Efficient Public Key Generation for Multivariate Cryptosystems

Asymmetric cryptographic systems using multivariate polynomials over finite fields have been proposed several times since the 1980s. Although some of them have been successfully broken, the area is still vital and promises interesting algorithms with low computational costs, short message, and signature sizes. In this paper, we present two novel strategies “base transformation” and “adapted evaluation” for the generation of the public key in such schemes. We demonstrate both with the example of the Hidden Field Equations (HFE) system and outline how they can be adapted to similar systems. In addition, we compare the running time of the previously known “polynomial interpolation” with our new developments by empirical studies. We conclude that the running time of polynomial interpolation is approximately 30% higher than for base transformation.