Scalable Zero-knowledge Proofs for Non-linear Functions in Machine Learning

Meng Hao; Hanxiao Chen; Hongwei Li; Chenkai Weng; Yuan Zhang; Haomiao Yang; Tianwei Zhang

Paper 2025/507

Scalable Zero-knowledge Proofs for Non-linear Functions in Machine Learning

Meng Hao, University of Electronic Science and Technology of China

Hanxiao Chen, University of Electronic Science and Technology of China

Hongwei Li, University of Electronic Science and Technology of China

Chenkai Weng, Northwestern University

Yuan Zhang, University of Electronic Science and Technology of China

Haomiao Yang, University of Electronic Science and Technology of China

Tianwei Zhang, Nanyang Technological University

Abstract

Zero-knowledge (ZK) proofs have been recently explored for the integrity of machine learning (ML) inference. However, these protocols suffer from high computational overhead, with the primary bottleneck stemming from the evaluation of non-linear functions. In this paper, we propose the first systematic ZK proof framework for non-linear mathematical functions in ML using the perspective of table lookup. The key challenge is that table lookup cannot be directly applied to non-linear functions in ML since it would suffer from inefficiencies due to the intolerably large table. Therefore, we carefully design several important building blocks, including digital decomposition, comparison, and truncation, such that they can effectively utilize table lookup with a quite small table size while ensuring the soundness of proofs. Based on these blocks, we implement complex mathematical operations and further construct ZK proofs for current mainstream non-linear functions in ML such as ReLU, sigmoid, and normalization. The extensive experimental evaluation shows that our framework achieves 50 ∼ 179× runtime improvement compared to the state-of-the-art work, while maintaining a similar level of communication efficiency.

Metadata

Available format(s): PDF
Category: Cryptographic protocols
Publication info: Published elsewhere. Major revision. USENIX Security 2024
Keywords: Zero-knowledge proofs ZKML
Contact author(s): menghao303 @ gmail com
History: 2025-03-20: approved; 2025-03-18: received; See all versions
Short URL: https://ia.cr/2025/507
License: CC BY

BibTeX

@misc{cryptoeprint:2025/507,
      author = {Meng Hao and Hanxiao Chen and Hongwei Li and Chenkai Weng and Yuan Zhang and Haomiao Yang and Tianwei Zhang},
      title = {Scalable Zero-knowledge Proofs for Non-linear Functions in Machine Learning},
      howpublished = {Cryptology {ePrint} Archive, Paper 2025/507},
      year = {2025},
      url = {https://eprint.iacr.org/2025/507}
}