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On Black-Box Extension of a Non-Interactive Zero-Knowledge Proof System for Secret Equality

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Progress in Cryptology – INDOCRYPT 2020 (INDOCRYPT 2020)

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Abstract

A non-interactive zero-knowledge proof system (NIZK) for a composite language (i.e., a language that combines distinct statements by AND or OR) is widely used in cryptographic applications. The (im)possibility of black-box constructions of such NIZKs has been studied so far. We extend it to the case of proving equality of a witness behind distinct statements that often plays a central role in cryptographic constructions as illustrated by the seminal work by Naor and Yung (STOC, 1990). In this paper, we investigate the impossibility of a black-box construction of NIZKs for equality of witnesses from those proving the validity of the witnesses. Concretely, we prove that there exists no black-box construction of NIZKs for equality of plaintexts in two distinct ciphertexts of public-key encryption schemes based on NIZKs for proving validity of ciphertexts. It implies that one has to exploit specific properties of the underlying encryption schemes or NIZKs to construct NIZKs for proving equality, and hence justifies existing constructions.

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Notes

  1. 1.

    While the terminology “composite statement” in [3] includes nested functions, we only focus on statements combined by AND or OR in this paper.

  2. 2.

    Since \({O}.g\) is injective, \({O}.g^{-1}\) is uniquely defined.

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Acknowledgements

We thank Takahiro Matsuda for very insightful discussions in the proof of Sect. 4.

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Authors and Affiliations

  1. Graduate School of Informatics, Kyoto University, Kyoto, Japan

    Kyosuke Yamashita, Mehdi Tibouchi & Masayuki Abe

  2. Cyber Physical Security Research Center, National Institute of Advanced Industrial Science and Technology, Tokyo, Japan

    Kyosuke Yamashita

  3. Secure Platform Laboratories, NTT Corporation, Tokyo, Japan

    Mehdi Tibouchi & Masayuki Abe

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  1. Kyosuke Yamashita
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Correspondence to Kyosuke Yamashita .

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  1. Inria Paris, Paris, France

    Karthikeyan Bhargavan

  2. University of Klagenfurt, Klagenfurt, Austria

    Elisabeth Oswald

  3. Department of Computer Science and Engineering, Indian Institute of Technology Bombay, Mumbai, Maharashtra, India

    Manoj Prabhakaran

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Yamashita, K., Tibouchi, M., Abe, M. (2020). On Black-Box Extension of a Non-Interactive Zero-Knowledge Proof System for Secret Equality. In: Bhargavan, K., Oswald, E., Prabhakaran, M. (eds) Progress in Cryptology – INDOCRYPT 2020. INDOCRYPT 2020. Lecture Notes in Computer Science(), vol 12578. Springer, Cham. https://doi.org/10.1007/978-3-030-65277-7_39

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