Lattice-Based Group Signatures with Logarithmic Signature Size [chapter]

Fabien Laguillaumie, Adeline Langlois, Benoît Libert, Damien Stehlé
2013 Lecture Notes in Computer Science  
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
more » ... st latticebased 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.
doi:10.1007/978-3-642-42045-0_3 fatcat:7lofdls57bdmroxmnfvvnxitai