Lattice-Based Group Signatures with Logarithmic Signature Size

  • Fabien Laguillaumie
  • Adeline Langlois
  • Benoît Libert
  • Damien Stehlé
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8270)

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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