The OpenSSH project added support for a hybrid Streamlined NTRU Prime post-quantum key encapsulation method sntrup761 to strengthen their X25519-based default in their version 8.5 released on 2021-03-03. While there has been a lot of talk about post-quantum crypto generally, my impression has been that there has been a slowdown in implementing and deploying them in the past two years. Why is that? Regardless of the answer, we can try to collaboratively change things, and one effort that appears strangely missing are IETF documents for these algorithms.
Building on some earlier work that added X25519/X448 to SSH, writing a similar document was relatively straight-forward once I had spent a day reading OpenSSH and TinySSH source code to understand how it worked. While I am not perfectly happy with how the final key is derived from the sntrup761/X25519 secrets – it is a SHA512 call on the concatenated secrets – I think the construct deserves to be better documented, to pave the road for increased confidence or better designs. Also, reusing the RFC5656§4 structs makes for a worse specification (one unnecessary normative reference), but probably a simpler implementation. I have published draft-josefsson-ntruprime-ssh-00 here. Credit here goes to Jan Mojžíš of TinySSH that designed the earlier sntrup4591761x25519-sha512@tinyssh.org in 2018, Markus Friedl who added it to OpenSSH in 2019, and Damien Miller that changed it to sntrup761 in 2020. Does anyone have more to add to the history of this work?
Once I had sharpened my xml2rfc skills, preparing a document describing the hybrid construct between the sntrup761 key-encapsulation mechanism and the X25519 key agreement method in a non-SSH fashion was easy. I do not know if this work is useful, but it may serve as a reference for further study. I published draft-josefsson-ntruprime-hybrid-00 here.
Finally, how about a IETF document on the base Streamlined NTRU Prime? Explaining all the details, and especially the math behind it would be a significant effort. I started doing that, but realized it is a subjective call when to stop explaining things. If we can’t assume that the reader knows about lattice math, is a document like this the best place to teach it? I settled for the most minimal approach instead, merely giving an introduction to the algorithm, included SageMath and C reference implementations together with test vectors. The IETF audience rarely understands math, so I think it is better to focus on the bits on the wire and the algorithm interfaces. Everything here was created by the Streamlined NTRU Prime team, I merely modified it a bit hoping I didn’t break too much. I have now published draft-josefsson-ntruprime-streamlined-00 here.
I maintain the IETF documents on my ietf-ntruprime GitLab page, feel free to open merge requests or raise issues to help improve them.
To have confidence in the code was working properly, I ended up preparing a branch with sntrup761 for the GNU-project Nettle and have submitted it upstream for review. I had the misfortune of having to understand and implement NIST’s DRBG-CTR to compute the sntrup761 known-answer tests, and what a mess it is. Why does a deterministic random generator support re-seeding? Why does it support non-full entropy derivation? What’s with the key size vs block size confusion? What’s with the optional parameters? What’s with having multiple algorithm descriptions? Luckily I was able to extract a minimal but working implementation that is easy to read. I can’t locate DRBG-CTR test vectors, anyone? Does anyone have sntrup761 test vectors that doesn’t use DRBG-CTR? One final reflection on publishing known-answer tests for an algorithm that uses random data: are the test vectors stable over different ways to implement the algorithm? Just consider of some optimization moved one randomness-extraction call before another, then wouldn’t the output be different? Are there other ways to verify correctness of implementations?
As always, happy hacking!