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Lattice-Based Group Signatures: Achieving Full Dynamicity with Ease

机译：基于格的组签名：轻松实现完全动态

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摘要

Lattice-based group signature is an active research topic in recent years. Since the pioneering work by Gordon et al. (Asi-acrypt 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.
机译：基于格子的组签名是近年来活跃的研究主题。自戈登等人的开创性工作以来。 （Asi-acrypt 2010）提出了其他八种方案，在安全性，效率和功能方面提供了各种改进。但是，大多数现有构造仅在静态环境下工作，在静态环境中，组人口固定在设置阶段。仅有的两个例外是Langlois等人的方案。 （PKC 2014）处理用户撤销（但新用户无法加入），并由Libert等人撰写。 （Asiacrypt 2016）解决了动态用户注册的正交问题（但无法撤销用户）。在这项工作中，我们提供了第一个基于格子的小组签名，该小组签名具有完全的动态性（即用户可以灵活地加入和离开小组），从而解决了先前工作提出的一个突出的开放性问题。此外，我们以相对简单的方式实现了这一非凡的壮举。从Libert等人的全静态构造（Eurocrypt 2016）开始-这可以说是迄今为止最有效的基于格的组签名，我们引入了简单但无见识的调整，可将其直接升级为全动态设置。更令人吃惊的是，我们的方案产生的签名甚至比前者短一些。在短整数解决方案（SIS）和有错误学习（LWE）的假设下，该方案满足了Bootle等人模型（ACNS 2016）的强大安全性要求。

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