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I am searching for a key exchange protocol that makes use of certificates. I already came across protocols like Authenticated Diffie-Hellman key exchange, but this protocol use public/private key pairs that are discussed beforehand. To solve this they have a CA with can sign the authenticity of the public key.

However, the protocol I am looking for would only be able to send a signed certificate about certain properties holding. Is there any way to set of secure communication based on these certificates? (With secure communication I mean communication between parties who have proved to satisfy the demanded properties.)

Specifically, this is in the context of local/remote attestation, so the certificates would proof that a program has a certain hash.

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