I know the definitions of both of the securities (against message recovery and semantic), but I don't know how to actually build a cipher that meets these conditions, I mean, I don't know how to define "let $\mathcal{E} = (E,D)$ where $E(k,m) = \;...$ and you can see that it is secury against MR because of ..., but is not semantically secure because of ..." yet.
I would like to know, at least, how to start building such cipher.
Message recovery attack:
Let $\mathcal{E} = (E,D)$ be a cipher. The challenger chooses a random $m$ from message space $\mathcal{M}$, a random $k$ from key space $\mathcal{K}$, computes a random $c \xleftarrow[]{\text{R}} E(m,k)$ and sends $c$ to the attacker.
The attacker, then, sends $\hat{m}$ back to the challenger.
The attacker wins the game if $\hat{m} = m$. Let $p$ be the probability $Pr[\hat{m} = m]$.
The advantage of this attacker is $\Big\vert \; p - \frac{1}{\Vert \mathcal{M} \Vert} \; \Big\vert$
The cipher is secure against MR attack if this advantage is negligible for all efficient attackers.