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Verifiable Decryption for Fully Homomorphic Encryption

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Information Security (ISC 2018)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11060))

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Abstract

Verifiable decryption allows one to prove the correct decryption of encrypted data. When the encrypted data is derived from homomorphic evaluations in the context of fully homomorphic encryption (FHE), verifiable decryption will be very useful in cloud computing or cryptographic protocols, e.g., secure medical computation, cryptographically verifiable election, etc. In this paper, we consider the problem of proving the correct decryption of an FHE ciphertext. Namely, we are interested in zero-knowledge proofs of knowledge of triples \((m, \mathbf {s}, \mathbf {c})\) such that the message m is the correct decryption of a ciphertext \(\mathbf {c}\) for a secret key \(\mathbf {s}\). While analogous statements admit efficient zero-knowledge proof protocols in the discrete logarithm setting, they have never been addressed in FHE so far. We provide such verifiable decryption for Brakerski-Gentry-Vaikuntanathan (BGV) scheme, since this scheme was recognized as one of the most efficient leveled FHE schemes. Our solution is nearly “one shot”, in the sense that a single instance of the proof already has negligible soundness error, yielding compact proofs even for individual ciphertexts. Furthermore, to illustrate the applicability of verifiable decryption, we also give two example instantiations.

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Acknowledgments

This research is supported in part by the National Basic Research Program of China (973 project, No. 2014CB340603) and the National Nature Science Foundation of China (Nos. 61672030 and 61272040). The authors would like to thank the anonymous reviewers for their detailed reviews and helpful comments.

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Authors and Affiliations

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

    Fucai Luo & Kunpeng Wang

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

    Fucai Luo & Kunpeng Wang

  3. Data Assurance and Communication Security Research Center, Chinese Academy of Sciences, Beijing, China

    Fucai Luo & Kunpeng Wang

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  1. Fucai Luo
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Correspondence to Fucai Luo .

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Editors and Affiliations

  1. University of Surrey, Guildford, United Kingdom

    Liqun Chen

  2. University of Surrey, Guildford, United Kingdom

    Mark Manulis

  3. University of Surrey, Guildford, United Kingdom

    Steve Schneider

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Luo, F., Wang, K. (2018). Verifiable Decryption for Fully Homomorphic Encryption. In: Chen, L., Manulis, M., Schneider, S. (eds) Information Security. ISC 2018. Lecture Notes in Computer Science(), vol 11060. Springer, Cham. https://doi.org/10.1007/978-3-319-99136-8_19

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  • DOI: https://doi.org/10.1007/978-3-319-99136-8_19

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