Clarifying this (having received emails misinterpreting my previous email), I’d 
like to point that the conclusion of the formal analysis very strongly supports 
the case for hybrids over pure ML-KEM.

This is clearly noted in the abstract and the conclusions, and is very clearly 
summarized in Table 2 on page 10.

Nadim Kobeissi
Symbolic Software • https://symbolic.software

> On 4 Jun 2026, at 5:28 PM, Nadim Kobeissi <[email protected]> wrote:
> 
> Hi Bas,
> 
> You’re most welcome, respected sir. It was a pleasure to work on this and I 
> certainly hope that I was able to provide something of value to this working 
> group. Also, I laughed so hard while writing the introduction that my sides 
> literally hurt. This was the reward I gave myself for the effort spent on 
> this.
> 
>> Would you agree that this can be summarized as: our existing informal 
>> understanding is now formalized.
> 
> Yes. I suspect the question behind your question is: can we lay to rest the 
> concerns behind draft-usama-tls-risks-of-mlkem. My answer is “yes” to both 
> your question and my imagined one.
> 
> Onward!
> 
> Nadim Kobeissi
> Symbolic Software • https://symbolic.software
> 
>> On 4 Jun 2026, at 5:25 PM, Bas Westerbaan <[email protected]> wrote:
>> 
>> Thanks for doing this, Nadim!
>> 
>> Would you agree that this can be summarized as: our existing informal 
>> understanding is now formalized.
>> 
>> Best,
>> 
>>  Bas
>> 
>> On Thu, Jun 4, 2026 at 1:53 PM Nadim Kobeissi <[email protected]> 
>> wrote:
>>> Hi everyone,
>>> 
>>> Two post-quantum upgrades to TLS 1.3 are being standardized in parallel: a 
>>> hybrid key exchange (already deployed) that runs an elliptic-curve 
>>> Diffie-Hellman exchange alongside ML-KEM, and a standalone mode that uses 
>>> ML-KEM on its own. The Internet-Draft draft-usama-tls-risks-of-mlkem points 
>>> out that the machine-checked symbolic proofs of TLS 1.3 rely on the 
>>> commutativity of Diffie-Hellman, which ML-KEM does not share: a key 
>>> encapsulation mechanism is asymmetric, one endpoint generating a key pair 
>>> and the other encapsulating against it. The existing proofs therefore no 
>>> longer apply, a new one is needed, and the draft argues that hybrids should 
>>> be preferred.
>>> 
>>> I’m writing in order to supply that proof. In this paper, I extend the 
>>> reftls ProVerif models with a faithful, non-commutative KEM and analyze 
>>> classical (EC)DHE, standalone ML-KEM, and the hybrid together, as unbounded 
>>> concurrent sessions against a single active attacker free to break any 
>>> cryptographic component.
>>> 
>>> The central result is a sharp and tight contrast in robustness: standalone 
>>> ML-KEM is a single point of failure, secure only while ML-KEM itself is 
>>> unbroken, whereas the hybrid stays secure as long as either of its 
>>> components survives: an attacker must break both, in one session, to learn 
>>> anything. This single point of failure reaches authentication as well as 
>>> confidentiality: with the sole key-exchange secret exposed and no secret 
>>> pre-shared key salting the key schedule, the server Finished message 
>>> becomes forgeable, so a client can complete a handshake that no server 
>>> completed, while the hybrid stays safe unless both components break.
>>> 
>>> The three modes also interoperate without ever confusing one another's 
>>> keys, so migrating from (EC)DHE to a hybrid is a strict improvement. Two 
>>> further experiments address the draft's remaining concerns: reusing an 
>>> ML-KEM key forfeits the forward secrecy that an ephemeral key preserves, 
>>> and a principal acting as both initiator and responder exposes no 
>>> role-confusion attack arising from the asymmetry. At the symbolic level, 
>>> and under stated assumptions, the analysis substantiates the draft's case 
>>> for preferring hybrid key exchange.
>>> 
>>> The paper is temporarily available here while I wait for it to be published 
>>> on ePrint (hopefully soon):
>>> https://github.com/symbolicsoft/reftls/blob/master/paper/tls-hybrid.pdf 
>>> 
>>> Once it’s on ePrint, please cite the ePrint version should you decide to 
>>> cite the paper for any future work.
>>> 
>>> The ProVerif models are available here:
>>> https://github.com/symbolicsoft/reftls/tree/master/pv
>>> 
>>> Happy to answer any questions.
>>> 
>>> Nadim Kobeissi
>>> Symbolic Software • https://symbolic.software <https://symbolic.software/>
>>> 
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