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Making Private Function Evaluation Safer, Faster, and Simpler

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Public-Key Cryptography – PKC 2022 (PKC 2022)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 13177))

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Abstract

In the problem of two-party private function evaluation (PFE), one party \(\mathsf {P}_{\mathsf {A}}\) holds a private function f and (optionally) a private input \(x_A\), while the other party \(\mathsf {P}_{\mathsf {B}}\) possesses a private input \(x_B\). Their goal is to evaluate f on \(x_A\) and \(x_B\), and one or both parties may obtain the evaluation result \(f(x_A, x_B)\) while no other information beyond \(f(x_A, x_B)\) is revealed.

In this paper, we revisit the two-party PFE problem and provide several enhancements. We propose the first constant-round actively secure PFE protocol with linear complexity. Based on this result, we further provide the first constant-round publicly verifiable covertly (PVC) secure PFE protocol with linear complexity to gain better efficiency. For instance, when the deterrence factor is \(\epsilon = 1/2\), compared to the passively secure protocol, its communication cost is very close and its computation cost is around \(2.6\times \). In our constructions, as a by-product, we design a specific protocol for proving that a list of ElGamal ciphertexts is derived from an extended permutation performed on a given list of elements. It should be noted that this protocol greatly improves the previous result and may be of independent interest. In addition, a reusability property is added to our two PFE protocols. Namely, if the same function f is involved in multiple executions of the protocol between \(\mathsf {P}_{\mathsf {A}}\) and \(\mathsf {P}_{\mathsf {B}}\), then the protocol could be executed more efficiently from the second execution. Moreover, we further extend this property to be global, such that it supports multiple executions for the same f in a reusable fashion between \(\mathsf {P}_{\mathsf {A}}\) and arbitrary parties playing the role of \(\mathsf {P}_{\mathsf {B}}\).

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Notes

  1. 1.

    The operator \(\oplus \) here is applied on the bit-representation of the right group element, and \(\tau \) specifies the length of proper padding to ensure the check of correct decryption.

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Acknowledgments

We thank the reviewers for their detailed and helpful comments. Y. Liu and Q. Wang were partially supported by the Shenzhen fundamental research programs under Grant no. 20200925154814002 and Guangdong Provincial Key Laboratory (Grant No. 2020B121201001). Y. Liu and S.-M. Yiu were also partially supported by ITF, Hong Kong (ITS/173/18FP) and the funding from HKU-SCF FinTech Academy.

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Authors and Affiliations

  1. Research Institute of Trustworthy Autonomous Systems and Guangdong Provincial Key Laboratory of Brain-Inspired Intelligent Computation, Department of Computer Science and Engineering, Southern University of Science and Technology, Shenzhen, 518055, China

    Yi Liu & Qi Wang

  2. National Center for Applied Mathematics Shenzhen, Southern University of Science and Technology, Shenzhen, 518055, China

    Qi Wang

  3. Department of Computer Science, The University of Hong Kong, Pokfulam, Hong Kong SAR, China

    Yi Liu & Siu-Ming Yiu

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  1. Yi Liu
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  2. Qi Wang
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  3. Siu-Ming Yiu
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Correspondence to Qi Wang .

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Editors and Affiliations

  1. National Institute of Advanced Industrial Science and Technology (AIST), Tokyo, Japan

    Goichiro Hanaoka

  2. Yokohama National University, Yokohama, Japan

    Junji Shikata

  3. The University of Electro-Communications, Tokyo, Japan

    Yohei Watanabe

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Liu, Y., Wang, Q., Yiu, SM. (2022). Making Private Function Evaluation Safer, Faster, and Simpler. In: Hanaoka, G., Shikata, J., Watanabe, Y. (eds) Public-Key Cryptography – PKC 2022. PKC 2022. Lecture Notes in Computer Science(), vol 13177. Springer, Cham. https://doi.org/10.1007/978-3-030-97121-2_13

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