On the complexity of verifiable secret sharing and multiparty computation

We first study the problem of doing Verifiable Secret Sharing (VSS) information theoretically secure for a general access structure. We do it in the model where private channels between players and a broadcast channel is given, and where an active, adaptive adversary can corrupt any set of players not in the access structure. In particular, we consider the complexity of protocols for this problem, as a function of the access structure and the number of players. For all access structures where VSS is possible at all, we show that, up to a polynomial time black-box reduction, the complexity of adaptively secure VSS is the same as that of ordinary secret sharing (SS), where security is only required against a passive, static adversary. Previously, such a connection was only known for linear secret sharing and VSS schemes. We then show an impossibility result indicating that a similar equivalence does not hold for Multiparty Computation (MPC): we show that even if protocols are given blac...

• Type: Conference
• Year: 2000
• Where: STOC
• Authors: Ronald Cramer, Ivan Damgård, Stefan Dziembowski
• Keywords: Access Structures, Algorithms, Secret Sharing, Secret Sharing Scheme, STOC 2000