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

  • Jacques Patarin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1070)

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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Jacques Patarin
    • 1
  1. 1.CP8 TransacLouveciennes CedexFrance

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