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Non-malleable Secret Sharing for General Access Structures

  • Vipul Goyal
  • Ashutosh Kumar
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10991)

Abstract

Goyal and Kumar (STOC’18) recently introduced the notion of non-malleable secret sharing. Very roughly, the guarantee they seek is the following: the adversary may potentially tamper with all of the shares, and still, either the reconstruction procedure outputs the original secret, or, the original secret is “destroyed” and the reconstruction outputs a string which is completely “unrelated” to the original secret. Prior works on non-malleable codes in the 2 split-state model imply constructions which can be seen as 2-out-of-2 non-malleable secret sharing (NMSS) schemes. Goyal and Kumar proposed constructions of t-out-of-n NMSS schemes. These constructions have already been shown to have a number of applications in cryptography.

We continue this line of research and construct NMSS for more general access structures. We give a generic compiler that converts any statistical (resp. computational) secret sharing scheme realizing any access structure into another statistical (resp. computational) secret sharing scheme that not only realizes the same access structure but also ensures statistical non-malleability against a computationally unbounded adversary who tampers each of the shares arbitrarily and independently. Instantiating with known schemes we get unconditional NMMS schemes that realize any access structures generated by polynomial size monotone span programs. Similarly, we also obtain conditional NMMS schemes realizing access structure in \(\mathbf {monotone \;P}\) (resp. \(\mathbf {monotone \;NP}\)) assuming one-way functions (resp. witness encryption).

Towards considering more general tampering models, we also propose a construction of n-out-of-n NMSS. Our construction is secure even if the adversary could divide the shares into any two (possibly overlapping) subsets and then arbitrarily tamper the shares in each subset. Our construction is based on a property of inner product and an observation that the inner-product based construction of Aggarwal, Dodis and Lovett (STOC’14) is in fact secure against a tampering class that is stronger than 2 split-states. We also show applications of our construction to the problem of non-malleable message transmission.

Notes

Acknowledgments

We thank the anonymous reviewers, as their detailed and insightful reviews significantly helped in improving the presentation of this article.

The first author is supported by a grant from Northrop Grumman.

A part of this work was done while the second author was at Microsoft Research, India. Work done at UCLA is supported in part from NSF grant 1619348, NSF frontier award 1413955, US-Israel BSF grants 2012366, 2012378, and by the Defense Advanced Research Projects Agency (DAPRA) SAFEWARE program through the ARL under Contract W911NF-15-C-0205 and through a subcontract with Galois, inc. The views expressed are those of the authors and do not reflect the official policy or position of the Department of Defense, the National Science Foundation, or the U.S. Government.

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Copyright information

© International Association for Cryptologic Research 2018

Authors and Affiliations

  1. 1.CMUMount PleasantUSA
  2. 2.UCLALos AngelesUSA

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