# Strong pseudo random permutation implies CCA-security

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 $$c:=\operatorname{F}(k,r\mathbin\|m)$$. Prove that this scheme is $$\text{CCA}$$-secure.

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

• Question: show that this scheme is CCA-secure for message length $n/2$ – kelalaka Jan 17 '19 at 18:51
• There is a similar question here. You might find the comments very helpful for your cause. – kelalaka Jan 17 '19 at 19:46
• – SEJPM Oct 26 '19 at 22:38