Multiproperty-Preserving Domain Extension Using Polynomial-Based Modes of Operation

Abstract

In this paper, we propose a new double-piped mode of operation for multiproperty-preserving domain extension of message authentication codes (MACs), pseudorandom functions (PRFs), and pseudorandom oracles (PROs). Our mode of operation performs twice as fast as the original double-piped mode of operation of Lucks while providing comparable security. Our construction, which uses a class of polynomial-based compression functions proposed by Stam, makes a single call to a $3n$ -bit to $n$ -bit primitive $f_{1}$ at each iteration and uses a finalization function $f_{2}$ at the last iteration, producing an $n$ -bit hash function $H[f_{1},f_{2}]$ satisfying the following properties. $H[f_{1},f_{2}]$ is unforgeable up to $O(2^{n}/n)$ query complexity as long as $f_{1}$ and $f_{2}$ are unforgeable.