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 ’79) 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.
| Original language | English |
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| Title of host publication | Theory of Cryptography - 14th International Conference, TCC 2016-B, Proceedings |
| Editors | Adam Smith, Martin Hirt |
| Publisher | Springer Verlag |
| Pages | 471-484 |
| Number of pages | 14 |
| ISBN (Print) | 9783662536438 |
| DOIs | |
| State | Published - 2016 |
| Externally published | Yes |
| Event | 14th International Conference on Theory of Cryptography, TCC 2016-B - Beijing, China Duration: 31 Oct 2016 → 3 Nov 2016 |
Publication series
| Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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| Volume | 9986 LNCS |
| ISSN (Print) | 0302-9743 |
| ISSN (Electronic) | 1611-3349 |
Conference
| Conference | 14th International Conference on Theory of Cryptography, TCC 2016-B |
|---|---|
| Country/Territory | China |
| City | Beijing |
| Period | 31/10/16 → 3/11/16 |
Bibliographical note
Publisher Copyright:© International Association for Cryptologic Research 2016.