Skip to Main content Skip to Navigation
Theses

Non linéarité parfaite généralisée au sens des actions de groupe, contribution aux fondements de la solidité cryptographique

Abstract : Notions of perfect nonlinearity and bent functions are particularly relevant in cryptography because they formalize maximal resistances against the very efficient differential and linear attacks. This thesis is then dedicated to the study of these cryptographic objects. We naturally interpret these notions in a more abstract and theoretical framework essentially by the substitution of the translations which occur in the definition of perfect nonlinearity by any group action. The properties of these actions as fidelity and regularity allow to decline this new concept into several alternatives. We develop as well its dual characterization using the Fourier transform that leads to an adapted notion of bentness. In particular in the case of a non Abelian group action, we use the linear representations theory to establish a dual matrix version. Furthermore, following the same principle, we generalize those combinatorics objects called difference sets which characterize perfect nonlinearity of functions with values in the finite field with two elements. This allows us to exhibit some constructions of functions which satisfy our generalized criteria, in particular in those cases where bent functions in the usual sense do not exist.
Document type :
Theses
Complete list of metadatas

https://tel.archives-ouvertes.fr/tel-00010216
Contributor : Laurent Poinsot <>
Submitted on : Tuesday, September 20, 2005 - 12:39:55 PM
Last modification on : Thursday, March 5, 2020 - 4:23:04 PM
Long-term archiving on: : Friday, April 2, 2010 - 10:19:33 PM

Identifiers

  • HAL Id : tel-00010216, version 1

Collections

Citation

Laurent Poinsot. Non linéarité parfaite généralisée au sens des actions de groupe, contribution aux fondements de la solidité cryptographique. Mathématiques [math]. Université du Sud Toulon Var, 2005. Français. ⟨tel-00010216⟩

Share

Metrics

Record views

399

Files downloads

908