Hello, please write with full explanation because I will be using it for understanding and revision purposes. This regards Computer Security. Thank you.

Suppose that someone suggests the following way to confirm that Alice and Bob are both in possession of the same secret key: Alice creates a random bit string the length of the key, XORs it with the key, and sends the result over the channel. Bob XORs the incoming block with the key (which should be the same as Alice's key) and sends it back. Alice checks, and if what she received is her original random string, she has verified that Bob has the same secret key, yet neither of them has ever transmitted the key. Explain the security problem with this suggestion