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Algebraic cryptanalysis of HFE using Gröbner bases

open access: yes, 2003
HFE (Hidden Fields Equations) is a public key cryptosystem using (multivariat- e) polynomial operations over finite fields. It has been proposed by Jacques Patarin following the ideas of Matsumoto and Imai. In this paper we present a new and efficient attack of this cryptosystem based on fast algorithms for computing Gröbner basis.
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