Abstract | ||
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We study secret sharing schemes for general (non-threshold) access structures. A general secret sharing scheme for n parties is associated to a monotone function F:{0,1}n→{0,1}. In such a scheme, a dealer distributes shares of a secret s among n parties. Any subset of parties T ⊆ [n] should be able to put together their shares and reconstruct the secret s if F(T)=1, and should have no information about s if F(T)=0. One of the major long-standing questions in information-theoretic cryptography is to minimize the (total) size of the shares in a secret-sharing scheme for arbitrary monotone functions F.
There is a large gap between lower and upper bounds for secret sharing. The best known scheme for general F has shares of size 2n−o(n), but the best lower bound is Ω(n2/logn). Indeed, the exponential share size is a direct result of the fact that in all known secret-sharing schemes, the share size grows with the size of a circuit (or formula, or monotone span program) for F. Indeed, several researchers have suggested the existence of a representation size barrier which implies that the right answer is closer to the upper bound, namely, 2n−o(n).
In this work, we overcome this barrier by constructing a secret sharing scheme for any access structure with shares of size 20.994n and a linear secret sharing scheme for any access structure with shares of size 20.999n. As a contribution of independent interest, we also construct a secret sharing scheme with shares of size 2Õ(√n) for 2nn/2 monotone access structures, out of a total of 2nn/2· (1+O(logn/n)) of them. Our construction builds on recent works that construct better protocols for the conditional disclosure of secrets (CDS) problem.
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Year | DOI | Venue |
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2018 | 10.1145/3188745.3188936 | STOC '18: Symposium on Theory of Computing
Los Angeles
CA
USA
June, 2018 |
Keywords | DocType | Volume |
Secret Sharing,Information-Theoretic Cryptography | Conference | 2018 |
ISSN | ISBN | Citations |
0737-8017 | 978-1-4503-5559-9 | 2 |
PageRank | References | Authors |
0.37 | 7 | 2 |
Name | Order | Citations | PageRank |
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Tianren Liu | 1 | 20 | 4.08 |
Vinod Vaikuntanathan | 2 | 5353 | 200.79 |