An Overview of the Sieve Algorithm for the Shortest Lattice Vector Problem
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We present an overview of a randomized 2g(n) time algorithm to compute a shortest non-zero vector in an n-dimensional rational lattice. The complete details of this algorithm can be found in .
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- 1.M. Ajtai. The shortest vector problem in L 2 is NP-hard for randomized reductions. Proc. 30th ACM Symposium on Theory of Computing, pp. 10–19, 1998.Google Scholar
- 2.M. Ajtai, R. Kumar, and D. Sivakumar. A sieve algorithm for the shortest lattice vector problem. Proc. 33rd ACM Symposium on Theory of Computing, 2001. To appear.Google Scholar
- 3.P. van Emde Boas. Another NP-complete partition problem and the complexity of computing short vectors in lattices. Mathematics Department, University of Amsterdam, TR 81-04, 1981.Google Scholar
- 4.C. F. Gauss. Disquisitiones Arithmeticae. English edition, (Translated by A. A. Clarke) Springer-Verlag, 1966.Google Scholar
- 7.C. Hermite. Second letter to Jacobi, Oeuvres, I, Journal für Mathematik, 40:122–135, 1905.Google Scholar
- 9.R. Kumar and D. Sivakumar. On polynomial approximations to the shortest lattice vector length. Proc. 12th Symposium on Discrete Algorithms, 2001.Google Scholar
- 12.D. Micciancio. The shortest vector in a lattice is hard to approximate to within some constant. Proc. 39th IEEE Symposium on Foundations of Computer Science, pp. 92–98, 1998.Google Scholar
- 13.H. Minkowski. Geometrie der Zahlen. Leipzig, Teubner, 1990.Google Scholar