Efficient implementations of multivariate quadratic systems

Abstract

This work investigates several methods to achieve efficient software implementations of systems of multivariate quadratic equations. Such systems of equations appear in several multivariate cryptosystems such as the signature schemes SFLASH, Rainbow, the encryption scheme PMI+, or the stream cipher QUAD. We describe various implementation strategies. These strategies were combined to implement the public computations of three asymmetric schemes as well as the stream cipher QUAD. We conducted extensive benchmarks on our implementations which are exposed in the final section of this paper. The obtained figures support the claim that when some care is taken, multivariate schemes can be efficiently implemented in software. © Springer-Verlag Berlin Heidelberg 2007.