I use the word mixing 4 times, with two meanings:
"...enough mixing can happen..." : mathematical sense, on pairs of edges around a node
"...yet highly mixing network..." : mathematical sense, on pairs of entry/exit Tor nodes
"...between mixing chains and Tor, and can be seen as a lot of mixing chains..." : traffic analysis sense, the first 'mixing chains' here should have said 'mix networks' instead
Informally, in the mathematical sense, some topology is mixing if random behaviour on it leads exponentially fast to the uniform distribution (which amounts to no information in the security sense). See the part around [3].
The short summary of the weakness of Tor here:
- We would like the whole protocol to be mixing (to an observer, the probability of exiting at any node C given entrance at node A is close to 1/N),
- The clique topology leads to a constant leak of information, because at any time traffic analysis around a node X can be performed to recover a non-uniform distribution on entry-exit pairs around that node.
Proposed solution:
- By simply lowering the number of allowed edges around a node, nodes can adopt mixing chains-like behaviour combined with Tor-like behaviour, at little cost. They have more or less the same amount of traffic to play with, but they need to make it look constant (to resist against traffic analysis) on less edges, so they need to fake a lot less traffic.
- Lowering the number of edges means that it increases danger of other attacks, relying on global information on the topology (if the topology is not a clique anymore, in 2 hops I might not be able to potentially be everywhere). The point of my email is that for specific network topologies (expanders) this is not really a problem (this was already observed in the literature), and that some type of expanders can be created easily, with the security guarantees needed (using Cayley graphs of matrix groups).
Paul