Geodesic
On the $\Delta$-equivalence of Boolean functions
Diskretnaya Matematika, Tome 30 (2018) no. 4, pp. 29-40

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A new equivalence relation on the set of Boolean functions is introduced: functions are declared to be $\Delta$-equivalent if their autocorrelation functions are equal. It turns out that this classification agrees well with the cryptographic properties of Boolean functions: for functions belonging to the same $\Delta $-equivalence class a number of their cryptographic characteristics do coincide. For example, all bent-functions (of a fixed number of variables) make up one class.
Keywords: Boolean function, discrete Fourier transform, Walsh–Hadamard transform, cross-correlation, autocorrelation, nonlinearity, curvature, correlation immunity, propagation criterion, global avalanche characteristics. 
@article{DM_2018_30_4_a2,
     author = {O. A. Logachev and S. N. Fedorov and V. V. Yashchenko},
     title = {On the $\Delta$-equivalence of {Boolean} functions},
     journal = {Diskretnaya Matematika},
     pages = {29--40},
     publisher = {mathdoc},
     volume = {30},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2018_30_4_a2/}
}
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O. A. Logachev; S. N. Fedorov; V. V. Yashchenko. On the $\Delta$-equivalence of Boolean functions. Diskretnaya Matematika, Tome 30 (2018) no. 4, pp. 29-40. http://geodesic.mathdoc.fr/item/DM_2018_30_4_a2/