Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Kanukurthi, Bhavana; Obbattu, Sai Lakshmi Bhavana; Sekar, Sruthi; Tomy, Jenit https://www.dagstuhl.de/lipics License: Creative Commons Attribution 4.0 license (CC BY 4.0)
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URN: urn:nbn:de:0030-drops-143302
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Locally Reconstructable Non-Malleable Secret Sharing

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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.

BibTeX - Entry

@InProceedings{kanukurthi_et_al:LIPIcs.ITC.2021.11,
  author =	{Kanukurthi, Bhavana and Obbattu, Sai Lakshmi Bhavana and Sekar, Sruthi and Tomy, Jenit},
  title =	{{Locally Reconstructable Non-Malleable Secret Sharing}},
  booktitle =	{2nd Conference on Information-Theoretic Cryptography (ITC 2021)},
  pages =	{11:1--11:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-197-9},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{199},
  editor =	{Tessaro, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14330},
  URN =		{urn:nbn:de:0030-drops-143302},
  doi =		{10.4230/LIPIcs.ITC.2021.11},
  annote =	{Keywords: Information Theoretic Cryptography, Secret Sharing, Non-malleability, Local Reconstructability}
}

Keywords: Information Theoretic Cryptography, Secret Sharing, Non-malleability, Local Reconstructability
Seminar: 2nd Conference on Information-Theoretic Cryptography (ITC 2021)
Issue date: 2021
Date of publication: 19.07.2021


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