Zero-knowledge proofs have emerged as a powerful tool for enhancing privacy and security in blockchain applications. However, the efficiency and scalability of proof systems remain a significant challenge, particularly in the context of Merkle tree inclusion proofs. Traditional proof aggregation techniques based on AND logic suffer from high verification complexity and data communication overhead, limiting their practicality for large-scale applications. In this paper, we propose a novel proof aggregation approach based on OR logic, which enables the generation of compact and universally verifiable proofs for Merkle tree inclusion. By aggregating proofs using OR logic, we achieve a proof size that is independent of the number of leaves in the tree, and verification can be performed using any single valid leaf hash. This represents a significant improvement over AND aggregation, which requires the verifier to process all leaf hashes. We formally define the OR aggregation logic, describe the process of generating universal proofs, and provide a comparative analysis demonstrating the advantages of our approach in terms of proof size, verification data, and universality. Furthermore, we discuss the potential of combining OR and AND aggregation logics to create complex acceptance functions, enabling the development of expressive and efficient proof systems for various blockchain applications. The proposed techniques have the potential to significantly enhance the scalability, efficiency, and flexibility of zero-knowledge proof systems, paving the way for more practical and adaptive solutions in the blockchain ecosystem.

翻译：零知识证明已成为增强区块链应用隐私性与安全性的有力工具。然而，证明系统的效率与可扩展性仍是重大挑战，尤其在Merkle树包含证明场景中。传统基于AND逻辑的证明聚合技术存在验证复杂度高、数据通信开销大等问题，限制了其在规模化应用中的实用性。本文提出一种基于OR逻辑的新型证明聚合方法，可生成紧凑且通用可验证的Merkle树包含证明。通过OR逻辑聚合证明，我们实现了与树中叶子节点数量无关的证明大小，且验证过程可借助任意单个有效叶子哈希完成。相较于要求验证者处理全部叶子哈希的AND聚合方案，本方法实现了显著改进。我们正式定义了OR聚合逻辑，描述了通用证明的生成流程，并通过对比分析展示了本方法在证明尺寸、验证数据量及通用性方面的优势。此外，我们探讨了OR与AND聚合逻辑的组合潜力以构建复杂接受函数，从而为各类区块链应用开发兼具表达力与高效性的证明系统。所提技术有望显著增强零知识证明系统的可扩展性、效率与灵活性，为区块链生态中更实用、自适应的解决方案铺平道路。