Leaking Arbitrarily Many Secrets: Any-out-of-Many Proofs and Applications to RingCT Protocols

Ring Confidential Transaction (RingCT) protocol is an effective cryptographic component for preserving the privacy of cryptocurrencies. However, existing RingCT protocols are instantiated from one-out-of-many proofs with only one secret, leading to low efficiency and weak anonymity when handling transactions with multiple inputs. Additionally, current partial knowledge proofs with multiple secrets are neither secure nor efficient to be applied in a RingCT protocol.In this paper, we propose a novel any-out-of-many proof, a logarithmic-sized zero-knowledge proof scheme for showing the knowledge of arbitrarily many secrets out of a public list. Unlike other partial knowledge proofs that have to reveal the number of secrets [ACF21], our approach proves the knowledge of multiple secrets without leaking the exact number of them. Furthermore, we improve the efficiency of our method with a generic inner-product transformation to adopt the Bulletproofs compression [BBB+18], which reduces the proof size to 2⌈log2(N)⌉+9.Based on our proposed proof scheme, we further construct a compact RingCT protocol for privacy cryptocurrencies, which can provide a logarithmic-sized communication complexity for transactions with multiple inputs. More importantly, as the only known RingCT protocol instantiated from the partial knowledge proofs, our protocol can achieve the highest anonymity level compared with other approaches like Omniring [LRR+19]. For other applications, such as multiple ring signatures, our protocol can also be applied with some modifications. We believe our techniques are also applicable in other privacy-preserving scenarios, such as multiple ring signatures and coin-mixing in the blockchain.