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A Provably Secure Group Signature Scheme from Code-Based Assumptions

  • Martianus Frederic Ezerman
  • Hyung Tae Lee
  • San Ling
  • Khoa Nguyen
  • Huaxiong Wang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9452)

Abstract

We solve an open question in code-based cryptography by introducing the first provably secure group signature scheme from code-based assumptions. Specifically, the scheme satisfies the CPA-anonymity and traceability requirements in the random oracle model, assuming the hardness of the McEliece problem, the Learning Parity with Noise problem, and a variant of the Syndrome Decoding problem. Our construction produces smaller key and signature sizes than the existing post-quantum group signature schemes from lattices, as long as the cardinality of the underlying group does not exceed the population of the Netherlands (\({\approx }2^{24}\) users). The feasibility of the scheme is supported by implementation results. Additionally, the techniques introduced in this work might be of independent interest: a new verifiable encryption protocol for the randomized McEliece encryption and a new approach to design formal security reductions from the Syndrome Decoding problem.

Keywords

Random Oracle Random Oracle Model Interactive Protocol Argument System Group Signature Scheme 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

The authors would like to thank Jean-Pierre Tillich, Philippe Gaborit, Ayoub Otmani, Nicolas Sendrier, Nico Döttling, and anonymous reviewers of ASIACRYPT 2015 for helpful comments and discussions. The research was supported by Research Grant TL-9014101684-01 and the Singapore Ministry of Education under Research Grant MOE2013-T2-1-041.

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Copyright information

© International Association for Cryptologc Research 2015

Authors and Affiliations

  • Martianus Frederic Ezerman
    • 1
  • Hyung Tae Lee
    • 1
  • San Ling
    • 1
  • Khoa Nguyen
    • 1
  • Huaxiong Wang
    • 1
  1. 1.Division of Mathematical Sciences, School of Physical and Mathematical SciencesNanyang Technological UniversitySingaporeSingapore

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