Buchmann, Johannes A. ;
Lindner, Richard
Density of Ideal Lattices
Abstract
The security of many emph{efficient} cryptographic constructions, e.g.~collision-resistant hash functions, digital signatures, and identification schemes, has been proven assuming the hardness of emph{worst-case} computational problems in ideal lattices. These lattices correspond to ideals in the ring of integers of some fixed number field $K$.
In this paper we show that the density of $n$-dimensional ideal lattices with determinant $le b$ among all lattices under the same bound is in $O(b^{1-n})$. So for lattices of dimension $> 1$ with bounded determinant, the subclass of ideal lattices is always vanishingly small.
BibTeX - Entry
@InProceedings{buchmann_et_al:DSP:2009:2125,
author = {Johannes A. Buchmann and Richard Lindner},
title = {Density of Ideal Lattices},
booktitle = {Algorithms and Number Theory },
year = {2009},
editor = {Johannes A. Buchmann and John Cremona and Michael E. Pohst},
number = {09221},
series = {Dagstuhl Seminar Proceedings},
ISSN = {1862-4405},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2009/2125},
annote = {Keywords: Post-quantum cryptography, provable security, ideal lattices}
}
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Keywords: |
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Post-quantum cryptography, provable security, ideal lattices |
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Seminar: |
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09221 - Algorithms and Number Theory
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Issue date: |
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2009 |
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Date of publication: |
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20.08.2009 |
20.08.2009
