The shortest vector problem is a central computational problem in the classical area of geometry of numbers. The approximation algorithm presented below has many applications in computational number theory and cryptography. Two of its most prominent applications are the derivation of polynomial time algorithms for factoring polynomials over the rationals and for simultaneous diophantine approximation.
Unable to display preview. Download preview PDF.
- 190.A.K. Lenstra, H.W. Lenstra, Jr., and L. Lovâsz. Factoring polynomials with rational coefficients. Math. Ann., 261:513–534, 1982. (Cited on p. 292)Google Scholar
- 105.C.F. Gauss. Disquisitiones Arithmeticae. English edition translated by A.A. Clarke. Springer-Verlag, New York, NY, 1986. (Cited on p. 292)Google Scholar
- 160.R. Kannan. Algorithmic geometry of numbers. In Annual Review of Computer Science, Vol. 2,pages 231–267. Annual Reviews, Palo Alto, CA, 1987. (Cited on p. 293)Google Scholar
- 3.M. Ajtai. The shortest vector problem in.f2 is NP-hard for randomized reductions. In Proc. 30th ACM Symposium on the Theory of Computing, pages 10–19, 1998.Google Scholar