This paper presents a new approach to precompute all odd points [3]P, [5]P, . . . , [2k− 1]P , k ≥ 2 on an elliptic curve over Fp. Those points are required for the efficient evaluation of a scalar multiplication, the most important operation in elliptic curve cryptography. The proposed method precomputes the points in affine coordinates and needs only one single field inversion for the computa...

Free energy simulation method is applied to calculate the virial coefficients of square-well (SW) fluids of variable well-width and square-well based dimer forming associating fluids. In this approach, Monte Carlo sampling is performed on a number of molecules equal to the order of integral, and configurations are weighted according to the absolute value of the integrand. An umbrella-sampling a...

Given a parameterization of an algebraic rational curve in a projective space of arbitrary dimension, we introduce and study a new implicit representation of this curve which consists in the locus where the rank of a single matrix drops. Then, we illustrate the advantages of this representation by addressing several important problems of Computer Aided Geometric Design: The point-on-curve and i...

Surface wave dispersion curve inversion is a challenging problem for linear inversion procedures due to its highly non-linear nature and to the large numbers of local minima and maxima of the objective function (multi-modality). In order to improve the reliability of the inversion results, we implemented and tested a two-step inversion scheme based on Genetic Algorithms (GAs). The proposed sche...

Elliptic curve cryptosystems have attracted much attention in recent years and one of major interests in ECC is to develop fast algorithms for elliptic curve arithmetic. In this paper we present various improvement techniques for eld arithmetic in GF(p n)(p a prime), in particular , fast eld multiplication and inversion algorithms, and provide our implementation results on Pentium II and Alpha ...