# Is Symmetric Security Solved? June 2017

Recently **T. Duong**, **D. Bleichenbacher**, **Q. Nguyen** and **B. Przydatek** released a crypto library intitled Tink. At its center lied an implementation of AES-GCM somehow different from the rest: it did not take a nonce as one of its input.

A few days ago, at the Crypto SummerSchool in Croatia, **Nik Kinkel** told me that he would generally recommend against letting developers tweak the nonce value, based on how AES-GCM tended to be heavily mis-used in the wild. For a recap, if a nonce is used twice to encrypt two different messages **AES-GCM will leak the authentication key**.

I think it's a fair improvement of AES-GCM to remove the nonce argument. By doing so, nonces have to be **randomly generated**. Now the new danger is that the same nonce is randomly generated twice for the same key. The birthday bound tells us that after \(2^{n/2}\) messages, \(n\) being the bit-size of a nonce, you have great odds of generating a previous nonce.

The optimal rekey point has been studied by Abdalla and Bellare and can computed with the cubic root of the nonce space. If more nonces are generated after that, chances of a nonce collision are too high. For AES-GCM this means that after \(2^{92/3} = 1704458900\) different messages, the key should be rotated.

This is of course assuming that you use 92-bit nonces with 32-bit counters. Some protocol and implementations will actually fix the first 32 bits of these 92-bit nonces reducing the birthday bound even further.

Isn't that a bit low?

Yes it kinda is. An interesting construction by Dan J. Bernstein called XSalsa20 (and that can be extended to XChacha20) allow us to use nonces of 192 bits. This would mean that you should be able to use the same key for up to \(2^{192/3} = 18446744073709551616\) messages. Which is already twice more that what a `BIG INT`

can store in a database

It seems like Sponge-based AEADs should benefit from large nonces as well since their rate can store even more bits. This might be a turning point for these constructions in the last round of the CAESAR competition. There are currently 4 of these: Ascon, Ketje, Keyak and NORX.

With that in mind, is nonce mis-use resistance now fixed?

**EDIT**: Here is a list of recent papers on the subject:

- Reconsidering the Security Bound of AES-GCM-SIV
- Better Bounds for Block Cipher Modes of Operation via Nonce-Based Key Derivation
- Increasing the Lifetime of Symmetric Keys for the GCM Mode by Internal Re-keying
- updatable Authenticated Encryption