Axolotol, an attempt at a summary

After Zooko introduced me to TextSecure/Signal a few months ago, I started using Signal for all of my encrypted asynchronous messaging. The app is terrifically usable, and most of my friends use it, so I was excited to start using the app. But I wasn’t satisfied with just using the app; I wanted to understand what was going on behind the scenes, so I dove in and tried to understand as much as I could about the cryptography that powers millions of people’s secure communications.

Along the way, I discovered that a number of people are also interested in understanding how TextSecure/Signal works – perhaps so they can implement a similar protocol themselves, or maybe they prefer to audit the code they install on their mobile device. It also became clear that a lot of people just didn’t understand it, and rightfully so. It’s an advanced protocol that requires a strong background in cryptography. Inspired by this StackOverflow post, I thought it might be helpful (for me and potential readers) to rehash what I’ve learned about the Axolotl protocol, utilized by TextSecure/Signal and WhatsApp, and originally conceived by Trevor Perrin and Moxie Marlinspike.

While I’m typically an advocate of RTFM, I think there’s value in reading an alternative explanation of a complex topic like this. That said, if you’ve tried understanding the Axolotl protocol before to no avail, this might be a good start, but please don’t stop here. I’ll reference a few articles and documents directly from Open Whisper Systems that I recommend you read (in the following order) after you finish this piece. There’s no substitute from learning from the people who invented the protocol. Additionally, it’s possible that I’ve made mistakes in the process of understanding the protocol and conveying it here.

  1. Simplifying OTR Deniability 2. Forward Secrecy for Asynchronous Messages 3. Advanced Cryptographic Ratcheting
  2. Axolotl Ratchet Specification

You might also find this illustrated primer by Christine Corbett Moran, the the Signal lead developer, helpful.

The Axolotl Ratchet Protocol

The Axolotl ratchet protocol is largely built on OTR’s protocol which, in addition to encrypting your messages, provides the following characteristics:

  • Authentication: you can be confident that your conversation partner is who you
  • think it is. Deniability: at the conclusion of a conversation, anyone can
  • forge messages to make them look like they came from you, which means you can
  • deny that messages you send were sent by you. Perfect forward secrecy: if your
  • keys are compromised, previously transmitted ciphertext can’t be decrypted.

If you’re familiar with using PGP for encrypting messages, you might recognize that while PGP does provide solid end-to-end encryption and authentication of the other party, it falls short on deniability and perfect forward secrecy. If you sign a message with your PGP private key, you can’t deny that you didn’t do so, unless you also admit that your private key was compromised, in which case you’d have much more to worry about. Furthermore, if an attacker with access to previously-transmitted ciphertext gains hold of your private key, she can decrypt all of your messages. This makes the stakes pretty high for protecting your private key, and for most users (and even for the technically apt) a surmountable challenge.

Thankfully OTR addresses some of the failings of PGP, and over the past two years, the folks at Open Whisper Systems conceived of some impressive improvements to the OTR protocol, and have implemented them into their apps, and along the way convinced developers of other end-to-end encryption applications like WhatsApp to do the same.

How Axolotl Improves Deniability

Deniability in OTR

In OTR, Alice and Bob both have a static identity key, denoted in the image below by A and B. These keys are used repeatedly throughout their conversation to sign [ephemeral keys](), denoted a and b. As you might already suspect, ephemeral keys are used only temporarily, and are essential to providing forward secrecy in OTR. Because Alice and Bob each generate new ephemeral keys every time they start a new conversation, and then generate a new shared secret using a Diffie Hellman handshake, if these keys are ever compromised, it will be no issue because new ephemeral keys will be generated for the next conversation and shared secret.

Every message in OTR includes a MAC, which is an identifier that uses Alice and Bob’s shared secret to create a hash of the message. Because Alice and Bob can verify that the MAC was actually derived from the shared secret, which was derived from an ephemeral key signed by the other’s identity key, they can be sure that any message they receive came from the other. How do MACs in OTR’s protocol contribute to providing deniability? Recall that the MAC keys are derived from the shared secret, which means that both Alice and Bob can produce the same MAC! Furthermore, OTR continuously dumps old MAC keys in the clear, so theoretically, an observer could use those to publish outdated, but valid MACs, which can never be reused for new messages.

It’s important to note that while Alice can deny that she sent a message because Bob could have forged ciphertext and a MAC, the pool of plausible deniability is limited to to Alice and Bob, and we might desire something less complex than publishing old MACs and only having a deniability pool of 2.

Conveniently, Trevor Perrin and Moxie Marlinspike conceived of an improvement to OTR’s protocol that does just that.

A New Kind of Deniability

Instead of using DSA to sign their ephemeral keys with their identity keys, in the Axolotl protocol, Alice and Bob instead perform three Diffie-Hellman handshakes and establish 3 shared secrets: gaB, gAb, and gab.

Since Alice and Bob exchange unsigned keys, anyone can now use either of their public identity keys to create ephemeral keys that could then be used to create shared secrets. This means that anyone can forge a transcript, and Alice and Bob each have improved deniability.

Maintaining Forward Secrecy in an Asynchronous Messaging Application

When you communicate with someone via an application like iMessage, you expect that even if you aren’t actively using the application, messages will still be delivered to your inbox and ready to read at your convenience. This delivery model is asynchronous – messages are pushed to the sender, even if the sender isn’t expecting the message or actively waiting for its arrival. Mobile users expect this from messaging applications, unlike OTR, which is used for synchronous desktop instant-messaging conversations in which both parties are present. Axolotl needed to come up with a way to deliver this asynchronous functionality, all the while generating keys, executing handshakes, and decrypting ciphertext.

This is a challenge, because these operations all involve round-trip communications between Alice and Bob. For example, to establish a shared secret in their initial exchange, Alice will say, “Hi Bob, here’s an ephemeral key” and Bob will reply, “Hi Alice, I got your key, here’s the next one I’ll use!” It’s unreasonable to expect Alice and Bob to both have the application running at the same time in order to exchange and acknowledge each other’s keys.

Generating Prekeys

Axolotl solves this by generating 100 “prekeys” when a user registers with the application. These prekeys are a batch of key exchange messages signed with Alice and Bob’s static identity key, just like Alice and Bob would have done before, except now when Alice wants to send a message to Bob, she need not wait for his reply! She can request one of his prekeys from the server, use it generate a shared secret, and then use the shared secret to encrypt her message. So now when Alice wants to send a message for Bob, she need not wait for his reply, she can simply sent the message ciphertext along with the ID associated with the prekey she used to indicate to Bob which she used to generate the shared secret. Additionally, forward secrecy is still preserved because the client will never send or accept the same prekey twice.

The importance of this feature should not be underestimated. Other messaging apps also provide forward secrecy, but they weren’t able to do so asynchronously, thus thwarting meaningful progress in the world of end-to-end encrypted communications.

That’s all for now. I hope this is heplful, and remember to read the original articles linked above. They’re clear and quite understandable if you take your time and do the necessary research when you encounter an unfamiliar concept. If you notice any errors here, feel free to send a note.

Next time I’ll talk about ratcheting, and how Axolotl makes some major improvements on that front.

*[RTFM]: reading the fucking manual [OTR]: Off-the-Record Messaging [PGP]: *Pretty Good Privacy [MAC]: message authentication code