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Cheating Detectable Ramp Secret Sharing with Optimal Cheating Resiliency

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Information Systems Security (ICISS 2020)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12553))

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Abstract

A (k, L, n) ramp secret sharing scheme allows a dealer to share a secret vector with a lesser share size compared to threshold secret sharing schemes. In this work, we formalize the definition of cheating in ramp secret sharing schemes and propose two constructions. The proposed constructions of ramp secret sharing scheme are capable of cheating detection even if \(n-1\) out of n participants conspire against the single honest participant and try to convince him of a valid but incorrect secret. This is the strongest possible adversarial setup known as the CDV\({}^{n-1}\) model of cheating. Moreover, we consider arbitrary secret distribution on the space of secrets. To the best of our knowledge, we are the first to address cheating in ramp setup against \(n-1\) cheaters. Both the constructions proposed in this work are optimal cheating resilient against a centralized adversary with unbounded computational resources.

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Notes

  1. 1.

    V can be chosen to be any subset of \(\mathbb {Z}_p\) of size D.

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Acknowledgement

The research of the fourth author is partially supported by DST-SERB Project MATRICS vide Sanction Order: MTR/2019/001573. In the end, authors would like to thank the annonymous reviewers who brought forward suggestions which improved this paper.

Author information

Authors and Affiliations

  1. Department of Mathematics, Taki Government College, Taki, 743429, India

    Jyotirmoy Pramanik

  2. Department of Computer Science, University of Calgary, 2500 University Drive, Calgary, NW, T2N1N4, Canada

    Sabyasachi Dutta

  3. School of Computing and Information Technology, University of Wollongong, Northfields Avenue, Wollongong, NSW, 2522, Australia

    Partha Sarathi Roy

  4. Department of Mathematics, Presidency University, 86, 1, College Street, Kolkata, 700073, India

    Avishek Adhikari

Authors
  1. Jyotirmoy Pramanik
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  2. Sabyasachi Dutta
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  3. Partha Sarathi Roy
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  4. Avishek Adhikari
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Corresponding author

Correspondence to Jyotirmoy Pramanik .

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Editors and Affiliations

  1. UNSW Sydney, Sydney, NSW, Australia

    Salil Kanhere

  2. IIT Bombay, Mumbai, India

    Vishwas T Patil

  3. IIT Kharagpur, Kharagpur, West Bengal, India

    Shamik Sural

  4. IIT Jammu, Jammu, India

    Manoj S Gaur

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Pramanik, J., Dutta, S., Roy, P.S., Adhikari, A. (2020). Cheating Detectable Ramp Secret Sharing with Optimal Cheating Resiliency. In: Kanhere, S., Patil, V.T., Sural, S., Gaur, M.S. (eds) Information Systems Security. ICISS 2020. Lecture Notes in Computer Science(), vol 12553. Springer, Cham. https://doi.org/10.1007/978-3-030-65610-2_11

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