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 ] 1 We are not claiming that polynomial-based compression functions provide significant practical advantages over the existing rate 1=2 schemes, since field multiplication is not trivial to implement. In this paper, we only focus on the theoretical aspects in terms of "rate." For a software benchmark for a wide range of blockcipher-based hash functions including a blockcipher-based variant of a polynomial-based compression function, we refer to [5].