I have an interesting question about mutual-authentication with a symmetric key.

Question

I have an interesting question about mutual-authentication with a symmetric key. Is this scheme possible and secure? And is this scheme a mutual-authentication scheme?

Alice -------"Im Alice"--------> Bob
<---------E(R,K)----------
----------E(R+1,K)------->

I think it is secure, because Bob and Alice shares different messages (R+1 != R). And nobody else could read the symmetric key k, because only Alice and Bob shares it to encrypt and decrypt. But I don't know if it's possible to do the 1st step that says "Im Alice" without a R.

Do you know if it's possible?

Explanation / Answer

Simple answer to your question: do not design your own protocol, it will not be secure.

Longer answer: it is not secure for general use. Problems off the top of my head:

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