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

## Abstract

In [6] T. Matsumoto and H. Imai described a new asymmet- ric algorithm based on multivariate polynomials of degree two over a finite field, which was subsequently broken in [9]. Here we present two new families of Asymmetric Algorithms that so far have resisted all at- tacks, 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 sig- natures, encryption or authentication in an asymmetric way, with very short signatures and short encryptions of short messages. IP can be used for signatures and for zero knowledge authentication.

An extended version of this paper can be obtained from the author. Another way to repair the Matsumoto-Imai Algorithm will be presented in [10].

## Keywords

Finite Field Authentication Scheme Affine Transformation Asymmetric Cryptography Hide Field Equation## References

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