Results 1  10
of
1,528
A Lattice Basis Reduction Algorithm ∗
"... In this paper, we give a definition of an optimally reduced basis for a lattice in the sense that an optimally reduced basis is a shortest basis for the lattice. Then we present an algorithm for computing an approximation of an optimally reduced basis for a lattice using a novel unimodular transform ..."
Abstract

Cited by 9 (9 self)
 Add to MetaCart
In this paper, we give a definition of an optimally reduced basis for a lattice in the sense that an optimally reduced basis is a shortest basis for the lattice. Then we present an algorithm for computing an approximation of an optimally reduced basis for a lattice using a novel unimodular
Solving exponential Diophantine equations using lattice basis reduction algorithms
 J. NUMBER THEORY
, 1987
"... Let S be the set of all positive integers with prime divisors from a fixed finite set of primes. Algorithms are given for solving the diophantine inequality 0 < x y < y” in x, y E S for Iixed 6 E (0, 1), and for the diophantine equation x + y = z in x, y, 2 G S. The method is based on multid ..."
Abstract

Cited by 20 (2 self)
 Add to MetaCart
dimensional diophantine approximation, in the real and padic case, respectively. The main computational tool is the L³Basis Reduction Algorithm. Elaborate examples are presented.
A PARALLEL JACOBITYPE LATTICE BASIS REDUCTION ALGORITHM
"... Abstract. This paper describes a parallel Jacobi method for lattice basis reduction and a GPU implementation using CUDA. Our experiments have shown that the parallel implementation is more than fifty times as fast as the serial counterpart, which is twice as fast as the wellknown LLL lattice reduct ..."
Abstract
 Add to MetaCart
reduction algorithm. Key words. Lattice basis reduction, Jacobi method, GPU. 1.
Cryptanalysis of a Publickey key Cryptosystem Using Lattice Basis Reduction Algorithm
"... In this paper, we proposed a new attack against Hwang et al.’s cryptosystem. This cryptosystem uses a superincreasing sequence as private key and the authors investigate a new algorithm called permutation combination algorithm to enhance density of knapsack to avoid the lowdensity attack. Sattar J ..."
Abstract
 Add to MetaCart
integer programming, Lagarias showed that Shamir’s attack is inefficient in practice; So, Aboud’s attack is impractical too. In this paper, we introduce a direct attack against Hwang et al.’s cryptosystem based on Lattice basis reduction algorithms. By computing complexity of propose attack, we show
Flags and lattice basis reduction
 IN PROCEEDINGS OF THE THIRD EUROPEAN CONGRESS OF MATHEMATICS
, 2001
"... In this lecture we give a selfcontained introduction to the theory of lattices in Euclidean vector spaces. We reinterpret a large class of lattice basis reduction algorithms by using the concept of a “flag”. In our reformulation, lattice basis reduction algorithms are more appropriately called “f ..."
Abstract

Cited by 11 (0 self)
 Add to MetaCart
In this lecture we give a selfcontained introduction to the theory of lattices in Euclidean vector spaces. We reinterpret a large class of lattice basis reduction algorithms by using the concept of a “flag”. In our reformulation, lattice basis reduction algorithms are more appropriately called
EntropyBased Algorithms For Best Basis Selection
 IEEE Transactions on Information Theory
, 1992
"... pretations (position, frequency, and scale), and we have experimented with featureextraction methods that use bestbasis compression for frontend complexity reduction. The method relies heavily on the remarkable orthogonality properties of the new libraries. It is obviously a nonlinear transformat ..."
Abstract

Cited by 675 (20 self)
 Add to MetaCart
pretations (position, frequency, and scale), and we have experimented with featureextraction methods that use bestbasis compression for frontend complexity reduction. The method relies heavily on the remarkable orthogonality properties of the new libraries. It is obviously a nonlinear
Lattice Basis Reduction: Improved Practical Algorithms and Solving Subset Sum Problems.
 Math. Programming
, 1993
"... We report on improved practical algorithms for lattice basis reduction. We propose a practical floating point version of the L3algorithm of Lenstra, Lenstra, Lov'asz (1982). We present a variant of the L3 algorithm with "deep insertions" and a practical algorithm for block KorkinZ ..."
Abstract

Cited by 327 (6 self)
 Add to MetaCart
We report on improved practical algorithms for lattice basis reduction. We propose a practical floating point version of the L3algorithm of Lenstra, Lenstra, Lov'asz (1982). We present a variant of the L3 algorithm with "deep insertions" and a practical algorithm for block Korkin
Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images.
 IEEE Trans. Pattern Anal. Mach. Intell.
, 1984
"... AbstractWe make an analogy between images and statistical mechanics systems. Pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a latticelike physical system. The assignment of an energy function in the physical system determines its Gibbs di ..."
Abstract

Cited by 5126 (1 self)
 Add to MetaCart
AbstractWe make an analogy between images and statistical mechanics systems. Pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a latticelike physical system. The assignment of an energy function in the physical system determines its Gibbs
Lattice Basis Reduction with Dynamic Approximation
"... Abstract. In this paper we present a heuristic based on dynamic approximations for improving the wellknown SchnorrEuchner lattice basis reduction algorithm. In particular, the new heuristic is more efficient in reducing large problem instances and extends the applicability of the SchnorrEuchner a ..."
Abstract
 Add to MetaCart
Abstract. In this paper we present a heuristic based on dynamic approximations for improving the wellknown SchnorrEuchner lattice basis reduction algorithm. In particular, the new heuristic is more efficient in reducing large problem instances and extends the applicability of the Schnorr
Parallel Lattice Basis Reduction Using a Multithreaded SchnorrEuchner LLL Algorithm
"... Abstract. In this paper, we introduce a new parallel variant of the LLL lattice basis reduction algorithm. Our new, multithreaded algorithm is the first to provide an efficient, parallel implementation of the SchorrEuchner algorithm for today’s multiprocessor, multicore computer architectures. E ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
Abstract. In this paper, we introduce a new parallel variant of the LLL lattice basis reduction algorithm. Our new, multithreaded algorithm is the first to provide an efficient, parallel implementation of the SchorrEuchner algorithm for today’s multiprocessor, multicore computer architectures
Results 1  10
of
1,528