Analysis of a kind of quantum cryptographic schemes based on secret sharing

Recently, Yang et al. proposed a kind of quantum cryptographic schemes based on secret sharing. The main idea is drawn from the case, where any n participants who share a secret K can co-operate as K does. This process can be applied to encryption, authentication, signature and so on. Unfortunately, since there is no identity authentication of the share’s holder, these schemes inherit the limitation of secret sharing in practice. If some participants do not follow the protocol, the protocol would be a failure at last. Moreover, these schemes encounter another serious attack. Any two participants can co-operate to defeat the schemes by sending different shares to the parties unknown to the distributor of the secret K, such that these parties can execute the protocol as well. The attack proves that it is not enough for quantum cryptographic schemes that only the secret key is secure. Supported by the National Basic Research Program of China (Grant No. 2007CB311100) and the National High Technology Research and Development Program of China (Grant No. 2006AA01Z440)