Lattice-Based Group Signatures with Logarithmic Signature Size
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- Laguillaumie F., Langlois A., Libert B., Stehlé D. (2013) Lattice-Based Group Signatures with Logarithmic Signature Size. In: Sako K., Sarkar P. (eds) Advances in Cryptology - ASIACRYPT 2013. ASIACRYPT 2013. Lecture Notes in Computer Science, vol 8270. Springer, Berlin, Heidelberg
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.
KeywordsLattice-based cryptography group signatures anonymity
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