We demonstrate that a version of non-slanderability is a natural definition of unforgeability for linkable ring signatures. We present a linkable ring signature construction with concise signatures and multi-dimensional keys that is linkably anonymous if a variation of the decisional Diffie-Hellman problem with random oracles is hard, linkable if key aggregation is a one-way function, and non-slanderable if a one-more variation of the discrete logarithm problem is hard. We remark on some applications in signer-ambiguous confidential transaction models without trusted setup.
Ring signatures are a common construction used to provide signer ambiguity among a non-interactive set of public keys specified at the time of signing. Unlike early approaches where signature size is linear in the size of the signer anonymity set, current optimal solutions either require centralized trusted setups or produce signatures logarithmic in size. However, few also provide linkability, a property used to determine whether the signer of a message has signed any previous message, possibly with restrictions on the anonymity set choice. Here we introduce Triptych, a family of linkable ring signatures without trusted setup that is based on generalizations of zero-knowledge proofs of knowledge of commitment openings to zero. We demonstrate applications of Triptych in signer-ambiguous transaction protocols by extending the construction to openings of parallel commitments in independent anonymity sets. Signatures are logarithmic in the anonymity set size and, while verification complexity is linear, collections of proofs can be efficiently verified in batches. We show that for anonymity set sizes practical for use in distributed protocols, Triptych offers competitive performance with a straightforward construction.
Confidential transactions are used in distributed digital assets to demonstrate the balance of values hidden in commitments, while retaining signer ambiguity. Previous work describes a signer-ambiguous proof of knowledge of the opening of commitments to zero at the same index across multiple public commitment sets and the evaluation of a verifiable random function used as a linking tag, and uses this to build a linkable ring signature called Triptych that can be used as a building block for a confidential transaction model. In this work, we extend Triptych to build Arcturus, a proving system that proves knowledge of openings of multiple commitments to zero within a single set, correct construction of a verifiable random function evaluated at each opening, and value balance across a separate list of commitments within a single proof. While soundness depends on a novel dual discrete-logarithm hardness assumption, we use data from the Monero blockchain to show that Arcturus can be used in a confidential transaction model to provide faster total batch verification time than other state-of-the-art constructions without a trusted setup.
Published: 4 April 2020, with <a href="https://github.com/UkoeHB/Monero-RCT-report">LaTeX source code here</a><br> A comprehensive conceptual (and technical) explanation of Monero.<br> We endeavor to teach anyone who knows basic algebra and simple computer science concepts like the ‘bit representation’ of a number not only how Monero works at a deep and comprehensive level, but also how useful and beautiful cryptography can be.
