Efficient zero-knowledge proof for quadratic matrix relation over finite field with two witnesses

Yuan Tian; Yongda Pang; Xinke Tian

doi:10.1117/12.3009401

11 October 2023 Efficient zero-knowledge proof for quadratic matrix relation over finite field with two witnesses

Yuan Tian, Yongda Pang, Xinke Tian

Proceedings Volume 12918, Fourth International Conference on Computer Science and Communication Technology (ICCSCT 2023); 129181E (2023) https://doi.org/10.1117/12.3009401
Event: International Conference on Computer Science and Communication Technology (ICCSCT 2023), 2023, Wuhan, China

Abstract

In large-scale private computing applications, various arithmetic relations appear as or can be reduced to matrix relations. In this paper, we establish the efficient zero-knowledge proof (ZKP) for the quadratic matrix relation over finite field Fp with two witness matrices. In private computing tasks, lots of typical relations are instances or special cases of this form, e.g., matrix multiplicative relation, inverse relation, isometric relation, etc. Different from the widely-applied vectorspecific method, our method is matrix-specific. The matrix equation is treated as a tensor equality and probabilisticequivalent reduction techniques are applied to reduce the non-linear matrix relation to simple vector relation. To the authors’ best knowledge, currently, there are no matrix-specific methods to ZKP for nonlinear matrix relations. Compared against the current (vector-specific) method, our method substantially outperforms it in all critical aspects, e.g., for n-raw t-column matrix witnesses, the required size of common reference string (c.r.s.) can be compressed by a factor of 2nt and the number of messages, group and field elements are all reduced by a factor of ≈2 for large-size witnesses. Computational complexities in both methods are almost the same.

(2023) Published by SPIE. Downloading of the abstract is permitted for personal use only.

Citation Download Citation

Yuan Tian, Yongda Pang, and Xinke Tian "Efficient zero-knowledge proof for quadratic matrix relation over finite field with two witnesses", Proc. SPIE 12918, Fourth International Conference on Computer Science and Communication Technology (ICCSCT 2023), 129181E (11 October 2023); https://doi.org/10.1117/12.3009401

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KEYWORDS

Matrices

Stochastic processes

Algorithm development

Computing systems

Data hiding

Digital Light Processing

Information security

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