I'm studying "mix networks" and I'm reading the book "Anonymous Communication Networks" written by Kun Peng.
In the beginning of chapter 2, section 2.2, it talks about the classification of Mix Networks and it says that a mix network is classified into those employing decryption chain (DMN) and those employing re-encryption (RMN).
From what I understand, a DMN corresponds to Chaum mix network, described by the wikipedia article: https://en.wikipedia.org/wiki/Mix_network
The weakness of this mix network is if a mix is unavailable on the chain, the message cannot be transmitted and we need to resend the message with another mix set.
So, actually, the majority of mix networks are RMN but I'm not sure about the difference between RMN and DMN.
With DMN, we have n-layer of encryption (n is the number of mix in the chain), which means the user needs to encrypt the message for each layer before sending the message.
With RMN, the message is re-encrypted by each mix and a private key is shared by server authorities. I have difficulties understanding this. Does that mean some authority server can decrypt all messages? Is it not a big anonymity problem?
Can I have an example of the functioning of an RMN with a basic example?
RMN uses El Gamal encryption properties that allows the reencryption. This article: A Survey on Mix Networks and Their Secure Applications gives a lot informations about the reencryption mix-network.
The page 2149 explains how the reencryption works but I have difficult to understand this part.