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

Abstract : 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.
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https://hal.inria.fr/hal-02912309
Contributor : Alain Monteil <>
Submitted on : Wednesday, August 5, 2020 - 4:00:00 PM
Last modification on : Wednesday, August 5, 2020 - 5:14:12 PM
Long-term archiving on: : Monday, November 30, 2020 - 3:01:26 PM

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  • HAL Id : hal-02912309, version 1

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Elisa Gorla, Daniela Mueller, Christophe Petit. Stronger bounds on the cost of computing Gröbner bases for HFE systems. MEGA 2019 - International Conference on Effective Methods in Algebraic Geometry, Jun 2019, Madrid, Spain. ⟨hal-02912309⟩

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