The Security of Abreast-DM in the Ideal Cipher Model

Abstract

As old as Tandem-DM, the compression function Abreast-DM is one of the most well-known constructions for double block length compression functions. In this paper, we give a security proof for Abreast-DM in terms of collision resistance and preimage resistance. The bounds on the number of queries for collision resistance and preimage resistance are given by Ω(2n). Based on a novel technique using query-response cycles, our security proof is simpler than those for MDC-2 and Tandem-DM. We also present a wide class of Abreast-DM variants that enjoy a birthday-type security guarantee with a simple proof.