Name
Abstract | ||
|---|---|---|
A black-box secret sharing scheme (BBSSS) for a given access structure works in exactly the same way over any finite Abelian group, as it only requires black-box access to group operations and to random group elements. In particular, there is no dependence on e.g. the structure of the group or its order. The expansion factor of a BBSSS is the length of a vector of shares (the number of group elements in it) divided by the number of players n. At CRYPTO 2002 Cramer and Fehr proposed a threshold BBSSS with an asymptotically minimal expansion factor Θ(log n). In this paper we propose a BBSSS that is based on a new paradigm, namely, primitive sets in algebraic number fields. This leads to a new BBSSS with an expansion factor that is absolutely minimal up to an additive term of at most 2, which is an improvement by a constant additive factor. We provide good evidence that our scheme is considerably more efficient in terms of the computational resources it requires. Indeed, the number of group operations to be performed is Õ(n2) instead of Õ(n3) for sharing and Õ(n1.6) instead of Õ(n2.6) for reconstruction. Finally, we show that our scheme, as well as that of Cramer and Fehr, has asymptotically optimal randomness efficiency. |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1007/11535218_21 | CRYPTO |
Keywords | Field | DocType |
random group element,finite abelian group,primitive set,algebraic number field,expansion factor,group element,asymptotically minimal expansion factor,new bbsss,group operation,black-box secret sharing,threshold bbsss,constant additive factor,secret sharing | Discrete mathematics,Abelian group,Combinatorics,Secret sharing,Algebraic number,Algebraic number field,Asymptotically optimal algorithm,Finite group,Access structure,Mathematics,Randomness | Conference |
Volume | ISSN | ISBN |
3621 | 0302-9743 | 3-540-28114-2 |
Citations | PageRank | References |
9 | 0.79 | 7 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ronald Cramer | 1 | 242 | 11.38 |
| Serge Fehr | 2 | 818 | 47.23 |
| Martijn Stam | 3 | 1659 | 67.36 |