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Verifiable outsourcing computation for modular exponentiation from shareable functions

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Abstract

Verifiable computation (VC) enables a computationally weak client to outsource the computation of a function f to a more powerful but untrusted server. The server returns an answer that allows the client to recover the correct result, accompanied by a proof of correctness. The basic requirement of a VC scheme is efficiency, i.e., the time consuming in preparing its input and verifying the server’s proof must be less than the time required to compute the function on its own. In this paper, we propose a novel outsourcing scheme for modular exponentiation from shareable functions, which is secure even in the presence of adaptive adversaries. Compared with previous works, our algorithm is superior in both efficiency and checkability. In order to keep the exponent privacy, our algorithm invokes the less subroutine, which accounts for the largest proportion of the time spent. The client can detect the error with overwhelming probability. We then gave a comparation that demonstrates the efficiency of the proposed outsourcing algorithm and scheme. Finally, we propose a generic scheme for shareable function family, and analyze the concrete security.

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Notes

  1. Although the low power devices currently use more Elliptic Curve algorithms, some computationally limited devices (e.g. RFID tag) also use public-key algorithms, such as Cramer-Shoup cryptosystem and Schnorr signatures. In these algorithms, the device needs to carry out expensive computations of modular exponentiation.

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Acknowledgements

This work is supported by the “Strategic Priority Research Program” of the Chinese Academy of Sciences, Grants No. XDA06010701, National Natural Science Foundation of China (Nos. 61402471, 61472414, 61170280), and IIE’s Cryptography Research Project.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, 471000, People’s Republic of China

    Muhua Liu

  2. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100049, People’s Republic of China

    Ying Wu, Rui Xue & Rui Zhang

  3. School of Cyber Security, University of Chinese Academy of Sciences, Beijing, 100049, People’s Republic of China

    Ying Wu, Rui Xue & Rui Zhang

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  1. Muhua Liu
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Correspondence to Muhua Liu.

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Liu, M., Wu, Y., Xue, R. et al. Verifiable outsourcing computation for modular exponentiation from shareable functions. Cluster Comput 23, 43–55 (2020). https://doi.org/10.1007/s10586-019-02930-4

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