Hidden Field Equations (HFE) and Isomorphisms of Polynomials (IP): two new Families of Asymmetric Algorithms (1996)
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BibTeX
@INPROCEEDINGS{Patarin96hiddenfield,
author = {Jacques Patarin},
title = {Hidden Field Equations (HFE) and Isomorphisms of Polynomials (IP): two new Families of Asymmetric Algorithms},
booktitle = {},
year = {1996},
pages = {33--48},
publisher = {Springer-Verlag}
}
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Abstract
In [11] T. Matsumoto and H. Imai described a new asymmetric algorithm based on multivariate polynomials of degree two over a finite field. Then in [14] this algorithm was broken. The aim of this paper is to show that despite this result it is probably possible to use multivariate polynomials of degree two in carefully designed algorithms for asymmetric cryptography. In this paper we will give some examples of such schemes. All the examples that we will give, belong to two large family of schemes: HFE and IP. With HFE we will be able to do encryption, signatures or authentication in an asymmetric way. Moreover HFE (with properly chosen parameters) resist to all known attacks and can be used in order to give very short asymmetric signatures or very short encrypted messages (of length 128 bits or 64 bits for example). IP can be used for asymmetric authentications or signatures. IP authentications are zero knowledge. Note 1 : Another title for this paper could be "How to repair Matsumoto-...
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