Piecewise Constructions of Bent and Almost Optimal Boolean Functions

Authors:
Claude Carlet;Joseph L. Yucas
Affiliations:
INRIA, Domaine de Voluceau, Rocquencourt, University of Paris 8, Cedex, France 78153;Department of Mathematics, Southern Illinois University, Carbondale, USA 62901
Venue:
Designs, Codes and Cryptography
Year:
2005

Citing 15
Cited 3

Spread spectrum communications; vols. 1-3

Spread spectrum communications; vols. 1-3
Designs and their codes

Designs and their codes
Partially-bent functions

Designs, Codes and Cryptography
Two new classes of bent functions

EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
Finite fields

Finite fields
A construction of bent function

FFA '95 Proceedings of the third international conference on Finite fields and applications
Results on bent functions

Journal of Combinatorial Theory Series A
Plateaued Functions

ICICS '99 Proceedings of the Second International Conference on Information and Communication Security
Constructing Large Cryptographically Strong S-boxes

ASIACRYPT '92 Proceedings of the Workshop on the Theory and Application of Cryptographic Techniques: Advances in Cryptology
On the confusion and diffusion properties of Maiorana-McFarland's and extended Maiorana-McFarland's functions

Journal of Complexity - Special issue on coding and cryptography
More correlation-immune and resilient functions over Galois fields and Galois rings

EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
On cryptographic properties of the cosets of R(1, m)

IEEE Transactions on Information Theory
Decomposing bent functions

IEEE Transactions on Information Theory
Normal extensions of bent functions

IEEE Transactions on Information Theory
Generalized partial spreads

IEEE Transactions on Information Theory

Best affine and quadratic approximations of particular classes of Boolean functions

IEEE Transactions on Information Theory
A characterization of bent functions on n + 1 variables

ISP'07 Proceedings of the 6th WSEAS international conference on Information security and privacy
On bent and highly nonlinear balanced/resilient functions and their algebraic immunities

AAECC'06 Proceedings of the 16th international conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes

Quantified Score

Hi-index	0.06

Visualization

Abstract

The first aim of this work was to generalize the techniques used in MacWilliams' and Sloane's presentation of the Kerdock code and develop a theory of piecewise quadratic Boolean functions. This generalization led us to construct large families of potentially new bent and almost optimal functions from quadratic forms in this piecewise fashion. We show how our motivating example, the Kerdock code, fits into this setting. These constructions were further generalized to non-quadratic bent functions. The resulting constructions design n-variable bent (resp. almost optimal) functions from n-variable bent or almost optimal functions.