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Lattice-based group signature scheme with verifier-local revocation. (English) Zbl 1335.94063
Krawczyk, Hugo (ed.), Public-key cryptography – PKC 2014. 17th international conference on practice and theory in public-key cryptography, Buenos Aires, Argentina, March 26–28, 2014. Proceedings. Berlin: Springer (ISBN 978-3-642-54630-3/pbk). Lecture Notes in Computer Science 8383, 345-361 (2014).
Summary: Support of membership revocation is a desirable functionality for any group signature scheme. Among the known revocation approaches, verifier-local revocation (VLR) seems to be the most flexible one, because it only requires the verifiers to possess some up-to-date revocation information, but not the signers. All of the contemporary VLR group signatures operate in the bilinear map setting, and all of them will be insecure once quantum computers become a reality. In this work, we introduce the first lattice-based VLR group signature, and thus, the first such scheme that is believed to be quantum-resistant. In comparison with existing lattice-based group signatures, our scheme has several noticeable advantages: support of membership revocation, logarithmic-size signatures, and weaker security assumption. In the random oracle model, our scheme is proved to be secure based on the hardness of the $$\mathsf{SIVP}_{\widetilde{\mathcal{O}}(n^{1.5})}$$ problem in general lattices – an assumption that is as weak as those of state-of-the-art lattice-based standard signatures. Moreover, our construction works without relying on encryption schemes, which is an intriguing feature for group signatures.
For the entire collection see [Zbl 1283.94002].

##### MSC:
 94A60 Cryptography
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