Improved Upper Bound on the Nonlinearity of High Order Correlation Immune Functions
SAC '00 Proceedings of the 7th Annual International Workshop on Selected Areas in Cryptography
Nonlinearity Bounds and Constructions of Resilient Boolean Functions
CRYPTO '00 Proceedings of the 20th 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
On Resilient Boolean Functions with Maximal Possible Nonlinearity
INDOCRYPT '00 Proceedings of the First International Conference on Progress in Cryptology
New Constructions of Resilient Boolean Functions with Maximal Nonlinearity
FSE '01 Revised Papers from the 8th International Workshop on Fast Software Encryption
Further Results on the Relation Between Nonlinearity and Resiliency for Boolean Functions
Proceedings of the 7th IMA International Conference on Cryptography and Coding
The bit extraction problem or t-resilient functions
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Exposure-resilient functions and all-or-nothing transforms
EUROCRYPT'00 Proceedings of the 19th 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
A Brief Outline of Research on Correlation Immune Functions
ACISP '02 Proceedings of the 7th Australian Conference on Information Security and Privacy
Evolving Boolean Functions Satisfying Multiple Criteria
INDOCRYPT '02 Proceedings of the Third International Conference on Cryptology: Progress in Cryptology
New Constructions of Resilient Boolean Functions with Maximal Nonlinearity
FSE '01 Revised Papers from the 8th International Workshop on Fast Software Encryption
Discrete Applied Mathematics - Special issue: Coding and cryptography
Discrete Applied Mathematics - Special issue: Coding and cryptography
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 consider matrices of special form introduced in [11] and used for the constructing of resilient functions with cryptographically optimal parameters. For such matrices we establish lower bound 1/log2(驴5+1) = 0.5902... for the important ratio t/t+k of its parameters and point out that there exists a sequence of matrices for which the limit of ratio of these parameters is equal to lower bound. By means of these matrices we construct m-resilient n-variable functions with maximum possible nonlinearity 2n-1-2m+1 for m = 0.5902 . . . n+O (log2 n). This result supersedes the previous record.