I want to prove the following statement: There is a private-key encryption scheme that has indistinguishable encryptions in the presence of an eavesdropper, but not indistinguishable multiple encryptions in the presence of an eavesdropper.
I must say, I am struggling quite a bit studying cryptography. I mostly really want to UNDERSTAND how to start and approach this question. I have all the definitions at hand, but I just have no clue on how to start proving this.
Definition indistinguishable encryptions in the presence of an eavesdropper:
$Pr[PrivK^{eav}_{A, \Pi}(n) = 1] = \frac{1}{2} + negl(n)$
Definition indistinguishable multiple encryptions in the presence of an eavesdropper:
$Pr[PrivK^{mult}_{A, \Pi}(n) = 1] \leq \frac{1}{2} + negl(n)$
Where $PrivK^{eav}_{A, \Pi}$ is the Adversarial Indistinguishability Experiment.
I was thinking, as a first approach, of a proof by contradiction, assuming it is smaller than $\frac{1}{2} + negl(n)$. BUT, can I even do that? Is $K^{mult}_{A, \Pi}(n)$ the same as $K^{eav}_{A, \Pi}(n)$? It feels wrong to assume that.
Any help is appreciated!