signing section draft

src/protocol/notarization/signing.md

@@ -1,16 +1,45 @@
-# Signing the session header.
+# Signing the session header
 
-The `Notary` signs the following artifacts called the `Session Header` which are required for the `User` to prove to a third-party `Verifier` the authenticity of the plaintext from the TLS session.
-We emphasize that throughout the whole TLSNotary protocol, the `Notary` never learns the plaintext neither learns what domain the `User` communicates with.
+The `Notary` signs the following artifacts called a `Session Header` thereby attesting to the authenticity of the plaintext from a TLS session. The `User` can then use a signed `Session Header` to prove data provenance to a third-party `Verifier`.
 
-// taken from tlsn/tlsn-core/src/session/header.rs
 
-// TODO: will explain the meaning of each
+We emphasize that throughout the whole TLSNotary protocol (including this signing stage), the `Notary` does not learn either the plaintext or the server which the `User` communicated with.
 
-- encoder_seed:  
-- merkle_root
-- sent_len
-- recv_len
-- time
-- server_public_key
-- handshake_commitment
+
+
+A `Session Header` consists of:
+
+### Server ephemeral public key
+
+In TLS the session keys are derived from a one-time per-TLS-session ephemeral public key. The server uses its certificate to sign this key and sends the key and the signature to the `User`.
+
+Since the `Notary` does not know the signature or the certificate, he is unaware of the identity of the server. The `User`, on the other hand, can reveal the server's identity to a `Verifier` by revealing the signature and the certificate.
+
+### Plaintext encodings
+ 
+Encodings used by the Notary to encode the plaintext.
+
+Note that the `Notary` did not learn the actual plaintext but sent these encodings to the `User` using [Oblivious Transfer](/mpc/oblivious_transfer.md).
+
+For efficiency, the `Notary` used a small PRG seed to generate random plaintext encodings.
+
+### Root of the Merkle tree of commitments
+
+The root of the Merkle tree where each leaf is the User's commitment to plaintext encodings.
+
+### Commitment to the TLS handshake data
+
+This is the `User`'s commitment to miscellaneous public data of the TLS handshake, namely:
+- server certificate chain
+- signature over the `server ephemeral public key` made using `server certificate chain`
+- client random
+- server random
+
+
+### Time
+
+The time when the Notary signed the `Session Header`.
+
+### Total bytes sent and received
+
+The total amount of application data bytes which the `User` sent to and received from the server.