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A zero-knowledge proof of transpose of a matrix of finite field elements

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Abstract

Interactive zero-knowledge arguments for some fundamental linear algebraic operations have been formulated. But those arguments cannot be used for operations involving vectors or matrices as such. In this paper, we explore the possibility of proving in zero-knowledge that two committed matrices of finite field elements are transposes of each other. To achieve this, we first present some reductions and additional communication rounds that are necessary, and then give a step-by-step procedure for an interactive proof that the committed matrices are transposes of each other.

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Acknowledgements

This research is undertaken as part of the project ‘Research and Development of Secure and Privacy Preserving Blockchain based Smart Contract and its Applications’ funded by Science and Engineering Research Board (SERB) [EEQ/2021/000305].

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Authors and Affiliations

  1. Department of Computer Science and Engineering, National Institute of Technology, Tiruchirapalli, Tamil Nadu, 620015, India

    Amalan Antony & Kunwar Singh

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  1. Amalan Antony
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  2. Kunwar Singh
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Correspondence to Amalan Antony.

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Antony, A., Singh, K. A zero-knowledge proof of transpose of a matrix of finite field elements. Int. j. inf. tecnol. 15, 3055–3061 (2023). https://doi.org/10.1007/s41870-023-01356-x

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