Locally reconstructable non-malleable secret sharing

Kanukurthi, B and Bhavana Obbattu, SL and Sekar, S and Tomy, J (2021) Locally reconstructable non-malleable secret sharing. In: 2nd Conference on Information-Theoretic Cryptography, ITC 2021, 23 - 26 July 2021, Virtual, Bertinoro.

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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, · · ·, mn (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.

Item Type:	Conference Paper
Publication:	Leibniz International Proceedings in Informatics, LIPIcs
Publisher:	Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Additional Information:	The copyright for this article belongs to Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing.
Keywords:	Automata theory; Transmissions, Communications networks; Information-theoretic cryptography; Local reconstructability; Non-malleability; Non-malleable; Reconstructable; Secret sharing schemes; Secret-sharing; Secure message transmission; Transmission schemes, Information theory
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	27 Nov 2023 10:19
Last Modified:	27 Nov 2023 10:19
URI:	https://eprints.iisc.ac.in/id/eprint/82957

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