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Asymptotic Behaviour of the Index of Regularity of Semi-Regular Quadratic Polynomial Systems

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Abstract

We compute the asymptotic expansion of the index of regularity for overdetermined quadratic semi-regular sequences of algebraic equations. This implies bounds for the generic complexity of Gr ̈obner bases algorithms, in particular the F 5 [Fau02] algorithm. Bounds can also be derived for the XL [SPCK00] family of algorithms used by the cryptographic community.
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hal-01486845 , version 1 (10-03-2017)

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  • HAL Id : hal-01486845 , version 1

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Magali Bardet, Jean-Charles Faugère, Bruno Salvy. Asymptotic Behaviour of the Index of Regularity of Semi-Regular Quadratic Polynomial Systems. MEGA 2005 - 8th International Symposium on Effective Methods in Algebraic Geometry, May 2005, Porto Conte, Alghero, Sardinia, Italy. pp.1-17. ⟨hal-01486845⟩
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