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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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Subject Classification

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

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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.

Cite As Get 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

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.

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