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Forward-Secure Linkable Ring Signatures

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Book cover Information Security and Privacy (ACISP 2018)

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Abstract

We present the first linkable ring signature scheme with both unconditional anonymity and forward-secure key update: a powerful tool which has direct applications in elegantly addressing a number of simultaneous constraints in remote electronic voting. We propose a comprehensive security model, and construct a scheme based on the hardness of finding discrete logarithms, and (for forward security) inverting bilinear or multilinear maps of moderate degree to match the time granularity of forward security. We prove efficient security reductions—which, of independent interest, apply to, and are much tighter than, linkable ring signatures without forward security, thereby vastly improving the provable security of these legacy schemes. If efficient multilinear maps should ever admit a secure realisation, our contribution would elegantly address a number of problems heretofore unsolved in the important application of (multi-election) practical internet voting. Even if multilinear maps never obtain, our minimal two-epoch construction instantiated from bilinear maps can be combinatorially boosted to synthesize a polynomial time granularity, which would be sufficient for internet voting and more.

X. Boyen—Supported as Australian Research Council Future Fellow, ARC grant FT140101145.

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Notes

  1. 1.

    The original linkable ring signatures of Liu et al. [18, 19] had proofs with losses exponential in the number of users, due to nested use of the forking lemma [23] on Pedersen commitments [22] in the random-oracle model. Our updated proofs and reductions are independent of the number of users, thanks to a single consolidated use of the forking lemma; and the same techniques directly apply to their construction.

  2. 2.

    In the UK there is a requirement that a judge be able to order a voter’s ballot revealed. Group signatures would be perfect for such subtle voter intimidation, though Continentals would of course disapprove.

  3. 3.

    In its standardasised version [2], Helios relies on a mixnet technique to distribute the election authority’s ability to deanonymise. Even for Helios implementations that use this technique, the ability to enforce anonymity in the authentication mechanism itself would provide stronger privacy guarantees.

  4. 4.

    Rate limitation in the context of authentication refers to an intentional bound on the number of uses, typically one, that can be made of a credential on a given target.

  5. 5.

    Our definations are fairly direct forward secure variants of Liu et al. [18].

  6. 6.

    The last two aspects are generalisations of the first two. We present them all because the standard variants use weaker assumptions than the forward-secure variants.

  7. 7.

    While it is possible for two different private keys to have the same public key, violating the assertion above, this would also break the Pedersen commitments and reveal the relationship between g and h. It is also possible for the hash function to collide. These events are assumed of negligible probability.

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Authors and Affiliations

  1. QUT, Brisbane, Australia

    Xavier Boyen & Thomas Haines

  2. Polyas GmbH, Berlin, Germany

    Thomas Haines

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  1. Xavier Boyen
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Correspondence to Thomas Haines .

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Editors and Affiliations

  1. University of Wollongong, Wollongong, NSW, Australia

    Willy Susilo

  2. University of Wollongong, Wollongong, NSW, Australia

    Guomin Yang

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Boyen, X., Haines, T. (2018). Forward-Secure Linkable Ring Signatures. In: Susilo, W., Yang, G. (eds) Information Security and Privacy. ACISP 2018. Lecture Notes in Computer Science(), vol 10946. Springer, Cham. https://doi.org/10.1007/978-3-319-93638-3_15

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  • DOI: https://doi.org/10.1007/978-3-319-93638-3_15

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