generators based on cellular automata. Current cellular automata designs either focus on i) ensuring desirable sequence properties such as maximum length period, balanced distribution of bits and uniform distribution of n-bit tuples etc. or ii) ensuring the generated sequences pass stringent randomness tests. In this work, important design patterns are first identified from the latter approach and then incorporated into cellular automata such that the desirable sequence properties are preserved like in the former approach. Preliminary experiment results show that the new cellular automata designed have potential in passing all DIEHARD tests