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?
Let’s reflect on some of my recent work that started with understanding Trisquel GNU/Linux, improving transparency into apt-archives, working on reproducible builds of Trisquel, strengthening verification of apt-archives with Sigstore, and finally thinking about security device threat models. A theme in all this is improving methods to have trust in machines, or generally any external entity. While I believe that everything starts by trusting something, usually something familiar and well-known, we need to deal with misuse of that trust that leads to failure to deliver what is desired and expected from the trusted entity. How can an entity behave to invite trust? Let’s argue for some properties that can be quantitatively measured, with a focus on computer software and hardware:
Deterministic Behavior – given a set of circumstances, it should behave the same.
Verifiability and Transparency – the method (the source code) should be accessible for understanding (compare scientific method) and its binaries verifiable, i.e., it should be possible to verify that the entity actually follows the intended deterministic method (implying efforts like reproducible builds and bootstrappable builds).
Accountable – the entity should behave the same for everyone, and deviation should be possible prove in a way that is hard to deny, implying efforts such as Certificate Transparency and more generic checksum logs like Sigstore and Sigsum.
Liberating – the tools and documentation should be available as free software to enable you to replace the trusted entity if so desired. An entity that wants to restrict you from being able to replace the trusted entity is vulnerable to corruption and may stop acting trustworthy. This point of view reinforces that open source misses the point; it has become too common to use trademark laws to restrict re-use of open source software (e.g., firefox, chrome, rust).
Essentially, this boils down to: Trust, Verify and Hold Accountable. To put this dogma in perspective, it helps to understand that this approach may be harmful to human relationships (which could explain the social awkwardness of hackers), but it remains useful as a method to improve the design of computer systems, and a useful method to evaluate safety of computer systems. When a system fails some of the criteria above, we know we have more work to do to improve it.
How far have we come on this journey? Through earlier efforts, we are in a fairly good situation. Richard Stallman through GNU/FSF made us aware of the importance of free software, the Reproducible/Bootstrappable build projects made us aware of the importance of verifiability, and Certificate Transparency highlighted the need for accountable signature logs leading to efforts like Sigstore for software. None of these efforts would have seen the light of day unless people wrote free software and packaged them into distributions that we can use, and built hardware that we can run it on. While there certainly exists more work to be done on the software side, with the recent amazing full-source build of Guix based on a 357-byte hand-written seed, I believe that we are closing that loop on the software engineering side.
So what remains? Some inspiration for further work:
Accountable binary software distribution remains unresolved in practice, although we have some software components around (e.g., apt-sigstore and guix git authenticate). What is missing is using them for verification by default and/or to improve the signature process to use trustworthy hardware devices, and committing the signatures to transparency logs.
Trustworthy hardware to run trustworthy software on remains a challenge, and we owe FSF’s Respect Your Freedom credit for raising awareness of this. Many modern devices requires non-free software to work which fails most of the criteria above and are thus inherently untrustworthy.
Verifying rebuilds of currently published binaries on trustworthy hardware is unresolved.
Completing a full-source rebuild from a small seed on trustworthy hardware remains, preferably on a platform wildly different than X86 such as Raptor’s Talos II.
We need improved security hardware devices and improved established practices on how to use them. For example, while Gnuk on the FST enable a trustworthy software and hardware solution, the best process for using it that I can think of generate the cryptographic keys on a more complex device. Efforts like Tillitis are inspiring here.
Onwards and upwards, happy hacking!
Update 2023-05-03: Added the “Liberating” property regarding free software, instead of having it be part of the “Verifiability and Transparency”.
I’d like to describe and discuss a threat model for computational devices. This is generic but we will narrow it down to security-related devices. For example, portable hardware dongles used for OpenPGP/OpenSSH keys, FIDO/U2F, OATH HOTP/TOTP, PIV, payment cards, wallets etc and more permanently attached devices like a Hardware Security Module (HSM), a TPM-chip, or the hybrid variant of a mostly permanently-inserted but removable hardware security dongles.
Our context is cryptographic hardware engineering, and the purpose of the threat model is to serve as as a thought experiment for how to build and design security devices that offer better protection. The threat model is related to the Evil maid attack.
Our focus is to improve security for the end-user rather than the traditional focus to improve security for the organization that provides the token to the end-user, or to improve security for the site that the end-user is authenticating to. This is a critical but often under-appreciated distinction, and leads to surprising recommendations related to onboard key generation, randomness etc below.
The Substitution Attack
An attacker is able to substitute any component of the device (hardware or software) at any time for any period of time.
