A quantum-resistant oracle-based conditional payment scheme from lattice

Oracle-based conditional (ObC) payments are a specific type of transaction whose execution is triggered by the outcome of a predetermined external real-world event, verified by a semi-trusted oracle. ObC payments have broad applications in blockchain systems and real-world scenarios, such as financial adjudication, contractual services, trading and betting. Despite their wide applicability, cryptographic schemes supporting ObC payments are still limited. To the best of our knowledge, no quantum-resistant construction has been proposed to date. We fill this gap and present the first quantum-resistant cryptographic solution for ObC payments. In particular, we propose a cryptographic framework called Relaxed Verifiable Witness Encryption based on Signatures (RVWeS) to fulfill the functionality and security requirements of ObC payments, especially one-wayness and verifiability. We further provide a provably secure construction of RVWeS based on the hardness of Ring-SIS and Ring-LWE in the random-oracle model. Additionally, by leveraging relaxed relations and approximate trapdoors, our construction achieves modularity and efficiency without the need for additional transformations. Finally, we compare our scheme with several functionally similar schemes and built-in blockchain mechanisms, and the results show that our scheme offers a good overall performance and cost.