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Let $F$ be a strong pseudo random permutation and define a fixed-length encryption scheme $(\operatorname{Enc,Dec})$ as follows:

On input $m \in \{0,1\}^{\frac{n}{2}}$ and key $k\in \{0,1\}^{n}$, algorithm $\operatorname{Enc}$ chooses a uniform string $r \in \{0,1\}^{\frac{n}{2}}$ of length $r/2$ and computes $c:=\operatorname{F}(k,r\|m)$. Prove that this scheme is $\text{CCA}$-secure.

How can I show that strong Pseudo random permutation implies $\text{CCA}$ security? I don't know how to do the reduction.

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  • $\begingroup$ Question: show that this scheme is CCA-secure for message length $n/2$ $\endgroup$ – kelalaka Jan 17 at 18:51
  • $\begingroup$ There is a similar question here. You might find the comments very helpful for your cause. $\endgroup$ – kelalaka Jan 17 at 19:46

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