MiTM on RSA public key encryption a) Alice just generated a new pair of public and private RSA keys (pkA , skA ) = ((N, e), d) and would like to start a private conversation with Bob. How can Alice interact with Bob and exchange a symmetric key? Describe a key exchange protocol between them which is secure against an eavesdropper adversary.
b) Fully specify a Man-in-The-Middle (MiTM) attack attack against the key exchange protocol you described above.
c) Assume now that Alice and Bob are very old friends and that Bob already knows a public key pkA owned by Alice.  How can you improve the above protocol in such a way that Bob can detect the presence of a MiTM? Can Alice also detect the presence of a MiTM?

In part a) I defined a protocol using the idea behind D Hellman, so this is vulnerable to MiTM.
However, I dont know how to work out part c
You need an authentic channel from Alice to Bob to get a secret channel from Bob to Alice. This assumption is missing in a), so anyone in control of the communication channel can play man in the middle on any protocol.

As long you don't have a secret channel from Alice to Bob or an authentic channel from Bob to Alice, Alice will never (= for any protocol) be sure who is sending her the secret messages.

See U. Maurer, P. Schmid, A calculus for secure channel establishment in open networks, ESORICS' 94, LNCS 875, pp 175-192.