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Generic 2-Party PFE with Constant Rounds and Linear Active Security, and Efficient Instantiation

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Security and Privacy in Communication Networks (SecureComm 2022)

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Abstract

The paper considers generic construction of 2-party private function evaluation (PFE) in the malicious adversary model. There is hitherto only one concrete design of actively secure 2-party PFE protocol (Liu et al. at PKC 2022, and LWY hereafter) with constant rounds and linear complexity. One interesting feature of LWY is its function reusability (i.e., the same function is involved in multiple executions of LWY) which makes its execution more efficiently from the second execution. Nevertheless, in its first execution (in particular for those settings where only one invocation of the function is required), LWY is quite involved and too inefficient to be of practical use. For these settings (of non-reusable private functions), we initiate a generic construction of 2-party PFE protocol with constant rounds and linear complexity in the malicious adversary model based on Yao’s garbled circuit and singly homomorphic encryption. When instantiated with ElGamal encryption and Groth secret shuffle (J. Cryptology 2010), the generic construction effectuates a novel concrete design of 2-party PFE, which has better performance and reduces 51.2% communication bits and 52.4% computation costs, compared to LWY (in its first execution) at the same security level. It even outperforms several 2-party PFE protocols (Katz and Malka at AISACRYPT 2011, and Mohassel and Sadeghian at EUROCRYPT 2013) that are secure in the semi-honest adversary model from the communication perspective. The proposed PFE and LWY thus make optimal solutions available for non-reusable and reusable private functions, respectively.

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Notes

  1. 1.

    The overhead required due to the EP operation on the function is no longer needed from the second execution, which accounts for the major part of the total overhead.

  2. 2.

    Note that these random wire keys do not represent outgoing wires, but rather a shuffle and re-randomization with the outgoing wires.

  3. 3.

    Usually \(||\mathbb {Z}_q|| = 160\).

  4. 4.

    The one-to-one here means that the i-th element of the former set (A) corresponds to the i-th element of the latter set (B), i.e., \(A_i\) corresponds to \(B_i\).

  5. 5.

    Exponentiation is the dominant computation in the protocol. We omit lightweight operations (e.g., symmetric cipher, addition, etc.).

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Acknowledgement

Xiangxue Li is supported by National Natural Science Foundation of China (61971192), Shanghai Municipal Education Commission (2021-01-07–00-08-E00101), and Shanghai Trusted Industry Internet Software Collaborative Innovation Center.

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Authors and Affiliations

  1. School of Software Engineering, East China Normal University, Shanghai, 200062, China

    Hanyu Jia & Xiangxue Li

  2. Shanghai Key Laboratory of Privacy-Preserving Computation, MatrixElements Technologies, Shanghai, 201204, China

    Hanyu Jia

  3. Shanghai Key Laboratory of Trustworthy Computing, Shanghai, 200062, China

    Xiangxue Li

  4. Institute of Cyber Science and Technology, Shanghai Jiaotong University, Shanghai, 200240, China

    Qiang Li

  5. CATARC Software Testing (Tianjin) Co., Ltd., Tianjin, 300300, China

    Yue Bao & Xintian Hou

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  1. Hanyu Jia
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Editors and Affiliations

  1. University of Kansas, Lawrence, KS, USA

    Fengjun Li

  2. Delft University of Technology, Delft, The Netherlands

    Kaitai Liang

  3. The Ohio State University, Columbus, OH, USA

    Zhiqiang Lin

  4. Norwegian University of Science and Tech, Gjøvik, Norway

    Sokratis K. Katsikas

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Jia, H., Li, X., Li, Q., Bao, Y., Hou, X. (2023). Generic 2-Party PFE with Constant Rounds and Linear Active Security, and Efficient Instantiation. In: Li, F., Liang, K., Lin, Z., Katsikas, S.K. (eds) Security and Privacy in Communication Networks. SecureComm 2022. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 462. Springer, Cham. https://doi.org/10.1007/978-3-031-25538-0_21

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