Failure of A Mix Network

A mix network by Wikstrom fails in correctness, provable privacy and soundness. Its claimed advantages in security and efficiency are compromised. The analysis in this paper illustrates that although the first two failures may be fixed by modifying the shuffling protocol, the last one is too serious to fix at a tolerable cost. Especially, an attack is proposed to show how easily soundness of the shuffling scheme can be compromised. Moreover, the most surprising discovery in this paper is that it is formally illustrated that in practice it is impossible to fix soundness of the shuffling scheme by Wikstrom.