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Erschienen in:
2013 | OriginalPaper | Buchkapitel
Lattice-Based Group Signatures with Logarithmic Signature Size
verfasst von : Fabien Laguillaumie, Adeline Langlois, Benoît Libert, Damien Stehlé
Erschienen in: Advances in Cryptology - ASIACRYPT 2013
Verlag: Springer Berlin Heidelberg
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Group signatures are cryptographic primitives where users can anonymously sign messages in the name of a population they belong to. Gordon
et al.
(Asiacrypt 2010) suggested the first realization of group signatures based on lattice assumptions in the random oracle model. A significant drawback of their scheme is its linear signature size in the cardinality
N
of the group. A recent extension proposed by Camenisch
et al.
(SCN 2012) suffers from the same overhead. In this paper, we describe the first lattice-based group signature schemes where the signature and public key sizes are essentially logarithmic in
N
(for any fixed security level). Our basic construction only satisfies a relaxed definition of anonymity (just like the Gordon
et al.
system) but readily extends into a fully anonymous group signature (
i.e.
, that resists adversaries equipped with a signature opening oracle). We prove the security of our schemes in the random oracle model under the SIS and LWE assumptions.