EUROCRYPT
2012
Springer
12 years 2 months ago
2012
Springer
Abstract. The goal of this paper is to further study the index calculus method that was first introduced by Semaev for solving the ECDLP and later developed by Gaudry and Diem. In...
IACR
2011
13 years 2 days ago
2011
The Isomorphism of Polynomials (IP) is one of the most fundamental problems in multivariate public key cryptography (MPKC). In this paper, we introduce a new framework to study th...
COMPGEOM
2011
ACM
13 years 4 months ago
2011
ACM
We report on a generic uni- and bivariate algebraic kernel that is publicly available with Cgal 3.7. It comprises complete, correct, though efficient state-of-the-art implementati...
CAP
2010
13 years 7 months ago
2010
Homotopy continuation methods to solve polynomial systems scale very well on parallel machines. In this paper we examine its parallel implementation on multiprocessor multicore wo...
MICS
2007
13 years 12 months ago
2007
The pseudozero set of a system P of polynomials in n variables is the subset of Cn consisting of the union of the zeros of all polynomial systems Q that are near to P in a suitable...
FCSC
2008
14 years 15 days ago
2008
Abstract. We discuss the verification of mathematical software solving polynomial systems symbolically by way of triangular decomposition. Standard verification techniques are high...
ISSAC
2005
Springer
14 years 6 months ago
2005
Springer
This paper presents a duality analysis and an algorithm for computing the multiplicity structure of a zero to a polynomial system, while the zero can be exact or approximate with ...
ICPPW
2005
IEEE
14 years 6 months ago
2005
IEEE
We report on a £rst parallel implementation of a recent algorithm to factor positive dimensional solution sets of polynomial systems. As the algorithm uses homotopy continuation,...
ADG
2006
Springer
14 years 6 months ago
2006
Springer
This paper describes the recent convergence of four topics: polynomial systems, flexibility of three dimensional objects, computational chemistry, and computer algebra. We discuss...
ICPPW
2006
IEEE
14 years 6 months ago
2006
IEEE
Homotopy methods to solve polynomial systems are well suited for parallel computing because the solution paths defined by the homotopy can be tracked independently. For sparse po...