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Cipher block chaining (CBC) is a method for encrypting large amounts of data with a block cipher that can only encrypt fixed length plaintexts. When used with an unpredictable initialization vector (IV), it is secure against chosen plaintext attacks (CPA-secure).

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CBC-MAC insecure with random IV

Let $m_1 = 0^n, IV_1 = 011$ then, \begin{align}&F_k(m_1 \oplus IV_1)\\ =& F_k(0^n \oplus 011)\\ =& F_k(011).\end{align} Now, we can construct a different message $m_2 = 010$ and a valid tag for it in …
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