We deal with two claws of Zhou-Gollmann's fair non-repudiationprotocol. Firstly, their protocol divides a message into 2 parts, i.e.,a key K and a ciphertext C. Then, C is delivered to the recipient, whileK is submitted to TTP (Trusted Third Party). If the originator doesn'tsubmit K to TTP, then the protocol appears to have no dispute betweenthe originator and the recipient. However the protocol depends on hisaction on whether the originator really submits K to TTP or not. We showthat the originator can make the protocol unfair by using hisadvantageous position, and present how to improve the fairness of theprotocol. Secondly, the protocol doesn't provide the message privacy.This means that additional protocols are required to transfer animportant message in private. We propose an improved version of theprotocol to guarantee the message privacy
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