Let $ F $ be a PRF and $ G$ be a PRG with expansion factor $n \to n +1 $ For the following encryption scheme, decide whether it has indistinguishable encryptions and whether it is CPA-secure.

Given $k \in \{0,1\}^n $, to encrypt $m \in \{0,1\}^{2n} $, parse $ m $ as $ m_1\|m_2 $ with $|m_1| = |m_2| = n $ then choose uniform $ r \in \{0,1\}^n$ and output the ciphertext $\langle r, m_1 \oplus F_k(r), m_2 \oplus F_k(r+1) \rangle $

I would need help to give a proof about if this ES is CPA secure or not, or at least some tips/ideas to try by myself first.


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