W.M. Lioen

Factorization of RSA-140 Using the Number Field Sieve

We propose a mathematical problem, and show how to solve it elegantly. This problem is related with elliptic curve cryptosystems (ECC). The solving methods can be applied to a new paradigm of key generations of the ECC.

On the diagonal approximation of full matrices

In this paper the construction of diagonal matrices, in some sense approximating the inverse of a given square matrix, is described. The matrices are constructed using the well-known computer algebra system Maple. The techniques we show are applicable to square matrices in general. Results are given for use in Parallel diagonal-implicit Runge-Kutta (PDIRK) methods. For an s-stage Radau IIA corrector we conjecture s! possibilities for the diagonal matrices.

Factoring with the quadratic sieve on large vector computers

Abstract The results are presented of experiments with the multiple polynomial version of the quadratic sieve factorization method on a CYBER 205 and on a NEC SX-2 vector computer. Various numbers in the 50–92 decimal digits range have been factorized, as a contribution to (i) the Cunningham project, (ii) Brents table of factors of Mersenne numbers, and (iii) a proof by Brent and G. Cohen of the non-existence of odd perfect numbers below 10 200 . The factorized 92-decimal digits number is a record for general purpose factorization methods.

HPCN and Air Quality Modeling

We discuss the implementation of an off-line air quality model (AQM). More precisely, how to design a code for an AQM that runs efficiently on a variety of computer platforms. We implemented our ideas in an AQM benchmark and we show the performance of this benchmark on the different architectural paradigms. A second subject of the paper is the I/O performance of the Cray T3E for an off-line model. We implemented the required I/O in different ways and show that none of these results in a truly scalable I/O.