Density of Ideal Lattices

Buchmann, Johannes A.; Lindner, Richard

doi:10.4230/DagSemProc.09221.2

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Density of Ideal Lattices

Authors Johannes A. Buchmann, Richard Lindner

Part of: Volume: Dagstuhl Seminar Proceedings, Volume 9221
Part of: Series: Dagstuhl Seminar Proceedings (DagSemProc)
License: Creative Commons Attribution 4.0 International license
Publication Date: 2009-08-20

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Document Identifiers

DOI: 10.4230/DagSemProc.09221.2
URN: urn:nbn:de:0030-drops-21256

Subject Classification

Keywords

Post-quantum cryptography
provable security
ideal lattices

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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.

Cite As Get BibTex

Johannes A. Buchmann and Richard Lindner. Density of Ideal Lattices. In Algorithms and Number Theory. Dagstuhl Seminar Proceedings, Volume 9221, pp. 1-6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009) https://doi.org/10.4230/DagSemProc.09221.2

Author Details

Johannes A. Buchmann

Richard Lindner

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