Coding and information theory (2nd ed.)
Coding and information theory (2nd ed.)
Enumerating boolean functions of cryptographic significance
Journal of Cryptology
A note on a conjecture concerning symmetric resilient functions
Information Processing Letters
Nonlinearly balanced Boolean functions and their propagation characteristics
CRYPTO '93 Proceedings of the 13th annual international cryptology conference 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
Improving bounds for the number of correlation immune Boolean functions
Information Processing Letters
On Correlation-Immune Functions
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
Decrypting a Class of Stream Ciphers Using Ciphertext Only
IEEE Transactions on Computers
The bit extraction problem or t-resilient functions
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
A Brief Outline of Research on Correlation Immune Functions
ACISP '02 Proceedings of the 7th Australian Conference on Information Security and Privacy
Highly Nonlinear Resilient Functions Optimizing Siegenthaler's Inequality
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
An Upper Bound on the Number of m-Resilient Boolean Functions
ASIACRYPT '02 Proceedings of the 8th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Equivalence classes of Boolean functions for first-order correlation
IEEE Transactions on Information Theory
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We introduce new ideas to tackle the enumeration problem for correlation immune functions and provide the best known lower and upper bounds. The lower bound is obtained from sufficient conditions, which are essentially construction procedures for correlation immune functions. We obtain improved necessary conditions and use these to derive better upper bounds. Further, bounds are obtained for the set of functions which satisfy the four conditions of correlation immunity, balancedness, nondegeneracy and nonaffinity. Our work clearly highlights the difficulty of exactly enumerating the set of correlation immune functions.