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Floppy-Sized Group Signatures from Lattices

Part of the Lecture Notes in Computer Science book series (LNSC,volume 10892)

Abstract

We present the first lattice-based group signature scheme whose cryptographic artifacts are of size small enough to be usable in practice: for a group of \(2^{25}\) users, signatures take 910 kB and public keys are 501 kB. Our scheme builds upon two recently proposed lattice-based primitives: the verifiable encryption scheme by Lyubashevsky and Neven (Eurocrypt 2017) and the signature scheme by Boschini, Camenisch, and Neven (IACR ePrint 2017). To achieve such short signatures and keys, we first re-define verifiable encryption to allow one to encrypt a function of the witness, rather than the full witness. This definition enables more efficient realizations of verifiable encryption and is of independent interest. Second, to minimize the size of the signatures and public keys of our group signature scheme, we revisit the proof of knowledge of a signature and the proofs in the verifiable encryption scheme provided in the respective papers.

Keywords

  • Lattices
  • Group signature
  • Verifiable encryption

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Notes

  1. 1.

    Boschini et al. proved that, for \(\mathcal {U}\subset \mathcal {R}_{3}^{(16)}\), this is actually a relaxed commitment scheme. We do not need the relaxed binding property, hence we can choose a larger set of messages (as long as it still guarantees the hiding property).

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Acknowledgements

The authors thank Vadim Lyubashevsky for many helpful discussions and the anonymous reviewers for the useful comments. 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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Boschini, C., Camenisch, J., Neven, G. (2018). Floppy-Sized Group Signatures from Lattices. In: Preneel, B., Vercauteren, F. (eds) Applied Cryptography and Network Security. ACNS 2018. Lecture Notes in Computer Science(), vol 10892. Springer, Cham. https://doi.org/10.1007/978-3-319-93387-0_9

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  • DOI: https://doi.org/10.1007/978-3-319-93387-0_9

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