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A Practical Group Signature Scheme Based on Rank Metric

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Arithmetic of Finite Fields (WAIFI 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10064))

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Abstract

In this work, we propose the first rank-based group signature. Our construction enjoys two major advantages compared to concurrent post-quantum schemes since it is both practicably instantiated with public key and signature sizes logarithmic in the number of group members, and dynamic in a relaxation of the reference BSZ model. For such a result, we introduce a new rank-based tool, referred as the Rank Concatenated Stern’s protocol, enabling to link different users to a common syndrome. This protocol, which could be of independent interest, can be seen as a Stern-like protocol with an additional property that permits a verifier to check the weight of each part of a split secret. Along with this work, we also define two rank-based adaptations of Hamming-based problems, referred as the One More Rank Syndrome Decoding and the Decision Rank Syndrome Decoding problems for which we discuss the security. Embedded into Fiat-Shamir paradigm, our authentication protocol leads to a group signature scheme secure in the Random Oracle Model assuming the security of rank-based systems (namely RankSign and LRPC codes) and the newly introduced problems. For a 100 bits security level, we give an example of parameters which lead to a signature size of 550 kB and 5 kB for the public key.

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Authors and Affiliations

  1. Université de Limoges, XLIM-DMI, Limoges, France

    Quentin Alamélou, Olivier Blazy & Philippe Gaborit

  2. R&D Department, Worldline, Seclin, France

    Quentin Alamélou & Stéphane Cauchie

Authors
  1. Quentin Alamélou
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  2. Olivier Blazy
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  3. Stéphane Cauchie
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  4. Philippe Gaborit
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Correspondence to Quentin Alamélou .

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Editors and Affiliations

  1. University of Rennes, Rennes, France

    Sylvain Duquesne

  2. University of Leuven, Leuven, Belgium

    Svetla Petkova-Nikova

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Alamélou, Q., Blazy, O., Cauchie, S., Gaborit, P. (2016). A Practical Group Signature Scheme Based on Rank Metric. In: Duquesne, S., Petkova-Nikova, S. (eds) Arithmetic of Finite Fields. WAIFI 2016. Lecture Notes in Computer Science(), vol 10064. Springer, Cham. https://doi.org/10.1007/978-3-319-55227-9_18

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  • DOI: https://doi.org/10.1007/978-3-319-55227-9_18

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