A certificate, in itself, (RFC 5280) does not seem to have any indicator of what algorithm was used (for example the argument to openssl req -newkey) to create the public and private keys ("Certificate Key Type"). That surprised me. A certificate has a "signature algorithm" field but that is the algorithm used by the CA to sign the certificate. Question 1: Is this observation correct? If so, why is the algo/key type of the certificate itself not in the certificate? After all its type too is required when used.
TLS 1.2 (RFC 5246). The Cipher Suite sent by the Client in the Client Hello has the Cipher Suite in the following form: TLS_part1_WITH_... I think only part1 is relevant to the derivation of the pre_master_secret. The part that follows the WITH is for securing the actual data. Question 2: Is this correct?
part1 is called "key exchange algorithm" (Section 188.8.131.52. Client Hello)
"The cipher suite... contains the combinations of cryptographic algorithms supported by the client in order of the client's preference (favorite choice first). Each cipher suite defines a key exchange algorithm..." . A Client Hello can have a "signature_algorithms" extension. "The client uses the "signature_algorithms" extension to indicate to the server which signature/hash algorithm pairs may be used in digital signatures." (Section 184.108.40.206.1.). For a key exchange, both algos, a signature and hash, are to be negotiated and if there is no signature_extension sent, then the hash is implied from the "key_exchange_algorithm" alone (220.127.116.11.1). So the implied hash algo is not based upon the type of Certificate.
Section 7.4.2. establishes some relations between the negotiated key_exchange_algorithms and the Certificate Type. The RFC lists a table with the two columns. One of the rows from the above mentioned table is:
DHE_RSA RSA public key; the certificate MUST allow the ECDHE_RSA key to be used for signing (the digitalSignature bit MUST be set if the key usage extension is present) with the signature scheme and hash algorithm that will be employed in the server key exchange message. Note: ECDHE_RSA is defined in [TLSECC].
Question 3: (Edited: Earlier mis-numbered it as Question 5). I think understanding this is the biggest hurdle for me. I understand the importance of Ephemerial keys (ECDHE vs. ECDH). The "RSA public key" refers to the key type in the certificate. Is that correct? Does the RSA in "DHE_RSA" and "ECDHE_RSA" also refer to the type of the key in the certificate? Is this key only used for authenticating the server? After all, ECDHE by itself, even without a certificate, can generate a common secret known only to the two parties but not to MiM. Can someone explain the role of the Certificate in the various stages of establishing the pre-master-secret?