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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 ------R--------> Bob
Alice <-----[R]B------ Bob
Alice ------[R+1]A---> 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 two parties. Is there any way I can modify this to get mutual authentication?

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