Traceable Ring Signatures Revisited: Extended Definitions, O(1) Tracing, and Efficient Log-Size Constructions

Abstract

Traceable Ring Signatures (TRS) were introduced by Fujisaki and Suzuki~[PKC'07], where a trace algorithm can publicly check if two signatures with the same event label were generated by the same signer (linkability). In addition, if the two signatures correspond to different messages, then the signer's identity is revealed (traceability). Following [PKC'07], most subsequent works adopt the same definitions and consider three security properties, anonymity, linkability, and exculpability. [PKC'07] proved that the latter two properties together imply unforgeability, a fundamental requirement for all signature-like primitives. ~~~~In this work, we identify a gap in the aforementioned proof, which arises from the insufficient consideration of linkability and exculpability in [PKC'07]. To address this, we revisit the syntax and security notions of TRS, and close this gap by defining extended linkability and extended exculpability. Building on these, we design a new framework of TRS from PseudoRandom Functions (PRF) and Zero-Knowledge Proofs of Knowledge (ZKPoK) that supports tracing, provided that both two signatures are valid. This constitutes a substantial improvement over existing approaches---all of which require tracing with the size of the ring---and elevates TRS to a level of practicality and efficiency comparable to Linkable Ring Signatures (LRS), which have already achieved widespread deployment in practice. Finally, we instantiate our generic framework from the DDH assumption and leverage the Bulletproofs [S\&P'18] to construct a TRS scheme with log-size signatures. The proposed scheme achieves highly optimized signature sizes in practice and remains compatible with most existing DLog-based systems. On Curve25519, the signature size is bytes, which to our best knowledge is the shortest LRS scheme for a ring .