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Amortizing Division and Exponentiation

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Information Security and Cryptology (Inscrypt 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13837))

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Abstract

Multiparty computation (MPC) has developed rapidly in the past three decades. The research on general MPC only considers addition and multiplication in a circuit because they are Turing-complete. However, when we consider other arithmetic operations, such as division and exponentiation, the customed protocols are often more efficient. In this work, we optimize the overhead of computing division and exponentiation. Our main idea is to use vector oblivious linear-function evaluation (VOLE) to generate correlation multiplication triples and use these triples to compute correlation multiplication in division and exponentiation protocols. Our method can reduce the cost of a single division to strictly no more than 2 multiplications. In the batch setting, we reduce the cost of n correlation division to almost the same as that of one division. In addition, we use the same method to reduce the cost of n correlation private exponentiation by about \(33\%\).

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Acknowledgement

We are grateful for the helpful comments from the anonymous reviewers. Our work is supported by the National Key Research and Development Program of China (No. 2020YFB1805402) and the National Natural Science Foundation of China (Grants No. 61872359 and No. 61936008).

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Authors and Affiliations

  1. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, China

    Cong Zhang, Shuaishuai Li & Dongdai Lin

  2. School of Cyber Security, University of Chinese Academy of Sciences, Beijing, 100049, China

    Cong Zhang, Shuaishuai Li & Dongdai Lin

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  1. Cong Zhang
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  2. Shuaishuai Li
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Correspondence to Dongdai Lin .

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  1. Institute of Information Engineering, CAS, Beijing, China

    Yi Deng

  2. Columbia University, New York, NY, USA

    Moti Yung

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Zhang, C., Li, S., Lin, D. (2023). Amortizing Division and Exponentiation. In: Deng, Y., Yung, M. (eds) Information Security and Cryptology. Inscrypt 2022. Lecture Notes in Computer Science, vol 13837. Springer, Cham. https://doi.org/10.1007/978-3-031-26553-2_10

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  • DOI: https://doi.org/10.1007/978-3-031-26553-2_10

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