On the last fall degree of zero-dimensional Weil descent systems

摘要

In this article we will discuss a mostly theoretical framework for solving zero-dimensional polynomial systems. Complexity bounds are obtained for solving such systems using a new parameter, called the last fall degree, which does not depend on the choice of a monomial order. The method is similar to certain MutantXL algorithms, but our abstract formulation has advantages. For example, we can prove that the cryptographic systems multi-HFE and HFE are insecure.