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Generating Hard Instances of the Short Basis Problem

  • Miklós Ajtai
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1644)

Abstract

A class of random lattices is given, in [1] so that (a) a random lattice can be generated in polynomial time together with a short vector in it, and (b) assuming that certain worst-case lattice problems have no polynomial time solutions, there is no polynomial time algorithm which finds a short vector in a random lattice with a polynomially large probability. In this paper we show that lattices of the same random class can be generated not only together with a short vector in them, but also together with a short basis. The existence of a known short basis may make the construction more applicable for cryptographic protocols.

Keywords

Polynomial Time Main Diagonal Cryptographic Protocol Lower Triangular Matrix Random Lattice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Miklós Ajtai
    • 1
  1. 1.IBM Almaden Research CenterUSA

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