Let $F : \{0,1\}^n \times \{0,1\}^n \rightarrow \{0,1\}^n $ be a PRF. And let the encryption function be $Enc{_k}(m) = r\mathbin\| (F{_k}(m\bigoplus r)$ , r being a random value.

Im trying to proof that this scheme is not CCA-secure, however I'm already failing at finding a correct decryption. Since a PRF is not invertible, how is it possible to recover the $m$ from the ciphertext?

  • 2
    $\begingroup$ What you have there can in general not be decrypted. Where did you find this supposed scheme? Are you sure it's not supposed to be $(r,F_k(r) \oplus m)$? $\endgroup$
    – Maeher
    Jul 11, 2020 at 20:24
  • $\begingroup$ Hint: Do you understand why CBC mode is not CCA secure? Notice that this scheme is CBC mode restricted to a single plaintext block (assuming F is a PRP). $\endgroup$
    – Mikero
    Oct 12, 2021 at 2:09


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