A Probabilistic Proof of the nCPA to CCA Bound

11/15/2022

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by   Ben Morris, et al.

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We provide a new proof of Maurer, Renard, and Pietzak's bound of the CCA advantage of P^-1∘ Q by the nCPA advantages of P and Q. Our proof uses probability directly, as opposed to information theory, and has the advantage of providing an alternate sufficient condition of low CCA advantage. Namely, the CCA advantage of a random permutation can be bounded by its separation distance from the uniform distribution. We use this alternate condition to improve the best known bound on the security of the Swap or Not shuffle in the special case of having fewer queries than the square root of the number of cards.