# Information Security and Cryptography Research Group

## Generating Shorter Bases for Hard Random Lattices

### Joël Alwen and Chris Peikert

26th International Symposium on Theoretical Aspects of Computer Science, STACS 2009, Leibniz International Proceedings in Informatics (LIPIcs), Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, vol. 3, pp. 75-86, 2009.

We revisit the problem of generating a “hard” random lattice together with a basis of relatively short vectors. This problem has gained in importance lately due to new cryptographic schemes that use such a procedure for generating public/secret key pairs. In these applications, a shorter basis directly corresponds to milder underlying complexity assumptions and smaller key sizes. The contributions of this work are twofold. First, using the Hermite normal form as an organizing principle, we simplify and generalize an approach due to Ajtai (ICALP 1999). Second, we improve the construction and its analysis in several ways, most notably by tightening the length of the output basis essentially to the optimum value.

## BibTeX Citation

@inproceedings{AlPe09,
author       = {Joël Alwen and Chris Peikert},
title        = {Generating Shorter Bases for Hard Random Lattices},
editor       = {Susanne Albers, Jean-Yves Marion},
booktitle    = {26th International Symposium on Theoretical Aspects of Computer Science, STACS 2009},
pages        = 75-86,
series       = {Leibniz International Proceedings in Informatics (LIPIcs)},
volume       = 3,
year         = 2009,
publisher    = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
}