Speeding up QUAD

QUAD is a provable secure stream cipher based on multivariate polynomials which was proposed in 2006 by Berbain, Gilbert and Patarin [1]. In this paper we show how to speed up QUAD over GF(256) by a factor of up to 5.8. We get this by using structured systems of polynomials, in particular partially circulant polynomials and polynomials generated by a linear recurring sequence (LRS), instead of random ones. By using this strategy, we can also reduce the system parameter of QUAD by about 99 %. We furthermore present experiments, which seem to show that using structured polynomials of this special choice does not influence the security of QUAD.