Worst-case complexity of the optimal LLL algorithm

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1776 LNCS, Issue , 2000, Pages 355-366

  Akhavi, Ali ^a  

^a UNIVERSITÉ DE CAEN   (France)

Author keywords

[No Author keywords available]

Indexed keywords

3-DIMENSION; EXPONENTIAL ORDERING; EXTREME VALUE; LINEAR ORDER; LLL ALGORITHM; NUMBER OF ITERATIONS; TIGHT BOUND; WORST-CASE COMPLEXITY; REDUCED BASIS;

INFORMATION SCIENCE; OPTIMIZATION; APPROXIMATION ALGORITHMS;

APPROXIMATION ALGORITHMS; ALGORITHMS;

EID: 84896693343     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/10719839_35     Document Type: Conference Paper

References (19)

1. 2 is NP-hard for randomized reduction. ECCC-TR97-047, 1997. http://www.eccc.uni-trier.de/eccc/.
2. A. Akhavi. The worst case complexity of the optimal LLL algorithm. Preprint. http://www.info.unicaen.fr/ãkhavi/publi.html, Caen, 1999.
3. L. Babai. On Lovász' lattice reduction and the nearest lattice point problem. Combinatorica, 6(1):1-13, 1986.
4. A. Bachem and R. Kannan. Lattices and the basis reduction algorithm. CMU-CS, pages 84-112, 1984.
5. J. Cai. Some recent progress on the complexity of lattice problems. ECCC-TR99-006, 1999. http://www.eccc.uni-trier.de/eccc/
6. H. Daudé, Ph. Flajolet, and B. Valleé. An average-case analysis of the Gaussian algorithm for lattice reduction. Comb., Prob. & Comp., 123:397-433, 1997.
7. R. Kannan. Improved algorithm for integer programming and related lattice problems. In 15th Ann. ACM Symp. on Theory of Computing, pages 193-206, 1983.
8. R. Kannan. Algorithmic geometry of numbers. Ann. Rev. Comp. Sci., 2:231-267, 1987.
9. M. Kaib and C. P. Schnorr. The generalized Gauss reduction algorithm. J. of Algorithms, 21:565-578, 1996.
10. J. C. Lagarias. Worst-case complexity bounds for algorithms in the theory of integral quadratic forms. J. Algorithms, 1:142-186, 1980.
11. H.W. Lenstra. Integer programming with a fixed number of variables. Math. Oper. Res., 8:538-548, 1983.
12. A. K. Lenstra, H. W. Lenstra, and L. Lovász. Factoring polynomials with rational coefficients. Math. Ann., 261:513-534, 1982.
13. J. C. Lagarias and A. M. Odlyzko. Solving low-density subset sum problems. In 24th IEEE Symposium FOCS, pages 1-10, 1983.
14. C. P. Schnorr. A hierarchy of polynomial time lattice basis reduction algorithm. Theoretical Computer Science, 53:201-224, 1987.
15. A. Joux and J. Stern. Lattice reduction: A toolbox for the cryptanalyst. J. of Cryptology, 11:161-185, 1998.
16. B. Valleé. Un problème central en geómétrie algorithmique des nombres: la réduction des réseaux. Inf. Th. et App., 3:345-376, 1989.
17. B. Valleé. Gauss' algorithm revisited. J. of Algorithms, 12:556-572, 1991.
18. P. van Emde Boas. Another NP-complete problem and the complexity of finding short vectors in a lattice. Rep. 81-04 Math. Inst. Amsterdam, 1981.
19. O. von Sprang. Basisreduktionsalgorithmen für Gitter kleiner Dimension. PhD thesis, Uni-versität des Saarlandes, 1994.