The anonymity is the most important property of group signature schemes. Traditional schemes suppose that a signer is reluctant to leak his identity to a verifier. In some real scenarios, this supposition does not hold. A signer may want to cooperate with a verifier secretly to achieve special interests. So the verifier needs to identify the signers signature among all the signatures he received. Among all the building blocks of group signature schemes, the Camenisch's signatures of knowledge are most widely used and their security is critical to group signature schemes. Unfortunately, the Simmons's type I subliminal channel is found in all the signatures of knowledge introduced by Camenisch in [1]. To evaluate the real security of group signature, the concept of strong anonymity is proposed and all the Camenisch's signature of knowledge are found unsatisfied with the requirement of strong anonymity.