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Group signatures from lattices: simpler, tighter, shorter, ring-based. (English) Zbl 1345.94075
Katz, Jonathan (ed.), Public-key cryptography – PKC 2015. 18th IACR international conference on practice and theory in public-key cryptography, Gaithersburg, MD, USA, March 30 – April 1, 2015. Proceedings. Berlin: Springer (ISBN 978-3-662-46446-5/pbk; 978-3-662-46447-2/ebook). Lecture Notes in Computer Science 9020, 427-449 (2015).
Summary: We introduce a lattice-based group signature scheme that provides several noticeable improvements over the contemporary ones: simpler construction, weaker hardness assumptions, and shorter sizes of keys and signatures. Moreover, our scheme can be transformed into the ring setting, resulting in a scheme based on ideal lattices, in which the public key and signature both have bit-size $$\widetilde{\mathcal {O}}(n\cdot \log N)$$, for security parameter $$n$$, and for group of $$N$$ users. Towards our goal, we construct a new lattice-based cryptographic tool: a statistical zero-knowledge argument of knowledge of a valid message-signature pair for Boyen’s signature scheme X. Boyen [PKC 2010, Lect. Notes Comput. Sci. 6056, 499–517 (2010; Zbl 1281.94074)], which potentially can be used as the building block to design various privacy-enhancing cryptographic constructions.
For the entire collection see [Zbl 1318.94002].

##### MSC:
 94A60 Cryptography
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