Assume that a scheme used to secure a specific system $Π=(Gen,Enc,Dec)$ which is thought have indistinguishable multiple encryption in the presence of an eavesdropper.

For any adversary $A$ that can break the scheme with

$\Pr[\text{PrivKmult}^A_Π(n) = 1] \leq 1/2 + \text{negl}(n)$

some PPT adversary $x$ breaks this scheme with probability

$\Pr[\text{PrivKmult}^x_Π(n) =1] \leq 1/2 + n^{-3}$.

Can I prove that any other PPT adversary can break this scheme with probability greater than $X$? If yes how can I do that?


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