Cryptology ePrint Archive: Report 2018/1147

Stronger Leakage-Resilient and Non-Malleable Secret-Sharing Schemes for General Access Structures

Divesh Aggarwal and Ivan Damgard and Jesper Buus Nielsen and Maciej Obremski and Erick Purwanto and Joao Ribeiro and Mark Simkin

Abstract: In this work we present a collection of compilers that take secret sharing schemes for an arbitrary access structures as input and produce either leakage-resilient or non-malleable secret sharing schemes for the same access structure. A leakage-resilient secret sharing scheme hides the secret from an adversary, who has access to an unqualified set of shares, even if the adversary additionally obtains some size-bounded leakage from all other secret shares. A non-malleable secret sharing scheme guarantees that a secret that is reconstructed from a set of tampered shares is either equal to the original secret or completely unrelated. To the best of our knowledge we present the first generic compiler for leakage-resilient secret sharing for general access structures. In the case of non-malleable secret sharing, we strengthen previous definitions, provide separations between them, and construct a non-malleable secret sharing scheme for general access structures that fulfills the strongest definition with respect to independent share tampering functions. More precisely, our scheme is secure against concurrent tampering: The adversary is allowed to (non-adaptively) tamper the shares multiple times, and in each tampering attempt can freely choose the qualified set of shares to be used by the reconstruction algorithm to re-construct the tampered secret. This is a strong analogue of the multiple-tampering setting for split-state non-malleable codes and extractors.

We show how to use leakage-resilient and non-malleable secret sharing schemes to construct leakage-resilient and non-malleable threshold signatures. Classical threshold signatures allow to distribute the secret key of a signature scheme among a set of parties, such that certain qualified subsets can sign messages. We construct threshold signature schemes that remain secure even if an adversary leaks from or tampers with all secret shares.

Category / Keywords: cryptographic protocols / Non-malleable secret sharing, Leakage-resilient secret sharing, Non-malleable extractors

Original Publication (with major differences): IACR-CRYPTO-2019

Date: received 24 Nov 2018, last revised 29 May 2020

Contact author: divesh at comp nus edu sg, ivan at cs au dk, jbn at cs au dk, obremski math at gmail com, erickp at comp nus edu sg, j lourenco-ribeiro17 at imperial ac uk, simkin at cs au dk

Available format(s): PDF | BibTeX Citation

Note: Added acknowledgments, some references, and an appendix for completeness.

Version: 20200529:102058 (All versions of this report)

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