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Leakage-Resilient Secret Sharing in Non-Compartmentalized Models

Authors Fuchun Lin, Mahdi Cheraghchi , Venkatesan Guruswami, Reihaneh Safavi-Naini, Huaxiong Wang

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Author Details

Fuchun Lin
  • Department of Electrical and Electronic Engineering, Imperial College London, UK
Mahdi Cheraghchi
  • EECS Department, University of Michigan, Ann Arbor, MI, USA
Venkatesan Guruswami
  • Computer Science Department, Carnegie Mellon University, Pittsburgh, PA, USA
Reihaneh Safavi-Naini
  • Department of Computer Science, University of Calgary, CA
Huaxiong Wang
  • Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, SG

Funding

  • Lin, Fuchun: The research of Fuchun Lin was supported in part by EPSRC grant EP/S021043/1 and Singapore Ministry of Education under Research Grant MOE2016-T2-2-014(S) and RG133/17(S).
  • Guruswami, Venkatesan: The research of Venkatesan Guruswami was supported in part by United States NSF grants CCF-1422045 and CCF-1563742.
  • Safavi-Naini, Reihaneh: The research of Reihaneh Safavi-Naini was in part supported by Natural Sciences and Engineering Research Council of Canada, Discovery Grants Program.
  • Wang, Huaxiong: The research of Huaxiong Wang was supported by Singapore Ministry of Education under Research Grant MOE2016-T2-2-014(S) and RG133/17(S).

Acknowledgements

Part of this work was done when the first author was in Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University. We would like to thank Vipul Goyal for helpful discussions. We also would like to thank the anonymous reviewers for comments.

Cite AsGet BibTex

Fuchun Lin, Mahdi Cheraghchi, Venkatesan Guruswami, Reihaneh Safavi-Naini, and Huaxiong Wang. Leakage-Resilient Secret Sharing in Non-Compartmentalized Models. In 1st Conference on Information-Theoretic Cryptography (ITC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 163, pp. 7:1-7:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.ITC.2020.7

Abstract

Leakage-resilient secret sharing has mostly been studied in the compartmentalized models, where a leakage oracle can arbitrarily leak bounded number of bits from all shares, provided that the oracle only has access to a bounded number of shares when the leakage is taking place. We start a systematic study of leakage-resilient secret sharing against global leakage, where the leakage oracle can access the full set of shares simultaneously, but the access is restricted to a special class of leakage functions. More concretely, the adversary can corrupt several players and obtain their shares, as well as applying a leakage function from a specific class to the full share vector. We explicitly construct such leakage-resilient secret sharing with respect to affine leakage functions and low-degree multi-variate polynomial leakage functions, respectively. For affine leakage functions, we obtain schemes with threshold access structure that are leakage-resilient as long as there is a substantial difference between the total amount of information obtained by the adversary, through corrupting individual players and leaking from the full share vector, and the amount that the reconstruction algorithm requires for reconstructing the secret. Furthermore, if we assume the adversary is non-adaptive, we can even make the secret length asymptotically equal to the difference, as the share length grows. Specifically, we have a threshold scheme with parameters similar to Shamir’s scheme and is leakage-resilient against affine leakage. For multi-variate polynomial leakage functions with degree bigger than one, our constructions here only yield ramp schemes that are leakage-resilient against such leakage. Finally, as a result of independent interest, we show that our approach to leakage-resilient secret sharing also yields a competitive scheme compared with the state-of-the-art construction in the compartmentalized models.

Subject Classification

ACM Subject Classification
  • Security and privacy → Cryptography
  • Security and privacy → Information-theoretic techniques
  • Theory of computation → Expander graphs and randomness extractors
Keywords
  • Leakage-resilient cryptography
  • Secret sharing scheme
  • Randomness extractor

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