I am a student taking a cryptography course so forgive me if this comes off as a silly question.
This is an assignment question:
$Alice \rightarrow R \rightarrow Bob$
$Alice \leftarrow [R]B \leftarrow Bob$
$Alice \rightarrow [R+1]A \rightarrow Bob$
Why doesn't this protocol provide mutual authentication?
Here's a plausible scenario:
Alice sends $R$. Trudy intercepts it and sends it to Bob impersonating Alice. Bob sends back $R$ signed by him to Trudy. Trudy now impersonates Bob and sends $R$ with Bob's signature to Alice impersonating Bob. Alice sends $[R+1]$ signed by Alice which Trudy can now use to impersonate as Alice to Bob.
If that is a valid attack. Wouldn't this work with every protocol? After all we're merely just relaying message back and forth among the two parties.