DagSemProc.09221.2.pdf
- Filesize: 179 kB
- 6 pages
Document
Density of Ideal Lattices
Authors
-
Part of:
Volume:
Dagstuhl Seminar Proceedings, Volume 9221
Series: Dagstuhl Seminar Proceedings (DagSemProc) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2009-08-20
Cite AsGet 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
https://doi.org/10.4230/DagSemProc.09221.2
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.
Keywords
- Post-quantum cryptography
- provable security
- ideal lattices
Metrics
- Access Statistics
-
Total Accesses (updated on a weekly basis)
0PDF Downloads