Paper 2023/1692

Traitor Tracing Revisited: New Attackers, Stronger Security Model and New Construction

Abstract

In Crypto 94, Chor, Fiat, and Naor first introduced the traitor tracing (TT) systems, which aim at helping content distributors identify pirates. Since its introduction, many traitor tracing schemes have been proposed. However, we observe until now almost all the traitor tracing systems using probabilistic public key (and secret key) encryption as the the content distribution algorithm, they do not consider this basic fact: the malicious encrypter can plant some trapdoor in the randomness of the ciphertexts and later he can use this trapdoor or the delegation of the trapdoor to construct decoding pirates, He can sell them to the black market and get his own benefits. At first sight, this new attack model is too strong to capture the real attack scenarios. But we think it is valuable at least for the following two reasons: (1) Note in many modern content distribution systems, there are at least existing three different roles: { the content provider, the content distributer and the content consumer. In this framework, the encrypter is not necessarily the content provider (or content owner). It can be a malicious employee in the content provider corporation, it can also be the malicious content distributer or its malicious employee}. In all these cases, the encrypter has its own benefits and has the potential intention to plant some trapdoor in the randomness for generating ciphertexts. (2) Also note in the related work, there is a conclusion that traitor tracing and differential privacy can have directly influence on each other, while differential privacy (DP) is at the heart of constructing modern privacy preserving systems. But if we consider this new insider attacker (the encrypter), at least some part arguments on the relationship between traitor tracing and differential privacy need more consideration. Therefore in this paper we carefully describe this new insider attacker and investigate thoroughly on its effect. Our main research results are the following: (1) We show that many existing public key traitor tracing systems with probabilistic encryption algorithm are failing to work correctly when facing this malicious encrypter.They are including the BSW, BW, GKSW, LCZ and BZ traitor tracing systems. Furthermore, we conclude that most of the existing traitor tracing systems using probabilistic encryption algorithm can not resist this attack. (2) When considering the insider attacker (the encrypter), if the traitor tracing schemes using probabilistic encryption algorithms, the conclusion on tight relationship between traitor tracing and differential privacy may need more consideration. (3) By employing the technique of hash function, we show how to design TT+ system which can resist this type of attack based on the existing traitor tracing system. Compared with the old traitor tracing system, our new proposal does not add much overhead and thus is practical too.