The paper presents a new generic black-box traitor tracing model where pirates employ a self-protection technique. This mechanism is simple and easy to implement, allowing pirates to evade detection. The authors present a necessary combinatorial condition for black-box traitor tracing of self-protecting devices and prove that any system failing this condition is incapable of tracing pirate-decoders with superlogarithmic numbers of traitor keys. They combine this condition with specific properties of concrete systems, showing that the Boneh-Franklin (BF) and Kurosawa-Desmedt schemes lack black-box tracing capability in the self-protecting model when the number of traitors is superlogarithmic, unless the ciphertext size is linear in the number of users. This partially settles the open problem regarding the general black-box traceability of the BF scheme. The paper also investigates a weaker form of black-box tracing called single-query "black-box confirmation" and shows that it fails against self-protecting pirate-decoders with superlogarithmic numbers of traitor keys, provided the confidence level of the tracer is below a certain threshold.The paper presents a new generic black-box traitor tracing model where pirates employ a self-protection technique. This mechanism is simple and easy to implement, allowing pirates to evade detection. The authors present a necessary combinatorial condition for black-box traitor tracing of self-protecting devices and prove that any system failing this condition is incapable of tracing pirate-decoders with superlogarithmic numbers of traitor keys. They combine this condition with specific properties of concrete systems, showing that the Boneh-Franklin (BF) and Kurosawa-Desmedt schemes lack black-box tracing capability in the self-protecting model when the number of traitors is superlogarithmic, unless the ciphertext size is linear in the number of users. This partially settles the open problem regarding the general black-box traceability of the BF scheme. The paper also investigates a weaker form of black-box tracing called single-query "black-box confirmation" and shows that it fails against self-protecting pirate-decoders with superlogarithmic numbers of traitor keys, provided the confidence level of the tracer is below a certain threshold.