Products of linear recurring sequences with maximum complexity
IEEE Transactions on Information Theory
Enumerating boolean functions of cryptographic significance
Journal of Cryptology
Nonlinearity criteria for cryptographic functions
EUROCRYPT '89 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
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
A characterization of binary bent functions
Journal of Combinatorial Theory Series A
Enumeration of Correlation Immune Boolean Functions
ACISP '99 Proceedings of the 4th Australasian Conference on Information Security and Privacy
On Correlation-Immune Functions
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
Coding and Information Theory
Decrypting a Class of Stream Ciphers Using Ciphertext Only
IEEE Transactions on Computers
More correlation-immune and resilient functions over Galois fields and Galois rings
EUROCRYPT'97 Proceedings of the 16th annual 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
Nonlinearity Bounds and Constructions of Resilient Boolean Functions
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
The Filter-Combiner Model for Memoryless Synchronous Stream Ciphers
CRYPTO '02 Proceedings of the 22nd 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
Efficient Implementation of "Large" Stream Cipher Systems
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
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Siegenthaler proved that an n input 1 output, m-resilient (balanced mth order correlation immune) Boolean function with algebraic degree d satisfies the inequality : m + d ≤ n - 1. We provide a new construction method using a small set of recursive operations for a large class of highly nonlinear, resilient Boolean functions optimizing Siegenthaler's inequality m + d = n - 1. Comparisons to previous constructions show that better nonlinearity can be obtained by our method. In particular, we show that as n increases, for almost all m, the nonlinearity obtained by our method is better than that provided by Seberry et al in Eurocrypt'93. For small values of n, the functions constructed by our method is better than or at least comparable to those constructed using the methods provided in papers by Filiol et al and Millan et al in Eurocrypt'98. Our technique can be used to construct functions on large number of input variables with simple hardware implementation.