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Leakage Resilient Cheating Detectable Secret Sharing Schemes

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Book cover Information Security and Privacy (ACISP 2021)

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Abstract

A secret sharing scheme generates shares of a secret that will be distributed among a set of participants such that the shares of qualified subsets of participants can reconstruct the secret, and shares of non-qualified subsets leak no information about the secret. Secret sharing is a fundamental cryptographic primitive in multiparty computation, threshold cryptography, and secure distributed systems. Leakage resilient secret sharing models side channel leakages from all the shares to the adversary, rendering the adversary more powerful. In CRYPTO’19 Srinivasan and Vasudevan (SV) proposed compilers that convert a secret sharing for a general access structure to a leakage resilient secret sharing for the same access structure in two leakage models: local leakage and strong local leakage. In this paper we consider cheater detectable secret sharing that provides security against active (cheating) attackers that modify their controlled shares with the goal of modifying the reconstructed secret. We extend the SV compilers to convert a linear secret sharing for a general access structure to a cheater detectable secret sharing for the same access structure when the adversary has access to the shares of a non-qualified subset and the leaked information from all other shares. Our extensions add a precoding step to the SV compilers that use Algebraic Manipulation Detection (AMD) codes, and work for both well established models of cheater detection known as \(\textsf {OKS}\) and \(\textsf {CDV}\) models, using weak and strong AMD codes, respectively. To prove our results we formalize two security notions for leakage resilient cheating detectable secret sharing, and prove relation between them, which can be of independent interest. We discuss directions for future work.

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Notes

  1. 1.

    The acronym is the authors’ initials.

  2. 2.

    The acronym is the authors’ initials.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Calgary, Calgary, Canada

    Sabyasachi Dutta & Reihaneh Safavi-Naini

Authors
  1. Sabyasachi Dutta
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  2. Reihaneh Safavi-Naini
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Correspondence to Sabyasachi Dutta .

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Editors and Affiliations

  1. University of Wollongong, Wollongong, NSW, Australia

    Joonsang Baek

  2. Data61, CSIRO, Marsfield, NSW, Australia

    Sushmita Ruj

A Appendix

A Appendix

1.1 A.1 The Scheme of Srinivasan-Vasudevan [39]

The compiler described in Fig. 2 was proposed in Srinivasan-Vasudevan [39]. We use Shamir’s scheme as the basic building block for a (t, n)-threshold secret sharing scheme. Note that, the compiler proposed in [39] is independent of the underlying basic secret sharing scheme and in fact, can transform any secret sharing scheme for 2-monotone (general) access structure into a leakage resilient one. Therefore in particular, we can use any linear secret sharing scheme realizing the given access structure for instantiation – e.g., Shamir scheme for threshold access structures and Ito-Saito-Nishizeki [27] for general access structures.

Fig. 2.
figure 2

Description of compiler of local leakage-resilient secret sharing for (t, n)-threshold access structures from [39].

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Dutta, S., Safavi-Naini, R. (2021). Leakage Resilient Cheating Detectable Secret Sharing Schemes. In: Baek, J., Ruj, S. (eds) Information Security and Privacy. ACISP 2021. Lecture Notes in Computer Science(), vol 13083. Springer, Cham. https://doi.org/10.1007/978-3-030-90567-5_1

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