> I would pair secp384r1 with Kyber768 for completely different reasons:
> Kyber768 is what the team kyber recommends.
Agreed.

> I don't think there are very good reasons for NIST curves here outside
> wanting CNSA1 compliance, and for that you need secp384r1 classical
> part. And for that, I would pick secp384r1_kyber768.
> 
>From my perspective, the two reasons for including a NIST curves are:
1. To have an option for those who require FIPS compliance. In a short term at 
least one key agreement scheme should be FIPS-approved. In the long term both 
of them should be fips-approved. That way, in case security of Kyber768 falls 
below 112-bits or simply implementation is broken, one can still run key 
agreement in FIPS compliant manner. In the end, the ultimate goal of hybrid-tls 
draft is to ensure that at least one of the schemes provides security if the 
other gets broken. Would be good to use this in FIPS context also.
2. NIST curves are more often implemented in HW than Curve25519. When working 
with chips like ATECC608B, one ideally only adds SW-based Kyber and can reuse 
existing HW-based ECDH. Such migration is simpler, less risky and 
time-consuming than adding SW-based X25519.

To accelerate migration, the hybrid-tls draft should move forward rather 
quickly and be useful variety of use-cases. Hence, I suggest we assign two 
codepoints one for X25519-Kyber768 and the other for ECDH/p256-Kyber768. X25519 
and P256 provide same security level, from my old days in Cloudflare I remember 
both schemes were used quite often in TLS, so I hope this choice is not to 
controversial.

Regarding CNSA, I've no experience with national security systems, but does it 
actually allows to use hybrid schemes? it seems to me that neither 1.0 nor 2.0 
allows usage of hybrid schemes (SP800-56C is mentioned but in regards to ECDH, 
not KDF). Maybe those needs can be addressed at later stage?

Kind regards,

---
Kris Kwiatkowski
Staff Cryptography Architect
PQShield

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