I'm trying to do the ex 11.15 of the Katz-Lindell book.
Consider the RSA-based encryption scheme in which a user encrypts a message $m ∈ $ {$0, 1$}$^l$ with respect to the public key $(N, e)$ by computing $m' := H(m)||m$ and outputting the ciphertext $c' := m'^e modN $. $(H : $ {$0, 1$}$^l → ${$0, 1$}$^n$ and assume $l + n < ||N||$, $||N||$ is the bit-length of N). The receiver recovers $m'$ in the usual way and verifies that it has the correct form before outputting the $l$ least-significant bits as $m$. Prove or disprove that this scheme is CCA-secure if $H$ is modeled as a random oracle.
I know that this scheme isn't CCA-secure because it's deterministic.
But I tried to transform the cyphertext without success, because if I modify the second part of $m'$ let's say computing $m''$, using another cyphertext and multiplying it to $c'$, then I need $H(m'')$ to compose a correct cyphertext but since I don't know $m'$ I'm not able to query $H(m'')$.