eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2009-08-20
9221
1
11
10.4230/DagSemProc.09221.1
article
09221 Abstracts Collection – Algorithms and NumberTheory
Buchmann, Johannes A.
Cremona, John
Pohst, Michael
From 24.05. to 29.05.2009, the Dagstuhl Seminar 09221 ``Algorithms and Number Theory '' was held in Schloss Dagstuhl~--~Leibniz Center for Informatics.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol09221/DagSemProc.09221.1/DagSemProc.09221.1.pdf
Algorithms
Number Theory
Cryptography
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2009-08-20
9221
1
6
10.4230/DagSemProc.09221.2
article
Density of Ideal Lattices
Buchmann, Johannes A.
Lindner, Richard
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.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol09221/DagSemProc.09221.2/DagSemProc.09221.2.pdf
Post-quantum cryptography
provable security
ideal lattices
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2009-08-20
9221
1
17
10.4230/DagSemProc.09221.3
article
Lattice-based Blind Signatures
Rückert, Markus
Motivated by the need to have secure blind signatures even in the presence of quantum computers, we present two efficient blind signature schemes based on hard worst-case lattice problems. Both schemes are provably secure in the random oracle model and unconditionally blind. The first scheme is based on preimage samplable functions that were introduced at STOC 2008 by Gentry, Peikert, and Vaikuntanathan. The scheme is stateful and runs in 3 moves. The second scheme builds upon the PKC 2008 identification scheme of Lyubashevsky. It is stateless, has 4 moves, and its security is based on the hardness of worst-case problems in ideal lattices.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol09221/DagSemProc.09221.3/DagSemProc.09221.3.pdf
Blind signatures
post-quantum
lattices
privacy
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2009-08-20
9221
1
6
10.4230/DagSemProc.09221.4
article
Probabilistic Analysis of LLL Reduced Bases
Schneider, Michael
LLL reduction, originally founded in 1982 to factor certain polynomials, is a useful tool in public key cryptanalysis. The search for short lattice vectors helps determining the practical hardness of lattice problems, which are supposed to be secure against quantum computer attacks.
It is a fact that in practice, the LLL algorithm finds much shorter vectors than its theoretic analysis guarantees. Therefore one can see that the guaranteed worst case bounds are not helpful for practical purposes. We use a probabilistic approach to give an estimate for the length of the shortest vector in an LLL-reduced bases that is tighter than the worst case bounds.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol09221/DagSemProc.09221.4/DagSemProc.09221.4.pdf
Lattice reduction
LLL algorithm
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2009-08-20
9221
1
4
10.4230/DagSemProc.09221.5
article
Rational Points on Curves of Genus 2: Experiments and Speculations
Stoll, Michael
I will present results of computations providing statistics on rational points on (small) curves of genus 2 and use them to present several conjectures. Some of them are based on heuristic considerations, others are not.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol09221/DagSemProc.09221.5/DagSemProc.09221.5.pdf
Rational points
genus 2