> Focusing on the HTTPS ecosystem, including components such as the TLS protocol and its underlying cryptographic algorithms, Project Everest began in 2016 aiming to build and deploy formally verified implementations of several of these components in the F* proof assistant.
> […] Code from HACL*, ValeCrypt and EverCrypt is deployed in several production systems, including Mozilla Firefox, Azure Confidential Consortium Framework, the Wireguard VPN, the upcoming Zinc crypto library for the Linux kernel, the MirageOS unikernel, the ElectionGuard electronic voting SDK, and in the Tezos and Concordium blockchains.
S2n is Amazon's formally verified TLS library. https://en.wikipedia.org/wiki/S2n
IDK about a formally proven PKIX. https://www.google.com/search?q=formally+verified+pkix lists a few things.
A formally verified stack for Certificate Transparency would be a good way to secure key distribution (and revocation); where we currently depend upon a TLS library (typically OpenSSL), GPG + HKP (HTTP Key Protocol).
Fuzzing on an actual hardware - with stochastic things that persist bits between points in spacetime - is a different thing.