Your takeaway should be that devices should be designed to mitigate harmful consequences if any component of the device (hardware or software) is substituted for a malicious component for some period of time, at any time, during the lifespan of that component. Some designs protect better against this attack than other designs, and the threat model can be used to understand which designs are really bad, and which are less so.
Terminology
The threat model involves at least one device that is well-behaving and one that is not, and we call these Good Device and Bad Device respectively. The bad device may be the same physical device as the good key, but with some minor software modification or a minor component replaced, but could also be a completely separate physical device. We don’t care about that distinction, we just care if a particular device has a malicious component in it or not. I’ll use terms like “security device”, “device”, “hardware key”, “security co-processor” etc interchangeably.
From an engineering point of view, “malicious” here includes “unintentional behavior” such as software or hardware bugs. It is not possible to differentiate an intentionally malicious device from a well-designed device with a critical bug.
Don’t attribute to malice what can be adequately explained by stupidity, but don’t naïvely attribute to stupidity what may be deniable malicious.
What is “some period of time”?
“Some period of time” can be any length of time: seconds, minutes, days, weeks, etc.
It may also occur at any time: During manufacturing, during transportation to the user, after first usage by the user, or after a couple of months usage by the user. Note that we intentionally consider time-of-manufacturing as a vulnerable phase.
Even further, the substitution may occur multiple times. So the Good Key may be replaced with a Bad Key by the attacker for one day, then returned, and later this repeats a month later.
What is “harmful consequences”?
Since a security key has a fairly well-confined scope and purpose, we can get a fairly good exhaustive list of things that could go wrong. Harmful consequences include:
Attacker learns any secret keys stored on a Good Key.
Attacker causes user to trust a public generated by a Bad Key.
Attacker is able to sign something using a Good Key.
Attacker learns the PIN code used to unlock a Good Key.
Attacker learns data that is decrypted by a Good Key.
Thin vs Deep solutions
One approach to mitigate many issues arising from device substitution is to have the host (or remote site) require that the device prove that it is the intended unique device before it continues to talk to it. This require an authentication/authorization protocol, which usually involves unique device identity and out-of-band trust anchors. Such trust anchors is often problematic, since a common use-case for security device is to connect it to a host that has never seen the device before.
A weaker approach is to have the device prove that it merely belongs to a class of genuine devices from a trusted manufacturer, usually by providing a signature generated by a device-specific private key signed by the device manufacturer. This is weaker since then the user cannot differentiate two different good devices.
In both cases, the host (or remote site) would stop talking to the device if it cannot prove that it is the intended key, or at least belongs to a class of known trusted genuine devices.
Upon scrutiny, this “solution” is still vulnerable to a substitution attack, just earlier in the manufacturing chain: how can the process that injects the per-device or per-class identities/secrets know that it is putting them into a good key rather than a malicious device? Consider also the consequences if the cryptographic keys that guarantee that a device is genuine leaks.
The model of the “thin solution” is similar to the old approach to network firewalls: have a filtering firewall that only lets through “intended” traffic, and then run completely insecure protocols internally such as telnet.
The networking world has evolved, and now we have defense in depth: even within strongly firewall’ed networks, it is prudent to run for example SSH with publickey-based user authentication even on locally physical trusted networks. This approach requires more thought and adds complexity, since each level has to provide some security checking.
I’m arguing we need similar defense-in-depth for security devices. Security key designs cannot simply dodge this problem by assuming it is working in a friendly environment where component substitution never occur.
Example: Device authentication using PIN codes
To see how this threat model can be applied to reason about security key designs, let’s consider a common design.
Many security keys uses PIN codes to unlock private key operations, for example on OpenPGP cards that lacks built-in PIN-entry functionality. The software on the computer just sends a PIN code to the device, and the device allows private-key operations if the PIN code was correct.
Let’s apply the substitution threat model to this design: the attacker replaces the intended good key with a malicious device that saves a copy of the PIN code presented to it, and then gives out error messages. Once the user has entered the PIN code and gotten an error message, presumably temporarily giving up and doing other things, the attacker replaces the device back again. The attacker has learnt the PIN code, and can later use this to perform private-key operations on the good device.
This means a good design involves not sending PIN codes in clear, but use a stronger authentication protocol that allows the card to know that the PIN was correct without learning the PIN. This is implemented optionally for many OpenPGP cards today as the key-derivation-function extension. That should be mandatory, and users should not use setups that sends device authentication in the clear, and ultimately security devices should not even include support for that. Compare how I build Gnuk on my PGP card with the kdf_do=required option.
