# Generating Hard Instances of the Short Basis Problem

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## 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
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## References

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## Copyright information

© Springer-Verlag Berlin Heidelberg 1999