Traceable Ring Signatures from Group Actions: Logarithmic, Flexible, and Quantum Resistant

Traceable ring signature (TRS) is a variation of ring signature, allowing to expose the user’s identity whenever he signs two different messages under the same tag. The accountable anonymity of TRS makes it widely used in many restrained anonymous applications, e.g., e-voting system, offline coupon service. Traditional TRS schemes are built on mathematical problems, which are believed to be easy to solve by quantum computers. While numerous post-quantum (traceable) ring signature schemes have been proposed so far, there has been no TRS scheme based on isogenies proposed. We construct two TRS schemes from group actions that can be instantiated with isogenies and lattices. The critical technique is to generate multiple tags for the message and design an OR sigma protocol to generate proofs for multiple tag sets, which provides traceability for the TRS scheme. The signature size can be expressed as \(O(\log N)\) , where N represents the ring size. Based on different instantiation parameters, our proposed scheme enables ring members to negotiate the signature size and signing time according to their specific requirements. Moreover, we prove the security of our scheme under the standard random oracle model.