Algebraic cryptanalysis of HFE and Filter Generators.
Résumé
HFE (Hidden Fields Equations) is a public key cryptosystem using polynomial operations over finite fields. It has been proposed by Jacques Patarin at Eurocrypt 96 following the ideas of Matsumoto and Imai. It has long been regarded as a very promising cryptosystem because it can be used to produce signatures as short as 128, 100 and even 80 bits. HFE gives the shortest (unbroken) signatures known except with the recent McEliece signature scheme. Without the secret univariate polynomial it is necessary to solve polynomial system of equations. One of the most efficient tool for solving algebraic system is Gröbner bases