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Lattice-based group signatures: achieving full dynamicity (and deniability) with ease. (English) Zbl 07093354
Summary: Lattice-based group signature is an active research topic in recent years. Since the pioneering work by S. D. Gordon et al. [Lect. Notes Comput. Sci. 6477, 395–412 (2010; Zbl 1253.94071)], eight other schemes have been proposed, providing various improvements in terms of security, efficiency and functionality. However, most of the existing constructions work only in the static setting where the group population is fixed at the setup phase. The only two exceptions are the schemes by A. Langlois et al. [ibid. 8383, 345–361 (2014; Zbl 1335.94063)] that handles user revocations (but new users cannot join), and by B. Libert et al. [ibid. 10032, 373–403 (2016; Zbl 1407.94136); ibid. 10032, 101–131 (2016; Zbl 1407.94135)] which addresses the orthogonal problem of dynamic user enrollments (but users cannot be revoked).
In this work, we provide the first lattice-based group signature that offers full dynamicity (i.e., users have the flexibility in joining and leaving the group), and thus, resolve a prominent open problem posed by previous works. Moreover, we achieve this non-trivial feat in a relatively simple manner. Starting with Libert et al.’s fully static construction [B. Libert et al., ibid. 9666, 1–31 (2016; Zbl 1369.94552)] - which is arguably the most efficient lattice-based group signature to date, we introduce simple-but-insightful tweaks that allow to upgrade it directly into the fully dynamic setting. More startlingly, our scheme even produces slightly shorter signatures than the former, thanks to an adaptation of a technique proposed by S. Ling et al. [ibid. 7778, 107–124 (2013; Zbl 1314.94087)], allowing to prove inequalities in zero-knowledge. The scheme satisfies the strong security requirements of Bootle et al.’s model [J. Bootle et al., ibid. 9696, 117–136 (2016; Zbl 1346.94141)], under the Short Integer Solution (SIS) and the Learning With Errors (LWE) assumptions.
Furthermore, we demonstrate how to equip the obtained group signature scheme with the deniability functionality in a simple way. This attractive functionality, put forward by A. Ishida et al. [ibid. 10052, 228–244 (2016; Zbl 1398.94197)], enables the tracing authority to provide an evidence that a given user is not the owner of a signature in question. In the process, we design a zero-knowledge protocol for proving that a given LWE ciphertext does not decrypt to a particular message.

MSC:
94A62 Authentication, digital signatures and secret sharing
94A60 Cryptography
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