Example: Onboard non-predictable key-generation
Many devices offer both onboard key-generation, for example OpenPGP cards that generate a Ed25519 key internally on the devices, or externally where the device imports an externally generated cryptographic key.
Let’s apply the subsitution threat model to this design: the user wishes to generate a key and trust the public key that came out of that process. The attacker substitutes the device for a malicious device during key-generation, imports the private key into a good device and gives that back to the user. Most of the time except during key generation the user uses a good device but still the attacker succeeded in having the user trust a public key which the attacker knows the private key for. The substitution may be a software modification, and the method to leak the private key to the attacker may be out-of-band signalling.
This means a good design never generates key on-board, but imports them from a user-controllable environment. That approach should be mandatory, and users should not use setups that generates private keys on-board, and ultimately security devices should not even include support for that.
Example: Non-predictable randomness-generation
Many devices claims to generate random data, often with elaborate design documents explaining how good the randomness is.
Let’s apply the substitution threat model to this design: the attacker replaces the intended good key with a malicious design that generates (for the attacker) predictable randomness. The user will never be able to detect the difference since the random output is, well, random, and typically not distinguishable from weak randomness. The user cannot know if any cryptographic keys generated by a generator was faulty or not.
This means a good design never generates non-predictable randomness on the device. That approach should be mandatory, and users should not use setups that generates non-predictable randomness on the device, and ideally devices should not have this functionality.
Case-Study: Tillitis
I have warmed up a bit for this. Tillitis is a new security device with interesting properties, and core to its operation is the Compound Device Identifier (CDI), essentially your Ed25519 private key (used for SSH etc) is derived from the CDI that is computed like this:
cdi = blake2s(UDS, blake2s(device_app), USS)
Let’s apply the substitution threat model to this design: Consider someone replacing the Tillitis key with a malicious key during postal delivery of the key to the user, and the replacement device is identical with the real Tillitis key but implements the following key derivation function:
cdi = weakprng(UDS’, weakprng(device_app), USS)
Where weakprng is a compromised algorithm that is predictable for the attacker, but still appears random. Everything will work correctly, but the attacker will be able to learn the secrets used by the user, and the user will typically not be able to tell the difference since the CDI is secret and the Ed25519 public key is not self-verifiable.
Conclusion
Remember that it is impossible to fully protect against this attack, that’s why it is merely a thought experiment, intended to be used during design of these devices. Consider an attacker that never gives you access to a good key and as a user you only ever use a malicious device. There is no way to have good security in this situation. This is not hypothetical, many well-funded organizations do what they can to derive people from having access to trustworthy security devices. Philosophically it does not seem possible to tell if these organizations have succeeded 100% already and there are only bad security devices around where further resistance is futile, but to end on an optimistic note let’s assume that there is a non-negligible chance that they haven’t succeeded. In these situations, this threat model becomes useful to improve the situation by identifying less good designs, and that’s why the design mantra of “mitigate harmful consequences” is crucial as a takeaway from this. Let’s improve the design of security devices that further the security of its users!
This is the kind of work that gets done while waiting for the build machines to attempt to reproducibly build PureOS. Unfortunately, the results is that a meager 16% of the 765 added/modifed packages are reproducible by me. There is some infrastructure work to be done to improve things: we should use sbuild for example. The build infrastructure should produce signed statements for each package it builds: One statement saying that it attempted to reproducible build a particular binary package (thus generated some build logs and diffoscope-output for auditing), and one statements saying that it actually was able to reproduce a package. Verifying such claims during apt-get install or possibly dpkg -i is a logical next step.
There is some code cleanups and release work to be done now. Which distribution will be the first apt-based distribution that includes native support for Sigstore? Let’s see.
Sigstore is not the only relevant transparency log around, and I’ve been trying to learn a bit about Sigsum to be able to support it as well. The more improved confidence about system security, the merrier!
Reflecting on this work made me realize that while the natural thing to do here was to differentiate two different apt-based distributions, I have realized the same way I did for debdistdiff that it would also be interesting to compare, say, Debian bookworm from Debian unstable, especially now that they should be fairly close together. My tooling should support that too. However, to really provide any benefit from the more complete existing reproducible testing of Debian, some further benefit from doing that would be useful and I can’t articulate one right now.
One ultimate goal with my effort is to improve trust in apt-repositories, and combining transparency-style protection a’la apt-sigstore with third-party validated reproducible builds may indeed be one such use-case that would benefit the wider community of apt-repositories. Imagine having your system not install any package unless it can verify it against a third-party reproducible build organization that commits their results in a tamper-proof transparency ledger. But I’m now on repeat here, so will stop.