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Stronger bounds on the cost of computing Gröbner bases for HFE systems

par Gorla, Elisa;Mueller, Daniela;Petit, Christophe
Référence Journal of symbolic computation
Publication Publié, 2020-04-01

Article révisé par les pairs

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Résumé :

We give upper bounds for the solving degree and the last fall degree of the polynomial system associated to the HFE (Hidden Field Equations) cryptosystem. Our bounds improve the known bounds for this type of systems. We also present new results on the connection between the solving degree and the last fall degree and prove that, in some cases, the solving degree is independent of coordinate changes.