Designs, Codes and Cryptography
Discrete Mathematics
On Propagation Characteristics of Resilient Functions
SAC '02 Revised Papers from the 9th Annual International Workshop on Selected Areas in Cryptography
A Larger Class of Cryptographic Boolean Functions via a Study of the Maiorana-McFarland Construction
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
On Correlation-Immune Functions
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
Propagation characteristics and correlation-immunity of highly nonlinear boolean functions
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
On some cosets of the first-order Reed-Muller code with high minimum weight
IEEE Transactions on Information Theory
On cryptographic properties of the cosets of R(1, m)
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Finding nonnormal bent functions
Discrete Applied Mathematics - Special issue: Coding and cryptography
Finding nonnormal bent functions
Discrete Applied Mathematics - Special issue: Coding and cryptography
Best affine and quadratic approximations of particular classes of Boolean functions
IEEE Transactions on Information Theory
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Dobbertin (Construction of bent functions and balanced Boolean functions with high nonlinearity, in: Fast Software Encryption, Lecture Notes in Computer Science, Vol. 1008, Springer, Berlin, 1994, pp. 61-74) introduced the normality of bent functions. His work strengthened the interest for the study of the restrictions of Boolean functions on k- dimensional flats providing the concept of k-normality. Using recent results on the decomposition of any Boolean functions with respect to some subspace, we present several formulations of k-normality. We later focus on some highly linear functions, bent functions and almost optimal functions. We point out that normality is a property for which these two classes are strongly connected. We propose several improvements for checking normality, again based on specific decompositions introduced in Canteaut et al. (IEEE Trans. Inform. Theory, 47(4) (2001) 1494), Canteaut and Charpin (IEEE Trans. Inform. Theory). As an illustration, we show that cubic bent functions of 8 variables are normal.