Define the injective map $\phi: \Omega\rightarrow \mathbb{N}$, such that $\Omega=\mathcal{A}^n$ denotes the set of all strings of length $n\in\mathbb{N}^*$ from an alphabet $\mathcal{A}$ of elements $a_i$ and length $m$. Define a string (to be encoded) of finite length, $\mathcal{M}\in\Omega$. A cipher text $\mathcal{C}$, of arbitrary length $\ell$, exists and may be generated from the probability distribution for all positive integers $i\leq m$ \begin{equation} p\left(a_i\right)=E\left(\phi\left(\mathcal{M}\right),\alpha,D\left(\mathcal{C},s,k\right)\right). \end{equation} Let the set of all ciphertexts $\bf{C}$ be generated from the set of all probability distributions $\bf{p}$$\left(a_i\right)/\sim$, such that there exists some $D'\neq D$ or $k'\neq k$ whereby \begin{equation*} E\left(\phi\left(\mathcal{M}\right),\alpha,D\left(\mathcal{C},s,k\right)\right)\sim E\left(\phi\left(\mathcal{M}'\right),\alpha,D'\left(\mathcal{C},s,k'\right)\right), \end{equation*} if and only if $\mathcal{M}\neq\mathcal{M}'$. The previous relation means that if the message $\mathcal{M}$ is changed, then there exists a decryption function $D'$ or key $k'$ such that the ciphertext is the same.
If such a system existed what would be its security? Since knowledge of the probability distribution provides no information of $\mathcal{M}$, I would expect it to be perfectly secure. If so, could this be shown using mutual information?
By the way, the distribution of ciphertext characters converges to $p(a_i)$ as $\ell\rightarrow\infty$, so the equivalence is at least asymptotically true. I would be grateful for any help.