On the Computational Security of a Distributed Key Distribution Scheme

In a distributed key distribution scheme, a set of servers help a set of users in a group to securely obtain a common key. Security means that an adversary who corrupts some servers and some users has no information about the key of a non-corrupted group. In this work we formalize the security analysis of one of such schemes \\cite{DHPS02}, which was not considered in the original proposal. We prove the scheme secure in the random oracle model, assuming that the Decisional Diffie-Hellman problem is hard to solve. We also detail a possible modification of that scheme and the one in \\cite{NPR99}, which allows to prove the security of the schemes without assuming that a specific hash function behaves as a random oracle. As usual, this improvement in the security of the schemes is at the cost of an efficiency loss.