2026-08-11T18:34:49Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:14330 2024-03-06T10:53:47Z ddc:004 open_access

Locally Reconstructable Non-Malleable Secret Sharing Kanukurthi, Bhavana Obbattu, Sai Lakshmi Bhavana Sekar, Sruthi Tomy, Jenit Information Theoretic Cryptography Secret Sharing Non-malleability Local Reconstructability 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Bhavana Kanukurthi and Sai Lakshmi Bhavana Obbattu and Sruthi Sekar and Jenit Tomy 2021 Is Part Of LIPIcs, Volume 199, 2nd Conference on Information-Theoretic Cryptography (ITC 2021) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ITC.2021.11 urn:nbn:de:0030-drops-143302 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2021.11 eng https://creativecommons.org/licenses/by/4.0/legalcode