Paper 2026/1348

On Canonical Liftings, Group Actions, and (Linkable) Ring Signatures

Abstract

We introduce the notion of canonical lifting for group actions. This generalises existing techniques for reducing the size of group-action-based signatures, such as the canonical forms used in the LESS signature scheme. Building on this framework, we construct a ring signature scheme and extend it to a linkable variant. Our approach avoids the key-reuse mechanism for linkability of the framework by Beullens, Katsumata, and Pintore (ASIACRYPT'20), which was shown to be insecure for group actions arising from linear code equivalence (ASIACRYPT'24) and lattice isomorphism (CiC'25). The resulting signatures have size logarithmic in the ring size. We provide security proofs at the level of the abstract canonical-lifting framework, which are then inherited by concrete instantiations satisfying the required assumptions. Finally, we instantiate our approach using the linear code equivalence group action, obtaining a ring signature scheme, $\mathsf{CERES}$, and a linkable ring signature scheme, $\mathsf{CELERES}$. Both schemes achieve signature sizes that compare favourably with the state of the art, and our AVX2-optimised C implementation supports their practical applicability.