Inverting square systems algebraically is exponential

Abstract

Abstract. In this paper, we prove that the degree of regularity of the family of Square systems, an HFE type of systems, over a prime finite field of odd characteristics q is exactly q, and therefore prove that• inverting Square systems algebraically is exponential, when q = O(n), where n is the number of variables of the system.

Building a new secure variant of Rainbow signature scheme

“…The most popular one:GF (2 8 ) is our choice. (Even though current research [17] indicates an odd characteristic field provides stronger security against direct attacks for a scheme such as HFE, it does not affect our choice). Also, the required security level should be higher than 2 80 .…”