On the second-order nonlinearities of some bent functions

Authors:
Deng Tang;Claude Carlet;Xiaohu Tang
Affiliations:
Provincial Key Lab of Information Coding and Transmission, Institute of Mobile Communications, Southwest Jiaotong University, Chengdu 610031, China;LAGA, Universities of Paris 8 and Paris 13, CNRS/ Adresse: Department of Mathematics, University of Paris 8, 2 rue de la liberté/, 93526 Saint-Denis cedex 02, France;Provincial Key Lab of Information Coding and Transmission, Institute of Mobile Communications, Southwest Jiaotong University, Chengdu 610031, China
Venue:
Information Sciences: an International Journal
Year:
2013

Citing 15
Cited 0

Finite fields

Finite fields
Quadratic Relation of S-box and Its Application to the Linear Attack of Full Round DES

CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
Probabilistic Higher Order Differential Attack and Higher Order Bent Functions

ASIACRYPT '99 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
The lower bounds on the second order nonlinearity of three classes of Boolean functions with high nonlinearity

Information Sciences: an International Journal
On the global avalanche characteristics between two Boolean functions and the higher order nonlinearity

Information Sciences: an International Journal
On the lower bounds of the second order nonlinearities of some Boolean functions

Information Sciences: an International Journal
Best affine and quadratic approximations of particular classes of Boolean functions

IEEE Transactions on Information Theory
Non-linear approximations in linear cryptanalysis

EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
The lower bound on the second-order nonlinearity of a class of Boolean functions with high nonlinearity

Applicable Algebra in Engineering, Communication and Computing
A note on fast algebraic attacks and higher order nonlinearities

Inscrypt'10 Proceedings of the 6th international conference on Information security and cryptology
Almost perfect nonlinear power functions on GF(2n): the Welch case

IEEE Transactions on Information Theory
The weights of the orthogonals of the extended quadratic binary Goppa codes

IEEE Transactions on Information Theory
Recursive Lower Bounds on the Nonlinearity Profile of Boolean Functions and Their Applications

IEEE Transactions on Information Theory
A Lower Bound of the Second-order Nonlinearities of Boolean Bent Functions

Fundamenta Informaticae
Higher-order nonlinearity of Kasami functions

International Journal of Computer Mathematics

Quantified Score

Hi-index	0.07

Visualization

Abstract

The rth-order nonlinearity of Boolean functions plays a central role against several known attacks on stream and block ciphers. It plays also an important role in coding theory, since its maximum equals the covering radius of the rth-order Reed-Muller code. But it is difficult to calculate and even to bound. In this paper, we show lower bounds on the second-order nonlinearity of two subclasses of well-known bent functions. We first improve a known lower bound on the second-order nonlinearity of the simplest partial spread bent functions, whose nonlinearity profile has been bounded by the second author. This improvement allows obtaining a better bound for the whole profile. We subsequently give a lower bound on the second-order nonlinearity of some infinite class of Maiorana-McFarland (M-M) bent functions, which generalizes a result by Gangopadhyay et al.