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» A parallel LLL algorithm
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ISSAC
2007
Springer
105views Mathematics» more  ISSAC 2007»
14 years 1 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
13 years 11 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»
13 years 7 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»
12 years 7 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
13 years 5 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