Name
Abstract | ||
|---|---|---|
We prove that for every n and 1 < t < n any t-out-of-n threshold secret sharing scheme for one-bit secrets requires share size log(t + 1). Our bound is tight when t = n - 1 and n is a prime power. In 1990 Kilian and Nisan proved the incomparable bound log(n - t + 2). Taken together, the two bounds imply that the share size of Shamir's secret sharing scheme (Comm ACM 1979) is optimal up to an additive constant even for one-bit secrets for the whole range of parameters 1 < t < n. More generally, we show that for all 1 < s < r < n, any ramp secret sharing scheme with secrecy threshold s and reconstruction threshold r requires share size log ((r + 1)/(r - s)). As part of our analysis we formulate a simple game-theoretic relaxation of secret sharing for arbitrary access structures. We prove the optimality of our analysis for threshold secret sharing with respect to this method and point out a general limitation. |
Year | DOI | Venue |
|---|---|---|
2020 | 10.4086/toc.2020.v016a002 | THEORY OF COMPUTING |
Keywords | DocType | Volume |
secret sharing,threshold,lower bound | Journal | 16 |
Issue | ISSN | Citations |
1 | 1557-2862 | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Andrej Bogdanov | 1 | 458 | 31.53 |
| Siyao Guo | 2 | 50 | 5.01 |
| Ilan Komargodski | 3 | 113 | 17.69 |