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International Conference on Information Security and Cryptology

ICISC 2020: Information Security and Cryptology – ICISC 2020 pp 16–39Cite as

Secret Sharing with Statistical Privacy and Computational Relaxed Non-malleability

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12593))

Abstract

Goyal and Kumar (STOC ’18, CRYPTO ’18) initiate the study of non-malleability for secret sharing and proposed the definition of information-theoretical non-malleability for secret sharing. Subsequently, Brian, Faonio, and Venturi (CRYPTO ’19, TCC ’19) proposed computational variants of non-malleability for secret sharing and showed that by focusing on computational non-malleability, it is possible to construct more efficient schemes compared to the existing ones. However, their schemes have a drawback that they do not satisfy statistical privacy.

In this paper, we propose a new definition of computational non-malleability for secret sharing in the public parameter model. Although our definition is relaxed compared to the one proposed by Brian et al., it captures a strong security notion called non-malleability against overlap-joint tampering. Then, we show how to transform any secret sharing scheme into the one satisfying our computational non-malleability with small efficiency overhead. This transformation has a nice property that it preserves the statistical privacy of the underlying secret sharing scheme. Thus, through our transformation, we can obtain efficient secret sharing schemes satisfying computational non-malleability and statistical privacy. We achieve this transformation using lossy encryption which satisfies IND-CCA security in the injective mode.

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Notes

  1. 1.

    For the definition of non-malleable commitment proposed by Crescenzo et al., see the Sect. 3.

  2. 2.

    In the definition of ordinary lossy encryption [BHY09], it is required to satisfy only IND-CPA security.

  3. 3.

    Intuitively, the obvious attack is the tampering performed by the adversary that once reconstructs the original message.

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Acknowledgments

A part of this work was supported by NTT Secure Platform Laboratories, JST OPERA JPMJOP1612, JST CREST JPMJCR14D6, JSPS KAKENHI JP16H01705, JP17H01695, JP19J22363.

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Authors and Affiliations

  1. Tokyo Institute of Technology, Tokyo, Japan

    Tasuku Narita, Yusuke Yoshida & Keisuke Tanaka

  2. NTT Secure Platform Laboratories, Tokyo, Japan

    Fuyuki Kitagawa

Authors
  1. Tasuku Narita
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  2. Fuyuki Kitagawa
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  3. Yusuke Yoshida
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  4. Keisuke Tanaka
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Correspondence to Tasuku Narita .

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Editors and Affiliations

  1. Jeonbuk National University, Jeonju-si, Korea (Republic of)

    Deukjo Hong

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Narita, T., Kitagawa, F., Yoshida, Y., Tanaka, K. (2021). Secret Sharing with Statistical Privacy and Computational Relaxed Non-malleability. In: Hong, D. (eds) Information Security and Cryptology – ICISC 2020. ICISC 2020. Lecture Notes in Computer Science(), vol 12593. Springer, Cham. https://doi.org/10.1007/978-3-030-68890-5_2

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  • DOI: https://doi.org/10.1007/978-3-030-68890-5_2

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