Propagation characteristics of Boolean functions
EUROCRYPT '90 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
On constructions and nonlinearity of correlation immune functions
EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
New Results on Correlation Immunity
ICISC '00 Proceedings of the Third International Conference on Information Security and Cryptology
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
Autocorrelation Properties of Correlation Immune Boolean Functions
INDOCRYPT '01 Proceedings of the Second International Conference on Cryptology in India: Progress in Cryptology
On the Constructing of Highly Nonlinear Resilient Boolean Functions by Means of Special Matrices
INDOCRYPT '01 Proceedings of the Second International Conference on Cryptology in India: Progress in Cryptology
On the Correlation Immune Functions and Their Nonlinearity
ASIACRYPT '96 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
New Constructions of Resilient Boolean Functions with Maximal Nonlinearity
FSE '01 Revised Papers from the 8th International Workshop on Fast Software Encryption
Coding and Information Theory
Construction of nonlinear boolean functions with important cryptographic properties
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Further constructions of resilient Boolean functions with very high nonlinearity
IEEE Transactions on Information Theory
Construction of nonlinear resilient Boolean functions using "small" affine functions
IEEE Transactions on Information Theory
Spectral Domain Analysis of Correlation Immune and Resilient Boolean Functions
Finite Fields and Their Applications
Constructions of almost optimal resilient Boolean functions on large even number of variables
IEEE Transactions on Information Theory
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In this paper, we present a construction method of m-resilient Boolean functions with very high nonlinearity for low values of m. The construction only considers functions in even number of variables n. So far the maximum nonlinearity attainable by resilient functions was 2n-1 - 2n/2 + 2n/2-2. Here, we show that given any m, one can construct n-variable, m-resilient functions with nonlinearity 2n-1 - 11 ċ 2n/2-4 for all n ≥ 8m + 6 which is strictly greater than 2n-1 - 2n/2 + 2n/2-2. We also demonstrate that in some specific cases one may get such nonlinearity even for some values of n, where n m + 6. Further, we show that for sufficiently large n, it is possible to get such functions with nonlinearity reaching almost 2n-1 - 2n/2 + (4/3)2n/2-2. This is the upper bound on nonlinearity when one uses our basic construction recursively. Lastly, we discuss the autocorrelation property of the functions and show that the maximum absolute value in the autocorrelation spectra is ≤ 2n-3.