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

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.
Document type :
Conference papers
Complete list of metadatas

https://hal.archives-ouvertes.fr/hal-01486845
Contributor : Lip6 Publications <>
Submitted on : Friday, March 10, 2017 - 3:06:21 PM
Last modification on : Tuesday, May 14, 2019 - 10:55:40 AM

Identifiers

  • HAL Id : hal-01486845, version 1

Citation

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⟩

Share

Metrics

Record views

80