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