Analyzing Euler-Fermat Theorem Based Multicast Key Distribution Schemes with Chinese Remainder Theorem

Many emerging network applications are based upon group communication models and are implemented with multicast communications. We address the problem of distributing a secret session key to a secure multicast group. In a pair of such key management schemes, the session key is distributed mathematically based upon the Euler-Fermat Theorem, such that upon receiving the broadcast keying material known as the rekey message, each member in the privileged multicast group can derive with a modular operation this group oriented common shared secret. In this work, however, following the Chinese Remainder Theorem, we present some unusual analysis results concerning the two novel rekey schemes. We show that the first scheme is highly vulnerable to certain attacks, while the second one actually collapses on itself. Therefore, both schemes are revealed to have failed to effectively protect the multicast session key.