Alice proposes the following method to verify that she and Bob share the same AES-128 key. Alice generates a 128-bit binary string r using BBS, encrypts r, and sends the ciphertext block rₐ ​= Eₖₐ(r) to Bob, where E is the AES-128 encryption algorithm and KA​ is Alice's AES-128 encryption key. Bob decrypts rₐ​ to get r′ = DKB​​(rA​) and sends r′ to Alice, where D is the AES-128 decryption algorithm and KB is Bob's AES-128 encryption key. Alice checks whether r′=r. If so, then Kₐ = KB​. Is this protocol secure? Justify your answer.



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