The complexity of Boolean functions
The complexity of Boolean functions
Dual distances of completely regular codes
Discrete Mathematics
Propagation characteristics of Boolean functions
EUROCRYPT '90 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
Orphan structure of the first-order Reed-Muller codes
Discrete Mathematics
On Correlation-Immune Functions
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
Bounds for Resilient Functions and Orthogonal Arrays
CRYPTO '94 Proceedings of the 14th Annual International Cryptology Conference on Advances 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
A Note on the Construction and Upper Bounds of Correlation-Immune Functions
Proceedings of the 6th IMA International Conference on Cryptography and Coding
Proceedings of the 1983 International FCT-Conference on Fundamentals of Computation Theory
Construction of t-resilient functions over a finite alphabet
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Construction of nonlinear boolean functions with important cryptographic properties
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
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
IEEE Transactions on Information Theory
On the iterative construction of bent functions
ISP'06 Proceedings of the 5th WSEAS International Conference on Information Security and Privacy
A new iterative method to construct bent functions
ISP'06 Proceedings of the 5th WSEAS International Conference on Information Security and Privacy
WCC'05 Proceedings of the 2005 international conference on Coding and Cryptography
| Hi-index | 0.00 |
We introduce the notion of covering sequence of a Boolean function, related to the derivatives of the function. We give complete characterizations of balancedness, correlation immunity and resiliency of Boolean functions by means of their covering sequences. By considering particular covering sequences, we define subclasses of (correlation-immune) resilient functions. We derive upper bounds on their algebraic degrees and on their nonlinearities. We give constructions of resilient functions belonging to these classes. We show that they achieve the best known trade-off between order of resiliency, nonlinearity and algebraic degree.