Paper 2025/038

Cauchyproofs: Batch-Updatable Vector Commitment with Easy Aggregation and Application to Stateless Blockchains

Abstract

Stateless blockchain designs have emerged to address the challenge of growing blockchain size by utilizing 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 in updating proofs with every transaction. This paper introduces Cauchyproofs, a batch-updatable vector commitment enabling proof-serving nodes to efficiently update proofs in quasi-linear time relative to the number of users and transactions, utilizing an optimized KZG scheme to achieve complexity $O\left(\left(\left|\vec{\alpha}\right| + \left|\vec{\beta}\right|\right) \log^2 (\left|\vec{\alpha}\right| + \left|\vec{\beta}\right|)\right)$, compared to previous $O\left(\left|\vec{\alpha}\right|\cdot|\vec{\beta}|\right)$ approaches. This advancement reduces the computational burden on proof-serving nodes, allowing for efficient proof maintenance across large user groups. We demonstrate that our approach is approximately five times faster than the naive approach at the Ethereum-level block size. 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.