### Lattice-Based Group Signatures: Achieving Full Dynamicity with Ease

San Ling, Khoa Nguyen, Huaxiong Wang, and Yanhong Xu

##### Abstract

Lattice-based group signature is an active research topic in recent years. Since the pioneering work by Gordon, Katz and Vaikuntanathan (Asiacrypt 2010), 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 Langlois et al. (PKC 2014) that handles user revocations (but new users cannot join), and by Libert et al. (Asiacrypt 2016) 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 (Eurocrypt 2016) - 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. The scheme satisfies the strong security requirements of Bootle et al.'s model (ACNS 2016), under the Short Integer Solution (SIS) and the Learning With Errors (LWE) assumptions.

Available format(s)
Category
Cryptographic protocols
Publication info
Published elsewhere. MAJOR revision.ACNS 2017
Keywords
lattice-based group signaturesfull dynamicityupdatable Merkle treesStern-like zero-knowledge protocols
Contact author(s)
khoantt @ ntu edu sg
History
Short URL
https://ia.cr/2017/353

CC BY

BibTeX

@misc{cryptoeprint:2017/353,
author = {San Ling and Khoa Nguyen and Huaxiong Wang and Yanhong Xu},
title = {Lattice-Based Group Signatures: Achieving Full Dynamicity with Ease},
howpublished = {Cryptology ePrint Archive, Paper 2017/353},
year = {2017},
note = {\url{https://eprint.iacr.org/2017/353}},
url = {https://eprint.iacr.org/2017/353}
}

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