Lattice-Based Group Signatures with Logarithmic Signature Size

Fabien Laguillaumie (1, 2) , Adeline Langlois (1, 2) , Benoît Libert (3) , Damien Stehlé (1, 2)

1 ARIC - Arithmetic and Computing
2 LIP - Laboratoire de l'Informatique du Parallélisme
3 Security & Content Protection Labs

Group signatures are cryptographic primitives where users can anonymously sign messages in the name of a population they belong to. Gordon {\em 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 {\em 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 {\it et al.} system) but readily extends into a fully anonymous group signature ({\it 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.

Domaines: Cryptographie et sécurité [cs.CR]

Fabien Laguillaumie, Adeline Langlois, Benoît Libert, Damien Stehlé. Lattice-Based Group Signatures with Logarithmic Signature Size. ASIACRYPT 2013 - 19th International Conference on the Theory and Application of Cryptology and Information Security, Dec 2013, Bangaluru, India. ⟨10.1007/978-3-642-42045-0_3⟩. ⟨hal-00920420⟩