Fast reduction of ternary quadratic forms

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

Volumn 2146, Issue , 2001, Pages 32-44

  Eisenbrand, Friedrich ^a   Rote, Günter ^b  

^a MAX PLANCK INSTITUTE FOR INFORMATICS   (Germany)

^b FREIE UNIVERSITÄT BERLIN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BINS; NUMBER THEORY;

ARITHMETIC OPERATIONS; BINARY ENCODINGS; BIT COMPLEXITY; BIT-OPERATIONS; GAUSSIAN ALGORITHMS; HIGHER DIMENSIONS; LATTICE BASIS REDUCTION; QUADRATIC FORM;

CRYPTOGRAPHY;

EID: 84958958901     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-44670-2_4     Document Type: Conference Paper

References (16)

1. A.V. Aho, J.E. Hopcroft, and J.D. Ullman. The Design and Analysis of Computer Algorithms. Addison-Wesley, Reading, 1974.
2. J.W.S. Cassels. Rational quadratic forms. Academic Press, 1978.
3. F. Eisenbrand. Short vectors of planar lattices via continued fractions. Information Processing Letters, 2001, to appear. http://www.mpi-sb.mpg.de/~eisen/report_lattice.ps.gz
4. C.F. Gauÿ. Disquisitiones arithmeticae. Gerh. Fleischer Iun., 1801.
5. C.F. Gauÿ. Recension der “Untersuchungen über die Eigenschaften der positive ternären quadratischen Formen von Ludwig August Seeber.” Reprinted in Journal für die reine und angewandte Mathematik, 20:312-320, 1840.
6. Ch. Hermite. Extraits de lettres de M. Ch. Hermite à M. Jacobi sur diérents objets de la théorie des nombres. Journal für die reine und angewandte Mathematik, 40, 1850.
7. J. C. Lagarias. Worst-case complexity bounds for algorithms in the theory of integral quadratic forms. Journal of Algorithms, 1:142-186, 1980.
8. A.K. Lenstra, H.W. Lenstra, and L. Lovász. Factoring polynomials with rational coe-cients. Math. Annalen, 261:515-534, 1982.
9. H.W. Lenstra. Integer programming with a fixed number of variables. Mathematics of Operations Research, 8(4):538-548, 1983.
10. A. Schönhage. Fast reduction and composition of binary quadratic forms. In International Symposium on Symbolic and Algebraic Computation, ISSAC'91, pages 128-133. ACM Press, 1991.
11. A. Schönhage and V. Strassen. Schnelle Multiplikation grosser Zahlen (Fast multiplication of large numbers). Computing, 7:281-292, 1971.
12. A. Schrijver. Theory of Linear and Integer Programming. John Wiley, 1986.
13. L.A. Seeber. Untersuchung über die Eigenschaften der positiven ternären quadratis-chen Formen. Loeer, Mannheim, 1831.
14. I. Semaev. A 3-dimensional lattice reduction algorithm. In Cryptography and Lattices Conference, CALC 2001. This volume, pp. 181-193, 2001.
15. B. Vallée. An a-ne point of view on minima finding in integer lattices of lower dimensions. In Proceedings of the European Conference on Computer Algebra, EUROCAL'87, volume 378 of Lecture Notes in Computer Science, pp. 376-378. Springer, Berlin, 1989.
16. C.K. Yap. Fast unimodular reduction: Planar integer lattices. In Proceedings of the 33rd Annual Symposium on Foundations of Computer Science, pages 437-446, Pittsburgh, 1992. IEEE Computer Society Press.