RE ⇒ Statistically rerandomizable encryption

Fully-black-box reduction · standard model · folklore · security loss: none

Statement

If $\mathsf{ReRand}(\mathsf{pk},c)$ is distributed exactly as $\mathsf{Enc}(\mathsf{pk},m)$ for every $c$ in the support of $\mathsf{Enc}(\mathsf{pk},m)$, as for rerandomizable encryption, then conditioned on $c\leftarrow \mathsf{Enc}(\mathsf{pk},m)$ the rerandomized ciphertext is a fresh encryption independent of $c$, so the scheme is statistically rerandomizable with statistical distance $0$ — folklore.