A Probabilistic Proof of the nCPA to CCA Bound

TL;DR

This paper offers a new probabilistic proof relating the advantages of certain cryptographic permutations, providing an alternative bound on CCA security that improves understanding of the swap-or-not shuffle's security with limited queries.

Contribution

It introduces a probabilistic proof method for the nCPA to CCA bound, offering a new sufficient condition based on separation distance, and tightens security bounds for the swap-or-not shuffle.

Findings

Probabilistic proof of nCPA to CCA bound.

Bound on CCA advantage via separation distance.

Improved security bounds for swap-or-not shuffle with fewer queries.

Abstract

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.