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A voice-over-Internet protocol technique with a new hierarchical data security protection (HDSP) scheme using a secret chaotic bit sequence has been recently proposed. Some insecure properties of the HDSP scheme are pointed out and then used to develop known/chosen-plaintext attacks. The main findings are: given n known plaintexts, about (100-(50/2n))% of secret chaotic bits can be uniquely determined; given only one specially-chosen plaintext, all secret chaotic bits can be uniquely derived; and the secret key can be derived with practically small computational complexity when only one plaintext is known (or chosen). These facts reveal that HDSP is very weak against known/chosen-plaintext attacks. Experiments are given to show the feasibility of the proposed attacks. It is also found that the security of HDSP against the brute-force attack is not practically strong. Some countermeasures are discussed for enhancing the security of HDSP and several basic principles are suggested for the design of a secure encryption scheme.