Cryptology ePrint Archive: Report 2021/657

Locally Reconstructable Non-malleable Secret Sharing

Bhavana Kanukurthi and Sai Lakshmi Bhavana Obbattu and Sruthi Sekar and Jenit Tomy

Abstract: Non-malleable secret sharing (NMSS) schemes, introduced by Goyal and Kumar (STOC 2018), ensure that a secret $m$ can be distributed into shares $m_1,...,m_n$ (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 $l$ each, our scheme would only require reading $l + log k$ bits (in addition to a few more bits, whose quantity is independent of $l$ 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.

Category / Keywords: foundations / non-malleability, locality, secret-sharing, information-theoretic cryptography

Original Publication (in the same form): Information Theoretic Cryptography (ITC) 2021

Date: received 20 May 2021

Contact author: bhavana at iisc ac in, oslbhavana@gmail com, sruthi sekar1@gmail com, jenittomy@gmail com

Available format(s): PDF | BibTeX Citation

Version: 20210520:203501 (All versions of this report)

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