New constructions of universal hash functions based on function sums

Abstract

In this paper, we propose a generalization of the SQUARE hash function family to the function sum hash, which is based on functions with low maximal differential over arbitrary Abelian groups. These new variants allow the designer to construct SQUARE-like hash functions on different platforms for efficient and secure message authentication. A variant using functions with low algebraic degree over a finite field is also proposed which enables the user to use a shorter key. For more versatility, we also propose a trade-off between the hash key length and security bound. Finally, we show that we can use an SPN structure in the function sum hash to construct a provably secure MAC with performance which is several times faster than the traditional CBC-MAC. Moreover, there are implementation advantages like parallelizability to increase the speed further and re-use of cipher components which help save on implementation resources. © Springer-Verlag Berlin Heidelberg 2006.