Solutions based on error-correcting codes for the blacklisting problem of a broadcast distribution system have been proposed by Kumar, Rajagopalan and Sahai. In this paper, detailed analysis of the solutions is presented. By choosing parameters properly in their constructions, we show that the performance is improved significantly.

A broadcast distribution system (BDS) is a system for the distribution of digital contents over broadcast channel where the data supplier broadcasts the contents in encrypted form and gives each subscriber a decoder containing a secret decryption key. A traitor is a subscriber who offers the information which allows to decrypt the broadcast. When a pirate decoder is captured, if at least one traitor can be identified from it, a BDS is said to be traitor-tracing. If the data supplier can prevent subscribers from obtaining the contents without recalling their decoders, a BDS is said to be subscriber-excluding. In this paper, we propose an efficient BDS which is both subscriber-excluding and traitor-tracing. We use similar mathematics to a threshold cryptosystem. In the proposed BDS, the maximum number of excluded subscribers reaches the maximum number of traitors in a coalition for which at least one traitor can be identified. We prove that the proposed BDS is secure against ciphertext-only attack if and only if ElGamal cryptosystem is secure against the attack and the discrete logarithm problem is hard. The proposed BDS is the first one which satisfies all the following features: Both subscriber-excluding and traitor-tracing, identifying all the traitors, black box tracing and public key system.