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Secure matrix multiplication based on fully homomorphic encryption

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Abstract

Fully homomorphic encryption allows to perform arbitrary computation over encrypted data which has great practical implications in the secure outsourced computation on an untrusted computation environment. This paper investigates secure matrix multiplication based on fully homomorphic encryption. We propose an efficient secure matrix multiplication scheme for arbitrary matrix such as \(A_{m\times l}\times B_{l\times n}\) based on the hypercube structure. Our proposal is the first single-ciphertext and composable secure matrix multiplication scheme for arbitrary matrix based on fully homomorphic encryption. Our scheme takes only l homomorphic multiplications and experimental results show that it has excellent performance for the matrices of different dimensions.

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Authors and Affiliations

  1. Information School, Zhejiang Sci-Tech University, Hangzhou, 310018, Zhejiang, China

    Hai Huang & Haoran Zong

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  1. Hai Huang
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  2. Haoran Zong
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Correspondence to Hai Huang.

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Huang, H., Zong, H. Secure matrix multiplication based on fully homomorphic encryption. J Supercomput 79, 5064–5085 (2023). https://doi.org/10.1007/s11227-022-04850-4

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