Paper 2026/1348 Original: eprint.iacr.org/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 Sigma protocols and a linkable ring signature scheme. Notably, our approach avoids the key-reuse mechanism for linkability used in the framework of Beullens et al. (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 and obtain a linkable ring signature scheme CELeReS, achieving signature sizes that compare favourably with the state of the art, and our AVX2-optimised C implementation demonstrates its practical applicability.