Random lattices, threshold phenomena and efficient reduction algorithms

Theoretical Computer Science

Volumn 287, Issue 2, 2002, Pages 359-385

  Akhavi, Ali ^a  

^a UNIVERSITÉ DE CAEN   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; ITERATIVE METHODS; SET THEORY; VECTORS;

REDUCTION ALGORITHMS;

COMPUTER SCIENCE;

EID: 0037190374     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3975(01)00251-1     Document Type: Conference Paper

References (25)

1. 2 is NP-hard for randomized reduction
2. Threshold phenomena in random lattices and efficient reduction algorithms
3. An upper bound on the average number of iterations of the LLL algorithm
4. Minkowski reduction of integral matrices
5. On the asymptotic evaluation of a class of multiple integrals involving a parameter
6. Lattice reduction: A toolbox for the cryptanalyst
7. Improved algorithm for integer programming and related lattice problems
8. Algorithmic geometry of numbers
9. The computational complexity of simultaneous Diophantine approximation problems
10. Factoring polynomials with rational coefficients
11. Integer programming with a fixed number of variables
12. Flags and lattice basis reduction
13. A hierarchy of polynomial time lattice basis reduction algorithm
14. Lattice basis reduction: Improved practical algorithms and solving subset sum problems
15. Factorization of univariate integer polynomials by diophantine approximation and an improved basis reduction algorithm
16. Un problème central en géométrie algorithmique des nombres: La réduction des réseaux, Autour de l'algorithme LLL