Even though the Prover can prove data provenance directly to the Verifier, in some scenarios it may be beneficial for the Verifier to outsource the verification of the TLS session to a trusted Notary as explained here.

As part of the TLSNotary protocol, the Prover creates authenticated commitments to the plaintext and has the Notary sign them without the Notary ever seeing the plaintext. This offers a way for the Prover to selectively prove the authenticity of arbitrary portions of the plaintext to an application-specific Verifier later.

Please refer to the Commitments section for low-level details on the commitment scheme.

Signing the Session Header

The Notary signs an artifact known as a Session Header, thereby attesting to the authenticity of the plaintext from a TLS session. A Session Header contains a Prover's commitment to the plaintext and a Prover's commitment to TLS-specific data which uniquely identifies the server.

The Prover can later use the signed Session Header to prove data provenance to an application-specific Verifier.

It's important to highlight that throughout the entire TLSNotary protocol, including this signing stage, the Notary does not gain knowledge of either the plaintext or the identity of the server with which the Prover communicated.