Security of truncated random permutations

Abstract

Here, we address truncated random permutations as a pseudorandom function (PRF). We prove the security of truncated random permutations as PRFs and improve previous results. More specifically, we improve the $\chi^2$ method to be applicable in the indifferentiability model and to prove the security bound of truncated random permutations in the indistinguishability model and the indifferentiability model. We also propose improved generic attacks on truncated random permutations in the indifferentiability model. We compare our results with previous results.