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Approximation and Interpolation of High Dimensional Functions by generalized Walsh Polynomials

A new method for the approximation of a special class of functions that are representable by absolute convergent Walsh series by means of Walsh polynomials in a base b is introduced. In contrast to the classical case of the Discrete Walsh Transform which soon becomes intractable when the dimension increases, this approach uses number theoretic integration methods for the computation of the Walsh coefficients. Also the generalization from the one dimensional partial sum to the s-dimensional case is carried out by hyperbolic index sets instead of cube-like sets.This reduces the number of Walsh coefficients to compute from N s to an order O(N logN s\Gamma1 ). Nevertheless the computational complexity demands the distribution of the whole algorithm to a greater number of processors to compute the results in a reasonable amount of time. In the following paper we will give an overview of the approximation algorithm, error estimates, an overview of the distribution method and a comparisi..

Parallel Computing in Cryptoanalysis: Experiences in a Graduate Students' Project - Workpackage WP5.1

This work reports on a graduate students' project on parallel computing in cryptoanalysis. Major hardware- and softwaretypes have been used to implement basic cryptoanalytic algorithms. 1 Introduction In this work we report experiences made within a graduate students' project performed at the department of Computer Science and System Analysis (Univ. Salzburg). The topic of the project was "Parallel Computing in Cryptoanalysis". The security of most of the public key cryptosystems known today relies on computationally infeasible problems in computational number theory (e.g. RSA -- factoring of large integers, ElGamal -- calculating discrete logarithms in a finite field; for more examples see [10]). The goal of this project was to exploit to power of parallel and distributed computing in order to perform the necessary computations to break such cryptosystems in reasonable time. Since the projects' underlying course was not theory-focused we had to choose simple algorithms to be parallel..