In a distributed key distribution scheme, a set of servers helps 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 noncorrupted group. In this work, we formalize the security analysis of one such scheme which was not considered in the original proposal. We prove the scheme is secure in the random oracle model, assuming that the Decisional Diffie-Hellman (DDH) problem is hard to solve. We also detail a possible modification of that scheme and the one in which allows us 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.

The work of the first two authors was partially supported by the Spanish Ministry of Education and Science under Projects TSI2007-65406-C03-02 (“eAEGIS”) and CONSOLIDER CSD2007-00004 (“ARES”). The work of V. Daza was also supported by the Government of Catalonia under Grant 2005-SGR-00446. The work of J. Herranz was also supported by the Government of Catalonia under Grant 2005-SGR-00093. Finally, the work of G. Sáez was partially supported by the/nSpanish Ministry of Education and Science under Project TSI2006-02731.