Name
Abstract | ||
|---|---|---|
A secret -sharing scheme for a monotone Boolean (access) function F : {0, 1}n > {0, 1} is a randomized algorithm that on input a secret, outputs n shares Si,., 8 such that for any (xi,, x) E {0, 1}n, the collection of shares {8i : xi = 1} determine the secret if F(xi,, xn) = 1 and reveal nothing about the secret otherwise. The best secret sharing schemes for general monotone functions have shares of size 0(2n). It has long been conjectured that one cannot do much better than 2r2(n) share size, and indeed, such a lower bound is known for the restricted class of linear secret -sharing schemes. In this work, we refute two natural strengthenings of the above conjecture: - First, we present secret -sharing schemes for a family of 22'2 monotone functions over {0, 1}n with sub -exponential share size 2 (Y7' n). This unconditionally refutes the stronger conjecture that circuit size is, within polynomial factors, a lower bound on the share size. Second, we disprove the analogous conjecture for non-monotone functions. Namely, we present "non-monotone secret -sharing schemes" for every access function over {0, 1}n with shares of size 20(\/7 log n) Our construction draws upon a rich interplay amongst old and new problems in information-theoretic cryptography: from secret -sharing, to multi -party computation, to private information retrieval. Along the way, we also construct the first multi-party conditional disclosure of secrets (CDS) protocols for general functions F : {0, 1}n > {0, 1} with communication complexity 2 (-`/71"g n). |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1007/978-3-319-78381-9_21 | ADVANCES IN CRYPTOLOGY - EUROCRYPT 2018, PT I |
DocType | Volume | ISSN |
Conference | 10820 | 0302-9743 |
Citations | PageRank | References |
3 | 0.42 | 22 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Tianren Liu | 1 | 20 | 4.08 |
| Vinod Vaikuntanathan | 2 | 5353 | 200.79 |
| Hoeteck Wee | 3 | 1613 | 86.36 |