A mix network is an unreliable packet switching network which resists traffic analysis. Mix networks can be designed to provide various anonymity properties such as:
- sender anonymity
- receiver anonymity
- sender and receiver anonymity with respect to third party observers
Loopix is described in the paper "The Loopix Anonymity System" published at USENIX 2017, https://arxiv.org/pdf/1703.00536.pdf
Briefly, Loopix uses a collection of the best mix network designs to create a messaging system that has the property of sender and receiver anonymity with respect to third party observers. This particular meaning of "anonymity" is remarkably different than what Tor provides. Loopix does not have strong location hiding properties nor does it provide sender anonymity or receiver anonymity. That having been said it should be possible to create such systems based on the Loopix design.
The Loopix design is informed by over 15 years of mixnet literature and strives to reduce many kinds of metadata leakages that historically have made mix networks vulnerable to long term statistical disclosure attacks. Loopix has a defense against blending/n-1 attacks. Loopix explores the tradeoff between decoy traffic and latency, thus revitalizing mix networks with much lower latency for message transportation.
Loopix uses the Sphinx cryptographic packet format, the Poisson mix strategy, three kinds of decoy traffic and the stratified mix topology. It's Provider architecture forces long term statistical disclosure attacks to take place on the receiver's Provider, thus forcing such adversaries to actively compromise Providers instead of passively observing the mix network which is in contrast to historical mix network designs.
Katzenpost has the goal of implementing the Loopix designs with the additional property of message transport reliability. Reliability is achieved using a Stop and Wait ARQ which is half duplex and uses SURBs to create the reply channel for the ACKnowledgement messages.
Why is this a big deal? To our knowledge, no other mix network design has attempted to achieve reliability. We beleive that the lack of reliability has been one of the major obstacles to the adoption of mix networks. "Would you want to use a messaging system which might not even transport your messages to their destination?"
Tor is stream oriented. Mixnets are message oriented. Tor is low latency, easy to use, has a great primary application (Tor Browser), and functions as an extremely useful general purpose anonymity system. This is in contrast to mix networks which do not function well as general purpose anonymity systems. Instead mix networks are better suited to customization for specific applications, for example a mix network for instant messaging and a mix network for e-mail will have different traffic patterns and therefore require different decoy traffic patterns to achieve the desired traffic analysis resistant properties.
There are also many adversarial model differences between Tor and mix networks. For example, Tor can be easily be deanonymized by statistical correlation attacks by a sufficiently global adversary whereas mixnets are not immediately vulnerable to these kinds of attacks if they correctly use mix strategies and decoy traffic.
Both Tor and mix networks can scale well with respect to increasing user traffic, however Tor requires route unpredictability to achieve it's anonymity properties. Mix networks on the other hand do not require route unpredictability and therefore can achieve very strong anonymity properties with far fewer network nodes than Tor.
Pond doesn't actually mix anything whereas mix networks specifically contain component mixes, each containing a mix queue which "mixes" messages together via some specific mix strategy before sending them to the next hop in the route. Pond uses a group signature scheme to prevent the server from learning to whom a message is being sent to. Pond uses Tor onion services as it's transport while also using decoy traffic to prevent a passive network observer from determining when a user sends a message. Mix network designs can also use decoy traffic, however in the Loopix design there are three different kinds of decoy traffic that serve different purposes. Mix networks also scale much better with respect to increasing users and traffic whereas pond servers quickly become performance bottlenecks. This is in contrast to mix networks where additional mixes can be added to the network in order to efficiently process increases in user traffic.
Vuvuzela uses the cascade mix topology which does not scale well with respect to an increase in user traffic. Loopix uses the stratified topology which scales very well. In Vuvuzela, messages cannot be received when a user is offline. In Loopix messages received while a user is offline are queued by their Provider. Vuvuzela operates in rounds whereas Loopix does not. Vuvuzela does not provide reliable message transportation whereas Katzenpost does.
AnonPOP operates in rounds and provides offline storage of messages. Loopix uses a continuous time mix strategy so that it avoids user synchronization issues. AnonPOP does not provide reliable message transportation whereas Katzenpost does.