PGC: Decentralized Confidential Payment System with Auditability

Abstract

Modern cryptocurrencies such as Bitcoin and Ethereum achieve decentralization by replacing a trusted center with a distributed and append-only ledger (known as blockchain). However, removing this trusted center comes at significant cost of privacy due to the public nature of blockchain. Many existing cryptocurrencies fail to provide transaction anonymity and confidentiality, meaning that addresses of sender, receiver and transfer amount are publicly accessible. As the privacy concerns grow, a number of academic work have sought to enhance privacy by leveraging cryptographic tools. Though strong privacy is appealing, it might be abused in some cases. In decentralized payment systems, anonymity poses great challenges to system’s auditability, which is a crucial property for scenarios that require regulatory compliance and dispute arbitration guarantee. Aiming for a middle ground between privacy and auditability, we introduce the notion of decentralized confidential payment (DCP) system with auditability. In addition to offering transaction confidentiality, DCP supports privacy-preserving audit in which an external party can specify a set of transactions and then request the participant to prove their compliance with a large class of policies. We present a generic construction of auditable DCP system from integrated signature and encryption scheme and non-interactive zero-knowledge proof systems. We then instantiate our generic construction by carefully designing the underlying building blocks, yielding a standalone cryptocurrency called PGC. In PGC, the setup is transparent, transactions are less than 1.3KB and take under 38ms to generate and 15ms to verify. At the core of PGC is an additively homomorphic public-key encryption scheme that we introduce, twisted ElGamal, which is not only as secure as standard exponential ElGamal, but also friendly to Sigma protocols and range proofs. This enables us to easily devise zero-knowledge proofs for basic correctness of transactions as well as various application-dependent policies in a modular fashion. Moreover, it is very efficient. Compared with the most efficient reported implementation of Paillier PKE, twisted ElGamal is an order of magnitude better in key and ciphertext size and decryption speed (for small message space), two orders of magnitude better in encryption speed. We believe twisted ElGamal is of independent interest on its own right. Along the way of designing and reasoning zero-knowledge proofs for PGC, we also obtain two interesting results. One is weak forking lemma which is a useful tool to prove computational knowledge soundness. The other is a trick to prove no-knowledge of discrete logarithm, which is a complement of standard proof of discrete logarithm knowledge.