Design principles for HFEV-based multivariate signature schemes

Abstract

The Hidden Field Equations (HFE) Cryptosystem as proposed by Patarin is one of the best known and most studied multivariate schemes. While the security of the basic scheme a eared to be very weak, the HFEv-variant seems to be a good candidate for digital signature schemes on the basis of multivariate olynomials. However, the currently existing scheme of this type, the QUARTZ signature scheme, is hardly used in ractice because of its oor efficiency. In this a er we analyze recent results from Ding and Yang about the degree of regularity of HFEv-systems and derive from them design principles for signature schemes of the HFEv-type. Based on these results we propose the new HFEv-based signature scheme Gui, which is more than 100 times faster than QUARTZ and therefore highly com arable with classical signature schemes such as RSA and ECDSA.