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Simpler efficient group signatures from lattices. (English) Zbl 1345.94082
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, 401-426 (2015).
Summary: A group signature allows a group member to anonymously sign messages on behalf of the group. In the past few years, new group signatures based on lattice problems have appeared: the most efficient lattice-based constructions are due to F. Laguillaumie et al. [Asiacrypt 2013, Lect. Notes Comput. Sci. 8270, 41–61 (2013; Zbl 1314.94104)] and A. Langlois et al. [PKC 2014, Lect. Notes Comput. Sci. 8383, 345–361 (2014; Zbl 1335.94063)]. Both have at least $$O(n^2\log ^2 n \log N)$$-bit group public key and $$O(n\log ^3 n\log N)$$-bit signature, where $$n$$ is the security parameter and $$N$$ is the maximum number of group members. In this paper, we present a simpler lattice-based group signature, which is more efficient by a $$O(\log N)$$ factor in both the group public key and the signature size. We achieve this by using a new non-interactive zero-knowledge (NIZK) proof corresponding to a simple identity-encoding function. The security of our group signature can be reduced to the hardness of SIS and LWE in the random oracle model.
For the entire collection see [Zbl 1318.94002].

##### MSC:
 94A60 Cryptography
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