  We provide a new proof of Maurer, Renard, and Pietzak's result that the sum
of the nCPA advantages of random permutations $P$ and $Q$ bound the CCA
advantage of $P^{-1} \circ Q$. 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 tighten 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.
