Gerard Maze

PUBLIC KEY CRYPTOGRAPHY BASED ON SEMIGROUP ACTIONS

A generalization of the original Diffie-Hellman key exchange in

The contribution of patch topology and demographic parameters to population viability analysis predictions: the case of the European tree frog

(\mathbb Z

Efficient recovering of operation tables of black box groups and rings

∕

Partitions modulo n and circulant matrices

p\mathbb Z)

Analysis of a key distribution scheme in secure multicasting

* found a new depth when Miller [27] and Koblitz [16] suggested that such a protocol could be used with the group over an elliptic curve. In this paper, we propose a further vast generalization where abelian semigroups act on finite sets. We define a Diffie-Hellman key exchange in this setting and we illustrate how to build interesting semigroup actions using finite (simple) semirings. The practicality of the proposed extensions rely on the orbit sizes of the semigroup actions and at this point it is an open question how to compute the sizes of these orbits in general and also if there exists a square root attack in general. In Section 5 a concrete practical semigroup action built from simple semirings is presented. It will require further research to analyse this system.

Determinants of binary circulant matrices

Population viability analyses (PVA) are increasingly used in metapopulation conservation plans. Two major types of models are commonly used to assess vulnerability and to rank management options: population-based stochastic simulation models (PSM such as RAMAS or VORTEX) and stochastic patch occupancy models (SPOM). While the first set of models relies on explicit intrapatch dynamics and interpatch dispersal to predict population levels in space and time, the latter is based on spatially explicit metapopulation theory where the probability of patch occupation is predicted given the patch area and isolation (patch topology). We applied both approaches to a European tree frog (Hyla arborea) metapopulation in western Switzerland in order to evaluate the concordances of both models and their applications to conservation. Although some quantitative discrepancies appeared in terms of network occupancy and equilibrium population size, the two approaches were largely concordant regarding the ranking of patch values and sensitivities to parameters, which is encouraging given the differences in the underlying paradigms and input data.

Diffie-HellmanA public key cryptosystem based on actions by semigroups

People have been studying the following problem: Given a finite set S with a hidden (black box) binary operation * : S times S rarr S which might come from a group law, and suppose you have access to an oracle that you can ask for the operation x*y of single pairs (x, y) isin S2 you choose. What is the minimal number of queries to the oracle until the whole binary operation is recovered, i.e. you know x*y for all x,y isin S? This problem can trivially be solved by using |S|2 queries to the oracle, so the question arises under which circumstances you can succeed with a significantly smaller number of queries. In this presentation we give a lower bound on the number of queries needed for general binary operations. On the other hand, we present algorithms solving this problem by using |S| queries, provided that * is an abelian group operation. We also investigate black box rings and give lower und upper bounds for the number of queries needed to solve product recovering in this case.

A new family of almost identities

This paper is about a connection between a general problem of partitions in Z/nZ and the expression of determinants of certain circulant matrices. The main result of the article is a method for calculating, in certain special cases, explicit formulas for the number of partitions of elements in Z/nZ in distinct summands and the number of partitions of elements in Z/nZ with less than t repetitions. Explicit formulas for partitions in Z/nZ in the general case can be found by explicitly calculating the determinants of certain circulant matrices.

Natural density of rectangular unimodular integer matrices

Abstract. This article presents an analysis of the secure key broadcasting scheme proposed by Wu, Ruan, Lai and Tseng [Proceedings of the 25th Annual IEEE Conference on Local Computer Networks (2000), 208–212]. The study of the parameters of the system is based on a connection with a special type of symmetric equations over finite fields. We present two different attacks against the system, whose efficiency depends on the choice of the parameters. In particular, a time-memory tradeoff attack is described, effective when a parameter of the scheme is chosen without care. In such a situation, more than one third of the cases can be broken with a time and space complexity in the range of the square root of the complexity of the best attack suggested by Wu et al. against their system. This leads to a feasible attack in a realistic scenario.

Existence of a limiting distribution for the binary GCD algorithm

This paper investigate the problem of deciding whether or not determinants of binary circulant matrices (i.e. matrices with entries in either {0,1} or {-1,1} ) can reach Hadamards bound. It finds necessary and sufficient conditions for the existence of such matrices. A direct consequence of this study relates to the existence of Barker sequences.