Free Access
Issue
RAIRO-Theor. Inf. Appl.
Volume 23, Number 3, 1989
Page(s) 345 - 376
DOI https://doi.org/10.1051/ita/1989230303451
Published online 01 February 2017
  1. 1. L. BABAI, On Lovász's Lattice Reduction and the Nearest Lattice Point Problem, Combinatorica, vol. 5, 1985. [Zbl: 0593.68030] [Google Scholar]
  2. 2. A. FRIEZE, J. HASTAD, R. KANNAN, J. C. LAGARIAS et A. SHAMIR, Reconstructing Truncated Integer Variables Satisfying Linear Congruences,, in S.I.A.M. Journal on Computing (to appear). [MR: 935340] [Zbl: 0654.10006] [Google Scholar]
  3. 3. A. DUPRÉ, Journal de Mathématiques, vol.11, 1846, p. 41-64. [EuDML: 234093] [Google Scholar]
  4. 4. C. F. GAUSS, Recherches Arithmétiques, Paris, 1807, réimprimé par Blanchard, Paris, 1953. [Zbl: 0051.03003] [JFM: 42.0236.19] [Google Scholar]
  5. 4. J. HASTAD, B. JUST, J. C. LAGARIAS et C. P. SCHNORR, Polynomial Time Algorithms for Finding Integer Relations Among Real Numbers, Proceedings of S.T.A.C.S., Lecture Notes in Computer Science, 1986 [Zbl: 0606.68033] [Google Scholar]
  6. 6. B. HELFRICH, Algorithms to Construct Minkowski and Hermite Reduced Bases, Theoretical Computer Science, vol. 41, 1985, p. 125-139. [MR: 847673] [Zbl: 0601.68034] [Google Scholar]
  7. 7. J. W. S. CASSELS, Rational Quadratic Forms, Academic Press, 1978. [MR: 522835] [Zbl: 0395.10029] [Google Scholar]
  8. 8. E. KALTOFEN et H. ROLLETSCHEK, Arithmetic in Quadratic Fields with Unique Factorization, Comptes rendus de EUROCAL'85, Lectures notes in Computer Science, 204, Springer-Verlag. [MR: 826569] [Zbl: 0596.12001] [Google Scholar]
  9. 9. R. KANNAN, Improved Algorithms for Integer programming and Related Lattice Problem, J.A.C.M., 1983, p. 193-206. [Google Scholar]
  10. 10. R. KANNAN, H. W. LENSTRA et L. LOVÁSZ, Polynomial Factorization and Bits of Algebraic and Some Transcendental Numbers, Mathematics of Computation, vol. 50, n° 181, 1988, p. 235-250. [MR: 917831] [Zbl: 0654.12001] [Google Scholar]
  11. 11. J. C. LAGARIAS, Computational Complexity of Simultaneous Diophantine Approximation Problem, 23rd I.E.E.E. Symp. F.O.C.S., 1982. [MR: 780377] [Google Scholar]
  12. 12. J. C. LAGARIAS et A. ODLYZKO, Solving Low-Density Subset Sum Problems, 24th I.E.E.E. Symp. F.O.C.S., 1983. [Zbl: 0632.94007] [Google Scholar]
  13. 13. J. C. LAGARIAS, H. W. LENSTRA et C. P. SCHNORR, Korkine-Zolotarev Bases and Successive Minima of a Lattice and its Reciprocal Lattice, Technical Report, M.S.R.I. 07718-86, Mathematical Sciences Research Institute, Berkeley. [Zbl: 0723.11029] [Google Scholar]
  14. 14. S. LANDAU et G. L. MILLER, Solvability by Radicals is in Polynomial Time, 15th Annual A.C.M. Symposium on Theory of Computing, 1983. [Zbl: 0586.12002] [Google Scholar]
  15. 15. A. K. LENSTRA, H. W. LENSTRA et L. LOVASZ, Factoring Polynomial with Rational Coefficients, Math. Annalen, vol. 261, 1982, p. 513-534. [EuDML: 182903] [MR: 682664] [Zbl: 0488.12001] [Google Scholar]
  16. 16. H. W. LENSTRA, Integer Programming with a Fixed Number of Variables, Mathematics of Operations Research, vol 8, n° 4, nov. 1983. [MR: 727410] [Zbl: 0524.90067] [Google Scholar]
  17. 17. L. LOVASZ, An Algorithmic Theory of Numbers, Graphs and Convexity, Technical Report, Universitat Bonn. [Zbl: 0606.68039] [Google Scholar]
  18. 18. A. SHAMIR, A Polynomial Time Algorithmfor Breahing theMerkle-Hellman Cryptosystem, 23rd I.E.E.E. Symp. F.O.C.S., 1982. [Google Scholar]
  19. 19. A. SCHONHAGE, Factorization of Univariate Integer Polynomial by Diophantine Approximation and by an Improved Basis Reduction Algorithm, Proceedings of the 11th I.C.A.L.P., Antwerpen, 1984, Lecture Notes in Computer Science, Vol. 172, Springer, 1984. [MR: 784270] [Zbl: 0569.68030] [Google Scholar]
  20. 20. C. P. SCHNORR, A More efficient Algorithm for Lattice Basis Reduction, Proceedings of the 13th I.C.A.L.P., Rennes, 1986, Lecture Notes in Computer Science, vol. 226, Springer, 1986, dans Journal of Algorithms, 1987 (à paraître). [MR: 864698] [Zbl: 0595.68038] [Google Scholar]
  21. 21. C. P. SCHNORR, A Hierarchy of Polynomial Tume Lattice Basis Reduction Algorithms, Theoretical Computer Science, vol. 53, 1987, p. 201-224. [MR: 918090] [Zbl: 0642.10030] [Google Scholar]
  22. 22. J. STERN, Lectures Notes, University of Singapore, 1986. [Google Scholar]
  23. 23. J. STERN, Secret Linear Congruential Generatorsare not Cryptographically Secure, 28th I.E.E.E. Symp. F. O. C. S., 1987. [Google Scholar]
  24. 24. B. VALLÉE, Provably fast integor factoring algorithm with quasi-uniform small quadratic residues, ACM. STOC 89, p. 98-106. [Google Scholar]
  25. 25. B. VALLÉE, Une approche géométrique de la réduction des réseaux enpetite dimension, Thèse de doctorat de l'Université de Caen (1986), résumé paru dans le Séminaire de Théorie des Nombres de Bordeaux (1986), et dans Proceedings of EUROCAL'87, Lecture notes in Computer Science, Springer (à paraître). [Zbl: 0602.10022] [Google Scholar]
  26. 26. B. VALLÉE, M. GIRAULT et Ph. TOFFIN, HOW to Guess l-th Roots Modulo n by Reducing Lattice Bases, Prépublications de l'Université de Caen, 1988, First International Joint Conference of I.S.S.A.C.-88 and A.A.E.C.C-6, juillet 1988(soumis). [MR: 1008518] [Zbl: 0692.10005] [Google Scholar]
  27. 27. P. VAN EMDE BOAS, Another NP-Complete Partition Problem and the Complexity of Computing Short Vectors in a Lattice, Rep. MI, U.V.A. 81-04, Amsterdam, 1981 [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.