Paper 2009/145

Security of Single-permutation-based Compression Functions

Jooyoung Lee and Daesung Kwon

Abstract

In this paper, we study security for a certain class of permutation-based compression functions. Denoted $\lp 231$ in~\cite{RS08}, they are $2n$-bit to $n$-bit compression functions using three calls to a single $n$-bit random permutation. We prove that $\lp 231$ is asymptotically preimage resistant up to $(2^{\frac{2n}{3}}/n)$ queries, adaptive preimage resistant up to $(2^{\frac{n}{2}}/n)$ queries/commitments, and collision resistant up to $(2^{\frac{n}{2}}/n^{1+\epsilon})$ queries for $\epsilon>0$.