Nonlinearly balanced Boolean functions and their propagation characteristics
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
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EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
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ICISC '99 Proceedings of the Second International Conference on Information Security and Cryptology
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CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
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FSE '97 Proceedings of the 4th International Workshop on Fast Software Encryption
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IEEE Transactions on Computers
Design of SAC/PC(l) of order k boolean functions and three other cryptographic criteria
EUROCRYPT'97 Proceedings of the 16th annual 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
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
IEEE Transactions on Information Theory
Binary m-sequences with three-valued crosscorrelation: a proof of Welch's conjecture
IEEE Transactions on Information Theory
Modifications of Patterson-Wiedemann functions for cryptographic applications
IEEE Transactions on Information Theory
Cryptographic properties of the Welch-Gong transformation sequence generators
IEEE Transactions on Information Theory
A New Characterization of Semi-bent and Bent Functions on Finite Fields*
Designs, Codes and Cryptography
Partially perfect nonlinear functions and a construction of cryptographic boolean functions
SETA'06 Proceedings of the 4th international conference on Sequences and Their Applications
Constructions of 1-resilient Boolean functions on odd number of variables with a high nonlinearity
Security and Communication Networks
Construction of highly nonlinear resilient S-boxes with given degree
Designs, Codes and Cryptography
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We explore three applications of geometric sequences in constructing cryptographic Boolean functions. First, we construct 1-resilient functions of n Boolean variables with nonlinearity 2n-1-2(n-1)/2, n odd. The Hadamard transform of these functions is 3-valued, which limits the efficiency of certain stream cipher attacks. From the case for n odd, we construct highly nonlinear 1-resilient functions which disprove a conjecture of Pasalic and Johansson for n even. Our constructions do not have a potential weakness shared by resilient functions which are formed from concatenation of linear functions. Second, we give a new construction for balanced Boolean functions with high nonlinearity, exceeding 2n-1-2(n-1)/2, which is not based on the direct sum construction. Moreover, these functions have high algebraic degree and large linear span. Third, we construct balanced vectorial Boolean functions with nonlinearity 2n-1-2(n-1)/2 and low maximum correlation. They can be used as nonlinear combiners for stream cipher systems with high throughput.