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Locally Reconstructable Non-Malleable Secret Sharing

Authors Bhavana Kanukurthi, Sai Lakshmi Bhavana Obbattu, Sruthi Sekar, Jenit Tomy

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Author Details

Bhavana Kanukurthi
  • Department of Computer Science and Automation, Indian Institute of Science, Bangalore, India
Sai Lakshmi Bhavana Obbattu
  • Microsoft Research, Bangalore, India
Sruthi Sekar
  • Department of Mathematics, Indian Institute of Science, Bangalore, India
Jenit Tomy
  • Department of Computer Science and Automation, Indian Institute of Science, Bangalore, India

Funding

  • Kanukurthi, Bhavana: Microsoft Research Grant.
  • Sekar, Sruthi: Research supported in part by TCS Research Grant.

Acknowledgements

We thank the reviewers for their useful comments and suggestions.

Cite AsGet BibTex

Bhavana Kanukurthi, Sai Lakshmi Bhavana Obbattu, Sruthi Sekar, and Jenit Tomy. Locally Reconstructable Non-Malleable Secret Sharing. In 2nd Conference on Information-Theoretic Cryptography (ITC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 199, pp. 11:1-11:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.ITC.2021.11

Abstract

Non-malleable secret sharing (NMSS) schemes, introduced by Goyal and Kumar (STOC 2018), ensure that a secret m can be distributed into shares m₁,⋯,m_n (for some n), such that any t (a parameter ≤ n) shares can be reconstructed to recover the secret m, any t-1 shares doesn't leak information about m and even if the shares that are used for reconstruction are tampered, it is guaranteed that the reconstruction of these tampered shares will either result in the original m or something independent of m. Since their introduction, non-malleable secret sharing schemes sparked a very impressive line of research. In this work, we introduce a feature of local reconstructability in NMSS, which allows reconstruction of any portion of a secret by reading just a few locations of the shares. This is a useful feature, especially when the secret is long or when the shares are stored in a distributed manner on a communication network. In this work, we give a compiler that takes in any non-malleable secret sharing scheme and compiles it into a locally reconstructable non-malleable secret sharing scheme. To secret share a message consisting of k blocks of length ρ each, our scheme would only require reading ρ + log k bits (in addition to a few more bits, whose quantity is independent of ρ and k) from each party’s share (of a reconstruction set) to locally reconstruct a single block of the message. We show an application of our locally reconstructable non-malleable secret sharing scheme to a computational non-malleable secure message transmission scheme in the pre-processing model, with an improved communication complexity, when transmitting multiple messages.

Subject Classification

ACM Subject Classification
  • Security and privacy → Cryptography
Keywords
  • Information Theoretic Cryptography
  • Secret Sharing
  • Non-malleability
  • Local Reconstructability

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