Hidden Fields Equations (HFE) and Isomorphisms of Polynomials (IP): Two New Families of Asymmetric Algorithms

In [6] T. Matsumoto and H. Imai described a new asymmetric algorithm based on multivariate polynomials of degree two over a finite field, which was subsequently broken in 191. Here we present two new families of Asymmetric Algnrithrrrs t,liat so far have resisted all attacks, if properly used: Hidden Field Equations (HFE) and Isomorphism of Polynomials (IP). These algorithms can be seen as two candidate ways to repair the Matsumoto-Imai Algorithm. HFE can be used to do signatures, encryption or authenticat<ion in an asyrrirrietric way, with very short signatures and short encryptions of short messages. IP can be used for signatures and for zero knowledge aut,hent,icatinn. An extended version of this paper can be obtained from the author. Ariot,her way to repair the Matsumot,o-Irnai Algorithm will be presented in [lo].