I've read the Bitmessage whitepaper and I found it rather lacking on the details, but it promises anonymous routing. Can it be considered a variation on mix-networks, where each peer acts as a mix-node?
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YES. What mix-networks provide is anonymous routing. Using a chain of proxies, incoming messages are shuffled and then they are sent in random order. So, the sender remains anonymous. Similarly the Bitmessage protocol mixes all encrypted messages of a given user with all other encrypted messages of the network. As a result, the sender remains invisible. Here, each peer acts as a mix-node.