Information Sciences: an International Journal
Improved lower bound on the number of balanced symmetric functions over GF(p)
Information Sciences: an International Journal
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
On cryptographic properties of the cosets of R(1, m)
IEEE Transactions on Information Theory
Generating and counting binary bent sequences
IEEE Transactions on Information Theory
Improving the Upper Bounds on the Covering Radii of Binary Reed–Muller Codes
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
On cross-correlation indicators of an S-box
Frontiers of Computer Science in China
On the second-order nonlinearities of some bent functions
Information Sciences: an International Journal
The autocorrelation distribution of balanced Boolean function
Frontiers of Computer Science: Selected Publications from Chinese Universities
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The criterion for the global avalanche characteristics (GAC) of cryptographic functions is an important property. To measure the correlation between two arbitrary Boolean functions, we propose two new criteria called the sum-of-squares indicator and the absolute indicator of the cross-correlation between two Boolean functions. The two indicators generalize the GAC criterion. Based on the properties of the cross-correlation function, we deduce the rough lower and the rough upper bounds on the two indicators by hamming weights of two Boolean functions, and generalize some properties between the Walsh spectrum and the cross-correlation function. Furthermore, we give the tight upper and the tight lower bounds on the two indicators. Finally, we show some relationships between the upper bounds on the two indicators and the higher order nonlinearity.