Stateless blockchain designs have emerged to address the challenge of growing blockchain size using succinct global states. Previous works have developed vector commitments that support proof updates and aggregation to be used as such states. However, maintaining proofs for multiple users still demands significant computational resources, particularly to update proofs with every transaction. This paper introduces Cauchyproofs, a batch-updatable vector commitment that enables proof-serving nodes to efficiently update proofs in quasilinear time relative to the number of users and transactions, utilizing an optimized KZG scheme to achieve complexity$o((\vert \vec{\alpha}\vert +\vert \vec{\beta}\vert)\log^{2}(\vert \vec{\alpha}\vert +\vert \vec{\beta}\vert))$for$\vert \alpha\vert$users and$\vert \beta\vert$transactions, compared to the previous$O(\vert \vec{\alpha}\vert \cdot\vert \vec{\beta}\vert)$approaches. This advancement reduces the computational burden on proof-serving nodes, allowing efficient proof maintenance across large user groups. We demonstrate that our approach is approximately eight times faster than the naive approach at the Ethereumlevel transaction throughput if we perform batch update every hour. Additionally, we present a novel matrix representation for KZG proofs utilizing Cauchy matrices, enabling faster all-proof computations with reduced elliptic curve operations. Finally, we propose an algorithm for history proof query, supporting retrospective proof generation with high efficiency. Our contributions substantially enhance the scalability and practicality of proof-serving nodes in stateless blockchain frameworks.

Ring confidential transaction (RingCT) protocol is widely used in cryptocurrency to protect the privacy of both users’ identities and transaction amounts. Most recently, a new RingCT protocol (called RingCT 2.0) was proposed by leveraging cryptographic accumulators, which can achieve a constant-size output theoretically but still far from being practical due to the heavy zero-knowledge associated with the accumulator. In this article, we revisit the design of ring confidential transaction protocol and put forward a more efficient privacy-preserving payment protocol, which is built upon an extended version of one-out-of-many proof and a special multi-signature. Compared with previous works, the new protocol is not only more practical, but also does not suffer from a trusted setup. Besides, we show that the protocol satisfies the security requirements provided that the underlying cryptographic primitives are secure in the random oracle model. We implement our new payment protocol in Java, and the experimental results show that it is efficient enough to be used in practice.

The immutability of blockchain is crucial to the security of many blockchain applications, while it is still desired or even legally obliged to allow for redacting the contents of blockchain for some scenarios. In this work, we revisit the conflict between the immutability and redaction of blockchain, and put forward a new fine-grained redactable blockchain with a semi-trusted regulator, who follows our protocol but has a tendency to abuse his power. To the best of our knowledge, it is the first blockchain that not only supports the supervision of blockchain content, but also allows users themselves to manage their own data. To this end, we introduce a new variant of chameleon-hash function, named stateful Chameleon Hash with Revocable Subkey, which is important for building our redactable blockchain and may be of independent interest. We also propose a black-box construction from standard chameleon-hash functions, and prove its security properties under our proposed security notions. At last, we provide a proof-of-concept implementation. The evaluation results demonstrate that our redactable blockchain is practical and can be adopted with small additional overhead compared to the immutable blockchain.