The Equivalence of APN and AB Functions and Their Generalizations - Couverture souple

Budaghyan, Lilya

 
9786202311496: The Equivalence of APN and AB Functions and Their Generalizations
Couverture souple
ISBN 10 : 6202311495 ISBN 13 : 9786202311496
Editeur : Scholars' Press, 2018

Synopsis

Vectorial Boolean functions are used in cryptography, in particular in block ciphers. An important condition on these functions is a high resistance to the differential and linear cryptanalyses, which are the main attacks on block ciphers. The functions which possess the best resistance to the differential attack are called almost perfect nonlinear (APN). Almost bent (AB) functions are those mappings which oppose an optimum resistance to both linear and differential attacks. Up to this work only a few classes of APN and AB functions had been known and all these classes happened to be extended affine equivalent (EA-equivalent) to power functions. In this work we constructed the first classes of APN and AB polynomials EA-inequivalent to power mappings by using the equivalence relation (which we call CCZ-equivalence). Moreover we show that the number of different classes of AB polynomials EA-inequivalent to power functions is infinite. One of the constructed functions serves as a counterexample for a conjecture about nonexistence of AB functions EA-inequivalent to permutations.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

Vectorial Boolean functions are used in cryptography, in particular in block ciphers. An important condition on these functions is a high resistance to the differential and linear cryptanalyses, which are the main attacks on block ciphers. The functions which possess the best resistance to the differential attack are called almost perfect nonlinear (APN). Almost bent (AB) functions are those mappings which oppose an optimum resistance to both linear and differential attacks. Up to this work only a few classes of APN and AB functions had been known and all these classes happened to be extended affine equivalent (EA-equivalent) to power functions. In this work we constructed the first classes of APN and AB polynomials EA-inequivalent to power mappings by using the equivalence relation (which we call CCZ-equivalence). Moreover we show that the number of different classes of AB polynomials EA-inequivalent to power functions is infinite. One of the constructed functions serves as a counterexample for a conjecture about nonexistence of AB functions EA-inequivalent to permutations.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Scholars' Press
Date d'édition
2018
Langue
anglais
ISBN 10 
6202311495
ISBN 13 
9786202311496
Reliure
Broché
Nombre de pages
92
Coordonnées du fabricant
non disponible
Personne responsable
non disponible

Autres éditions populaires du même titre

9783836494106: The Equivalence of Apn and Ab Functions and Their Generalizations

Edition présentée

ISBN 10 :  3836494108 ISBN 13 :  9783836494106
Editeur : VDM Verlag Dr. Mueller E.K., 2008
Couverture souple