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I've seen questions where people have asked if AES-CBC mode is vulnerable to chosen cipher-text attacks if the IV is predictable.

But is it guaranteed to be secure against chosen cipher text attacks if the IV is not predictable?

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No, unpredictable IV won't solve the problem (cihpertext is malleable).

One example to demonstrate the insecurity:

in the CCA game, the adversary sends $m_0,m_1$ to the challenger, and receive back the ciphertext $c=(r,s)=(r, E_k(r\oplus m_b)$), where $r$ is the random IV.

Then the adversary sends $c'=(r\oplus t,s)$ where $t$ is a random string.

The oracle will decrypts becausee $c'\ne c$, and the adversary now gets $$ D_k(s)\oplus r\oplus t = D_{k}(E_k(r\oplus m_b))\oplus r\oplus t=m_b\oplus t $$

The adversary then compute $m_b\oplus t \oplus t =m_b$ and can decide $b$ by comparing the result with the messages it sent.

One way to obtain CCA security is to use a message authentication code and the encrypt-then-mac procedure (authenticated encryption).

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