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Short Threshold Dynamic Group Signatures

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Book cover Security and Cryptography for Networks (SCN 2020)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12238))

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Abstract

Traditional group signatures feature a single issuer who can add users to the group of signers and a single opening authority who can reveal the identity of the group member who computed a signature. Interestingly, despite being designed for privacy-preserving applications, they require strong trust in these central authorities who constitute single points of failure for critical security properties. To reduce the trust placed on authorities, we introduce dynamic group signatures which distribute the role of issuer and opener over several entities, and support \( t _I\)-out-of-\(n_I\) issuance and \( t _O\)-out-of-\(n_O\) opening. We first define threshold dynamic group signatures and formalize their security. We then give an efficient construction relying on the pairing-based Pointcheval–Sanders (PS) signature scheme (CT-RSA 2018), which yields very short group signatures of two first-group elements and three field elements. We also give a simpler variant of our scheme in which issuance requires the participation of all \(n_I\) issuers, but still supports \( t _O\)-out-of-\(n_O\) opening. It is based on a new multi-signature variant of the PS scheme which allows for efficient proofs of knowledge and is a result of independent interest. We prove our schemes secure in the random-oracle model under a non-interactive q-type of assumption.

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Acknowledgements

Most of the work of the first four authors was done while being at IBM Research – Zurich. The authors thank David Pointcheval for helpful discussions. This work was supported by the CHIST-ERA USEIT project and the EU H2020 Research and Innovation Program under Grant Agreement No. 786725 (OLYMPUS).

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Authors and Affiliations

  1. DFINITY, Zurich, Switzerland

    Jan Camenisch, Manu Drijvers & Gregory Neven

  2. Hasso-Plattner-Institute, University of Potsdam, Potsdam, Germany

    Anja Lehmann

  3. IBM Research, Zurich, Switzerland

    Patrick Towa

  4. DIENS, École Normale Supérieure, CNRS, PSL University, Paris, France

    Patrick Towa

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  1. Jan Camenisch
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Correspondence to Patrick Towa .

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  1. Università degli Studi di Salerno, Fisciano, Italy

    Clemente Galdi

  2. Georgia Institute of Technology, Atlanta, GA, USA

    Vladimir Kolesnikov

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Camenisch, J., Drijvers, M., Lehmann, A., Neven, G., Towa, P. (2020). Short Threshold Dynamic Group Signatures. In: Galdi, C., Kolesnikov, V. (eds) Security and Cryptography for Networks. SCN 2020. Lecture Notes in Computer Science(), vol 12238. Springer, Cham. https://doi.org/10.1007/978-3-030-57990-6_20

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  • DOI: https://doi.org/10.1007/978-3-030-57990-6_20

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