International Association for Cryptologic Research

International Association
for Cryptologic Research

IACR News item: 27 May 2013

Fabien Laguillaumie, Adeline Langlois, Benoit Libert, Damien Stehle
ePrint Report ePrint Report
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.

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