Hi Nadim, Nathanael,

Thanks for sharing the paper and the models. One implementation-facing
angle that may be worth spelling out, even if it is outside what the
symbolic model can prove, is which negative tests would best catch
hybrid-specific integration mistakes.

For example, it would be useful for implementers to have test cases that
exercise:

   - transcript binding of the complete selected key-share / KEM material,
   including group identifiers;
   - rejection when one component is malformed, absent, or associated with
   a different negotiated group;
   - no derivation of an application secret unless both advertised
   components are present and accepted under the negotiated hybrid group;
   - downgrade/confusion cases where a peer attempts to make a hybrid
   exchange look like a standalone KEM exchange, or vice versa.

That would not change the proof result, but it may help bridge the gap
Nathanael mentioned: the symbolic model says what must be true for hybrid
robustness, while implementers still need fairly concrete checks to avoid
accidentally losing one side of the hybrid binding.

Best,
Songbo Bu

On Thu, 4 Jun 2026 06:36:21 -0600, Nathanael Ritz [email protected]
wrote:

Hi Nadim,

Thank you for your recent updates to reftls and putting together this
paper. The outcome also seem to align with my own WIP (although my hybrid
modelling attempt dies to state explosion right now). Even with what I had
put together myself, the reality was that I could see PQ-KEMs act as single
points of failure just like DHE if standard cryptographic assumptions could
not hold. So the conclusion your paper makes, regarding the strict
improvement that a hybrid could provide makes sense.

Of course, symbolic models cannot reason over implementation challenges and
so the next question may be fall more to pure speculation. I am curious if
you might anticipate potential implementation errors moving from classical
DHE or pure PQ-KEM towards a hybrid that risks compromising both methods
due to complexity?

Again, as I understand, symbolic models can merely affirm the consequences
of dual compromise, but can’t help us reason about implementation
challenges, I get that. So this question is more or less probing your
personal PoV as an applied cryptographer

Thanks again,

Nathanael

On Thu, Jun 4, 2026 at 5:52 AM 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

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