Traceability code[1] 

Suppose \(n\) is the number of users, \(k\) is the number of users known by the pirates, and \(p\) is the probability that the pirates cannot be traced. An open (public) resilient scheme using a hash function has the personal keys of the users consisting of \(O(k^{2}\log n)\) decryption keys, which is the amount of decryptions needed to reveal the information. The amount of data redundancy overhead is about \(O(k^{4}\log n)\) [1].

A secret resilient scheme using a hash function has the personal keys of the users consisting of \(O(k \log(n/p))\) decryption keys, which is the amount of decryptions needed to reveal the information. The amount of data redundancy overhead is about \(O(k^{2} \log(n/p))\) [1].

A threshold (secret) scheme using a hash function that is successful against pirates which decrypt with probability \(> q\), has the personal keys of the users consisting of \((4k/3q)\log(n/p)\) decryption keys (note that this is the same as in the secret resilient scheme above). These types of schemes only need order \(O(1)\) decryption operations performed by users to decrypt the information successfully. Finally, the amount of data redundancy overhead is 4k encrypted keys, a large improvement compared to the above [1].