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Efficient Threshold Zero-Knowledge with Applications to User-Centric Protocols

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Information Theoretic Security (ICITS 2012)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7412))

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Abstract

In this paper, we investigate on threshold proofs, a framework for distributing the prover’s side of interactive proofs of knowledge over multiple parties. Interactive proofs of knowledge (PoK) are widely used primitives of cryptographic protocols, including important user-centric protocols, such as identification schemes, electronic cash (e-cash), and anonymous credentials.

We present a security model for threshold proofs of knowledge and develop threshold versions of well-known primitives such as range proofs, zero-knowledge proofs for preimages of homomorphisms (which generalizes PoKs of discrete logarithms, representations, p-th roots, etc.), as well as OR statements. These building blocks are proven secure in our model.

Furthermore, we apply the developed primitives and techniques in the context of user-centric protocols. In particular, we construct distributed-user variants of Brands’ e-cash system and the bilinear anonymous credential scheme by Camenisch and Lysyanskaya. Distributing the user party in such protocols has several practical advantages: First, the security of a user can be increased by sharing secrets and computations over multiple devices owned by the user. In this way, losing control of a single device does not result in a security breach. Second, this approach also allows groups of users to jointly control an application (e.g., a joint e-cash account), not giving a single user full control.

The distributed versions of the protocols we propose in this paper are relatively efficient (when compared to a general MPC approach). In comparison to the original protocols only the prover’s (or user’s) side is modified while the other side stays untouched. In particular, it is oblivious to the other party whether it interacts with a distributed prover (or user) or one as defined in the original protocol.

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Author information

Authors and Affiliations

  1. University of Bristol, UK

    Marcel Keller

  2. The Alexandra Institute, Denmark

    Gert Læssøe Mikkelsen

  3. AGT Group (R&D) GmbH, Germany

    Andy Rupp

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  1. Marcel Keller
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  2. Gert Læssøe Mikkelsen
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  3. Andy Rupp
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Editors and Affiliations

  1. Department of Computer Science and Engineering, Pennsylvania State University, 16802, University Park, PA, USA

    Adam Smith

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Keller, M., Mikkelsen, G.L., Rupp, A. (2012). Efficient Threshold Zero-Knowledge with Applications to User-Centric Protocols. In: Smith, A. (eds) Information Theoretic Security. ICITS 2012. Lecture Notes in Computer Science, vol 7412. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32284-6_9

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  • DOI: https://doi.org/10.1007/978-3-642-32284-6_9

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