Geodesic
Propagation criterion for monotone Boolean functions with least vector support set of 1 or 2 elements
Diskretnaya Matematika, Tome 34 (2022) no. 2, pp. 32-42.

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The propagation criterion for monotone Boolean functions with least vector support sets consisting of one or two vectors is studied. We obtain necessary and sufficient conditions for the validity of the propagation criterion for a vector in terms of the Hamming weights of vectors in least vector support set depending on whether these vectors share some nonzero components with the given vector. We find the cardinality of the set of vectors satisfying the propagation criterion for such functions.
Keywords: Boolean function, propagation criterion, monotone Boolean function, the least vector support set of a monotone Boolean function, Walsh spectrum. 
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     title = {Propagation criterion for monotone {Boolean} functions with least vector support set of 1 or 2 elements},
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     url = {http://geodesic.mathdoc.fr/item/DM_2022_34_2_a3/}
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G. A. Isaev. Propagation criterion for monotone Boolean functions with least vector support set of 1 or 2 elements. Diskretnaya Matematika, Tome 34 (2022) no. 2, pp. 32-42. http://geodesic.mathdoc.fr/item/DM_2022_34_2_a3/

[1] Logachev O. A., Salnikov A. A., Smyshlyaev S. V., Yaschenko V. V., Bulevy funktsii v teorii kodirovaniya i kriptologii, Moskovskii tsentr nepreryvnogo matematicheskogo obrazovaniya, M., 2012, 584 pp. | MR

[2] Yablonskii S. V., Vvedenie v diskretnuyu matematiku, Vysshaya shkola, M., 2008, 384 pp.

[3] Carlet C., Joyner D., Stănică P., Tang D., “Cryptographic properties of monotone Boolean functions”, J. Math. Cryptology, 10:1 (2016), 1–14 | DOI | MR | Zbl

[4] Carlet C., “On the nonlinearity of monotone Boolean functions”, Cryptography and Communications, 10 (2018), 1051–1061 | DOI | MR | Zbl

[5] Carlet C., Boolean Functions for Cryptography and Coding Theory, Cambridge University Press, Cambridge, 2020, 562 pp. | Zbl

[6] Carlet C., “Boolean functions for cryptography and error-correcting codes”: Crama Y., Hammer P. L., Boolean Methods and Models, Cambridge University Press, Cambridge, 2010, 257–397 | MR | Zbl

[7] Crama Y., Hammer P. L., Boolean Functions, Theory, Algorithms, and Applications, Cambridge University Press, Cambridge, 2011, 687 pp. | MR | Zbl

[8] Preneel B., Van Leekwijck W., Van Linden L., Govaerts R., Vandewalle J., “Propagation characteristics of Boolean functions”, EUROCRYPT 1990, Lect. Notes Comput. Sci., 473, 1991, 161–173 | DOI | MR | Zbl

[9] Rothaus O. S., “On “Bent” Functions”, J. Comb. Theory, Ser. A, 20:3 (1976), 300–305 | DOI | MR | Zbl