Orthogonal Arrays, Resilient Functions, Error-Correcting Codes, and Linear Programming Bounds
SIAM Journal on Discrete Mathematics
Split Orthogonal Arrays and Maximum Independent ResilientSystems of Functions
Designs, Codes and Cryptography
New Results on Correlation Immunity
ICISC '00 Proceedings of the Third International Conference on Information Security and Cryptology
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
CRYPTO '92 Proceedings of the 12th 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
The bit extraction problem or t-resilient functions
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
SFCS '92 Proceedings of the 33rd 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
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
A Brief Outline of Research on Correlation Immune Functions
ACISP '02 Proceedings of the 7th Australian Conference on Information Security and Privacy
Autocorrelation Properties of Correlation Immune Boolean Functions
INDOCRYPT '01 Proceedings of the Second International Conference on Cryptology in India: 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
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
SETA'04 Proceedings of the Third international conference on Sequences and Their Applications
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We apply autocorrelation and Walsh coefficients for the investigation of correlation immune and resilient Boolean functions. We prove new lower bound for the absolute indicator of resilient functions that improves significantly (for m (n - 3)/2) the bound of Zheng and Zhang [18] on this value. We prove new upper bound for the number of nonlinear variables in high resilient Boolean function. This result supersedes the previous record. We characterize all possible values of resiliency orders for quadratic functions and give a complete description of quadratic Boolean functions that achieve the upper bound on resiliency. We establish new necessary condition that connects the number of variables, the resiliency and the weight of anunbalanced nonconstant correlation immune function and prove that such functions do not exist for m 0.75n - 1.25. For high orders of m this surprising fact supersedes the well-known Bierbrauer-Friedman bound [8], [1] and was not formulated before even as a conjecture. We improve the upper bound of Zheng and Zhang [18] for the nonlinearity of high order correlation immune unbalanced Boolean functions and establish that for high orders of resiliency the maximum possible nonlinearity for unbalanced correlation immune functions is smaller than for balanced.