Efficient and Universal Merkle Tree Inclusion Proofs via OR Aggregation

Author:

Kuznetsov Oleksandr123ORCID,Rusnak Alex1ORCID,Yezhov Anton1,Kanonik Dzianis1ORCID,Kuznetsova Kateryna1,Domin Oleksandr1ORCID

Affiliation:

1. Proxima Labs, 1501 Larkin Street, Suite 300, San Francisco, CA 94109, USA

2. Faculty of Engineering, eCampus University, Via Isimbardi 10, 22060 Novedrate, Italy

3. Department of Information and Communication Systems Security, V. N. Karazin Kharkiv National University, 4 Svobody Sq., 61022 Kharkiv, Ukraine

Abstract

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 a 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 adapting and extending the concept of OR composition from Sigma protocols, 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 that demonstrates 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 large-scale blockchain ecosystems.

Funder

Proxima Labs

Publisher

MDPI AG

Reference37 articles.

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