Investigations in the design and analysis of key-stream generators

iv+113hlm.;24c

A formalism for describing and simulating systems with interacting components.

This thesis addresses the problem of descriptive complexity presented by systems involving a high number of interacting components. It investigates the evaluation measure of performability and its application to such systems. A new description and simulation language, ICE and it's application to performability modelling is presented. ICE (Interacting ComponEnts) is based upon an earlier description language which was first proposed for defining reliability problems. ICE is declarative in style and has a limited number of keywords. The ethos in the development of the language has been to provide an intuitive formalism with a powerful descriptive space. The full syntax of the language is presented with discussion as to its philosophy. The implementation of a discrete event simulator using an ICE interface is described, with use being made of examples to illustrate the functionality of the code and the semantics of the language. Random numbers are used to provide the required stochastic behaviour within the simulator. The behaviour of an industry standard generator within the simulator and different methods of number allocation are shown. A new generator is proposed that is a development of a fast hardware shift register generator and is demonstrated to possess good statistical properties and operational speed. For the purpose of providing a rigorous description of the language and clarification of its semantics, a computational model is developed using the formalism of extended coloured Petri nets. This model also gives an indication of the language's descriptive power relative to that of a recognised and well developed technique. Some recognised temporal and structural problems of system event modelling are identified. and ICE solutions given. The growing research area of ATM communication networks is introduced and a sophisticated top down model of an ATM switch presented. This model is simulated and interesting results are given. A generic ICE framework for performability modelling is developed and demonstrated. This is considered as a positive contribution to the general field of performability research

Applications of the Galois Model LFSR in Cryptography

The linear feedback shift-register is a widely used tool for generating cryptographic sequences. The properties of the Galois model discussed here offer many opportunities to improve the implementations that already exist. We explore the overall properties of the phases of the Galois model and conjecture a relation with modular Golomb rulers. This conjecture points to an efficient method for constructing non-linear filtering generators which fulfil Golic s design criteria in order to maximise protection against his inversion attack. We also produce a number of methods which can improve the rate of output of sequences by combining particular distinct phases of smaller elementary sequences

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

An experimental exploration of Marsaglia's xorshift generators, scrambled

Marsaglia proposed recently xorshift generators as a class of very fast, good-quality pseudorandom number generators. Subsequent analysis by Panneton and L'Ecuyer has lowered the expectations raised by Marsaglia's paper, showing several weaknesses of such generators, verified experimentally using the TestU01 suite. Nonetheless, many of the weaknesses of xorshift generators fade away if their result is scrambled by a non-linear operation (as originally suggested by Marsaglia). In this paper we explore the space of possible generators obtained by multiplying the result of a xorshift generator by a suitable constant. We sample generators at 100 equispaced points of their state space and obtain detailed statistics that lead us to choices of parameters that improve on the current ones. We then explore for the first time the space of high-dimensional xorshift generators, following another suggestion in Marsaglia's paper, finding choices of parameters providing periods of length $2^{1024} - 1$ and $2^{4096} - 1$. The resulting generators are of extremely high quality, faster than current similar alternatives, and generate long-period sequences passing strong statistical tests using only eight logical operations, one addition and one multiplication by a constant