Cryptanalysts representation of nonlinearly filtered ML-sequences
Proc. of a workshop on the theory and application of cryptographic techniques on Advances in cryptology---EUROCRYPT '85
Enumerating boolean functions of cryptographic significance
Journal of Cryptology
Balancing the n-Cube: A Census of Colorings
Journal of Algebraic Combinatorics: An International Journal
Improving bounds for the number of correlation immune Boolean functions
Information Processing Letters
Enumeration of Correlation Immune Boolean Functions
ACISP '99 Proceedings of the 4th Australasian Conference on Information Security and Privacy
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
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
A Note on the Construction and Upper Bounds of Correlation-Immune Functions
Proceedings of the 6th IMA International Conference on Cryptography and Coding
Decrypting a Class of Stream Ciphers Using Ciphertext Only
IEEE Transactions on Computers
Analytic Combinatorics
Construction of 1-resilient boolean functions with optimal algebraic immunity and good nonlinearity
Journal of Computer Science and Technology
| Hi-index | 754.84 |
This paper presents a complete characterization of the first order correlation immune Boolean functions that includes the functions that are 1-resilient. The approach consists in defining an equivalence relation on the full set of Boolean functions with a fixed number of variables. An equivalence class in this relation, called a first-order correlation class, provides a measure of the distance between the Boolean functions it contains and the correlation-immune Boolean functions. The key idea consists on manipulating only the equivalence classes instead of the set of Boolean functions. To achieve this goal, a class operator is introduced to construct a class with n variables from two classes of n - 1 variables. In particular, the class of 1-resilient functions on n variables is considered. An original and efficient method to enumerate all the Boolean functions in this class is proposed by performing a recursive decomposition of classes with less variables. A bottom up algorithm provides the exact number of 1-resilient Boolean functions with seven variables which is 23478015754788854439497622689296. A tight estimation of the number of 1-resilient functions with eight variables is obtained by performing a partial enumeration. It is conjectured that the exact complete enumeration for general n is intractable.