Improved algebraic cryptanalysis of QUAD, Bivium and Trivium via graph partitioning on equation systems

We present a novel approach for preprocessing systems of polynomial equations via graph partitioning. The variable-sharing graph of a system of polynomial equations is defined. If such graph is disconnected, then the corresponding system of equations can be split into smaller ones that can be solved individually. This can provide a tremendous speed-up in computing the solution to the system, but is unlikely to occur either randomly or in applications. However, by deleting certain vertices on the graph, the variable-sharing graph could be disconnected in a balanced fashion, and in turn the system of polynomial equations would be separated into smaller systems of near-equal sizes. In graph theory terms, this process is equivalent to finding balanced vertex partitions with minimum-weight vertex separators. The techniques of finding these vertex partitions are discussed, and experiments are performed to evaluate its practicality for general graphs and systems of polynomial equations. Applications of this approach in algebraic cryptanalysis on symmetric ciphers are presented: For the QUAD family of stream ciphers, we show how a malicious party can manufacture conforming systems that can be easily broken. For the stream ciphers Bivium and Trivium, we nachieve significant speedups in algebraic attacks against them, mainly in a partial key guess scenario. In each of these cases, the systems of polynomial equations involved are well-suited to our graph partitioning method. These results may open a new avenue for evaluating the security of symmetric ciphers against algebraic attacks.

A contextualised general systems theory

A system is something that can be separated from its surrounds, but this definition leaves much scope for refinement. Starting with the notion of measurement, we explore increasingly contextual system behaviour, and identify three major forms of contextuality that might be exhibited by a system: (a) between components; (b) between system and experimental method, and; (c) between a system and its environment. Quantum Theory is shown to provide a highly useful formalism from which all three forms of contextuality can be analysed, offering numerous tests for contextual behaviour, as well as modelling possibilities for systems that do indeed display it. I conclude with the introduction of a Contextualised General Systems Theory based upon an extension of this formalism.

On the zeros of the Abelian integrals for a class of Liénard systems

A planar polynomial differential system has a finite number of limit cycles. However, finding the upper bound of the number of limit cycles is an open problem for the general nonlinear dynamical systems. In this paper, we investigated a class of Liénard systems of the form x'=y, y'=f(x)+y g(x) with deg f=5 and deg g=4. We proved that the related elliptic integrals of the Liénard systems have at most three zeros including multiple zeros, which implies that the number of limit cycles bifurcated from the periodic orbits of the unperturbed system is less than or equal to 3.

Administrative Placement of the Information Systems Discipline in Universities - A SWOT Analysis of Queensland University of Technology

In some Queensland universities, Information Systems academics have moved out of Business Faculties. This study uses a pilot SWOT analysis to examine the ramifications of Information Systems academics being located within or outside of the Business Faculty. The analysis provides a useful basis for decision makers in the School studied, to exploit opportunities and minimise external threats. For Information Systems academics contemplating administrative relocation of their group, the study also offers useful insights. The study presages a series of further SWOT analyses to provide a range of perspectives on the relative merits of having Information Systems academics administratively located inside versus outside Business faculties.