Lattice-Based Group Signatures with Logarithmic Signature Size

  • Fabien Laguillaumie
  • Adeline Langlois
  • Benoît Libert
  • Damien Stehlé
Conference paper

DOI: 10.1007/978-3-642-42045-0_3

Part of the Lecture Notes in Computer Science book series (LNCS, volume 8270)
Cite this paper as:
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

Abstract

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.

Keywords

Lattice-based cryptography group signatures anonymity 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Fabien Laguillaumie
    • 1
    • 3
  • Adeline Langlois
    • 2
    • 3
  • Benoît Libert
    • 4
  • Damien Stehlé
    • 2
    • 3
  1. 1.Université Claude Bernard Lyon 1France
  2. 2.École Normale Supérieure de LyonFrance
  3. 3.LIP (U. Lyon, CNRS, ENS Lyon, INRIA, UCBL)Lyon Cedex 07France
  4. 4.TechnicolorCesson-SévignéFrance

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