Efficient Mix Network

Abstract—Shuffling is an effective method to build a publicly verifiable mix network to implement verifiable anonymous channels that can be used for important cryptographic applications like electronic voting and electronic cash. One shuffling scheme by Groth is claimed to be secure and efficient. However, its soundness has not been formally proven. An attack against the soundness of this shuffling scheme is presented in this paper. Such an attack compromises the soundness of the mix network based on it. Two new shuffling protocols are designed on the basis of Groth's shuffling and batch verification techniques. The first new protocol is not completely sound, but is formally analyzed in regards to soundness, so it can be applied to build a mix network with formally proven soundness. The second new protocol is completely sound, so is more convenient to apply. Formal analysis in this paper guarantees that both new shuffling protocols can be employed to build mix networks with formally provable soundness. Both protocols prevent the attack against soundness in Groth's scheme. Both new shuffling protocols are very efficient as batch-verification-based efficiency-improving mechanisms have been adopted. The second protocol is even simpler and more elegant than the first one as it is based on a novel batch cryptographic technique