Question
I have a scenario where a public key is exchanged out-of-band with exactly one person $A$ and is later used in a key-exchange scheme with $A$.
Is knowledge of the public key (i.e., producing a valid encrypted message to the public key) a good authentication of $A$?
Example
Let's say Alice wants to set up a secure channel to Bob. All cryptographic primitives are assumed to be secure, including message authentication, encryption, etc. This is obviously a simplified example. I only care about the properties of $p_{BA}$.
- Bob generates a new key pair $kp_{BA}$ that is only used for this session with Alice.
- Bob shares the public key $p_{BA}$ with Alice out-of-band (such that an attacker has no way of knowing $p_{BA}$)
- Alice generates a symmetric key $k$
- Alice sends $k$ encrypted with $p_{BA}$ to Bob.
- Bob successfully decrypts $k$.
- ... they use $k$ to encrypt messages to each other.
Now does 5) imply that the sender could only have been Alice?
Does 4) give an attacker information about the nature of $p_{BA}$?