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Relaxed Lattice-Based Signatures with Short Zero-Knowledge Proofs

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Information Security (ISC 2018)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11060))

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Abstract

Advanced cryptographic protocols such as anonymous credentials, voting schemes, and e-cash are typically constructed by suitably combining signature, commitment, and encryption schemes with zero-knowledge proofs. Indeed, a large body of protocols have been constructed in that manner from Camenisch-Lysyanskaya signatures and generalized Schnorr proofs. In this paper, we build a similar framework for lattice-based schemes by presenting a signature and commitment scheme that are compatible with Lyubashevsky’s Fiat-Shamir proofs with abort, currently the most efficient zero-knowledge proofs for lattices. The latter proofs provide a weaker, relaxed form of soundness, i.e., the witnesses that the knowledge extractor can obtain are guaranteed to lie only in a domain that is larger than the one from which the inputs of honest provers need to come. To cope with this soundness problem, we define corresponding notions of relaxed signature and commitment schemes. We demonstrate the flexibility and efficiency of our new primitives by constructing a new lattice-based anonymous attribute token scheme and providing concrete parameters to securely instantiate this scheme.

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Notes

  1. 1.

    We do not claim ours to be the first practical AAT. In fact, an AAT scheme based on discrete log is at the core of Microsoft’s U-Prove [50].

  2. 2.

    We do not consider in our comparison the lattice-based group signature built by Benhamouda et al. [10]. Indeed, it is a special case, as the authors avoided expensive zero-knowledge proofs on lattice signatures by bridging a lattice-based encryption scheme to a non-lattice-based signature scheme.

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Acknowledgements

Working on this paper, we have enjoyed many discussions with Vadim Lyubashevsky. Thank you! This work was supported by the ERC under grant #321310 PERCY) and the SNF under grant #\(200021\_157080\) (Efficient Lattice-Based Cryptographic Protocols).

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Authors and Affiliations

  1. IBM Research - Zurich, Zurich, Switzerland

    Cecilia Boschini, Jan Camenisch & Gregory Neven

  2. Università della Svizzera Italiana, Lugano, Switzerland

    Cecilia Boschini

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  1. Cecilia Boschini
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  2. Jan Camenisch
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  3. Gregory Neven
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Correspondence to Jan Camenisch .

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Editors and Affiliations

  1. University of Surrey, Guildford, United Kingdom

    Liqun Chen

  2. University of Surrey, Guildford, United Kingdom

    Mark Manulis

  3. University of Surrey, Guildford, United Kingdom

    Steve Schneider

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Boschini, C., Camenisch, J., Neven, G. (2018). Relaxed Lattice-Based Signatures with Short Zero-Knowledge Proofs. In: Chen, L., Manulis, M., Schneider, S. (eds) Information Security. ISC 2018. Lecture Notes in Computer Science(), vol 11060. Springer, Cham. https://doi.org/10.1007/978-3-319-99136-8_1

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