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» A parallel LLL algorithm
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ISSAC
2007
Springer
105views Mathematics» more  ISSAC 2007»
15 years 5 months ago
Certification of the QR factor R and of lattice basis reducedness
Given a lattice basis of n vectors in Zn, we propose an algorithm using 12n3 + O(n2) floating point operations for checking whether the basis is LLL-reduced. If the basis is redu...
Gilles Villard
EUROCRYPT
2006
Springer
15 years 3 months ago
Symplectic Lattice Reduction and NTRU
NTRU is a very efficient public-key cryptosystem based on polynomial arithmetic. Its security is related to the hardness of lattice problems in a very special class of lattices. Th...
Nicolas Gama, Nick Howgrave-Graham, Phong Q. Nguye...
TOC
2008
94views more  TOC 2008»
14 years 11 months ago
Optimal lower bounds for the Korkine-Zolotareff parameters of a lattice and for Schnorr's algorithm for the shortest vector prob
Abstract: Schnorr's algorithm for finding an approximation for the shortest nonzero vector in an n-dimensional lattice depends on a parameter k. He proved that for a fixed k ...
Miklós Ajtai
CRYPTO
2011
Springer
191views Cryptology» more  CRYPTO 2011»
13 years 11 months ago
Analyzing Blockwise Lattice Algorithms Using Dynamical Systems
Strong lattice reduction is the key element for most attacks against lattice-based cryptosystems. Between the strongest but impractical HKZ reduction and the weak but fast LLL redu...
Guillaume Hanrot, Xavier Pujol, Damien Stehl&eacut...
ICPP
2009
IEEE
14 years 9 months ago
A Parallel Algorithm for Computing Betweenness Centrality
In this paper we present a multi-grained parallel algorithm for computing betweenness centrality, which is extensively used in large-scale network analysis. Our method is based on ...
Guangming Tan, Dengbiao Tu, Ninghui Sun