Geodesic
Independence of events in spaces of equally probable ciphervalues
Prikladnaya Diskretnaya Matematika. Supplement, no. 17 (2024), pp. 102-106.

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Within the framework of the probabilistic cipher model, the problem of decomposition in some orthogonal coordinate system of the discrete space $\Omega$ of elementary events into pairs of families of incompatible events independent of any event of another family is considered. It is shown that the binary event independence relation is related to the number-theoretic nature of the number $N$ — the power of the discrete space $\Omega$ of elementary events. It is proved that for a composite number $N$ there are pairs of independent subspaces of the space $\Omega$, and for prime $N$ there are no independent subspaces. Examples illustrating the obtained theoretical statements are constructed.
Keywords: perfect ciphers, space of elementary events, independent events. 
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N. V. Medvedeva; S. S. Titov. Independence of events in spaces of equally probable ciphervalues. Prikladnaya Diskretnaya Matematika. Supplement, no. 17 (2024), pp. 102-106. http://geodesic.mathdoc.fr/item/PDMA_2024_17_a22/

[1] Medvedeva N. V., Titov S. S., “Opisanie neendomorfnykh maksimalnykh sovershennykh shifrov s dvumya shifrvelichinami”, Prikladnaya diskretnaya matematika, 2015, no. 4(30), 43–55 | Zbl

[2] Medvedeva N. V., “Ob analogakh teoremy Shennona dlya sovershennykh shifrov”, Proc. 3rd Russian Conf. MMIT (Ekaterinburg, Russia), 2016, 232–239

[3] Medvedeva N. V., Titov S. S., “Geometricheskaya model sovershennykh shifrov s tremya shifrvelichinami”, Prikladnaya diskretnaya matematika. Prilozhenie, 2019, no. 12, 113–116

[4] Medvedeva N. V., Titov S. S., “Kriterii minimalnosti po vklyucheniyu sovershennykh shifrov”, Prikladnaya diskretnaya matematika. Prilozhenie, 2022, no. 15, 51–54

[5] Shennon K., “Teoriya svyazi v sekretnykh sistemakh”, Raboty po teorii informatsii i kibernetike, Nauka, M., 1963, 333–402

[6] Alferov A. P., Zubov A. Yu., Kuzmin A. S., Cheremushkin A. V., Osnovy kriptografii, Gelios ARV, M., 2001, 478 pp.

[7] Zubov A. Yu., Sovershennye shifry, Gelios ARV, M., 2003, 160 pp.

[8] Zubov A. Yu., “Pochti sovershennye shifry i kody autentifikatsii”, Prikladnaya diskretnaya matematika, 2011, no. 4(14), 28–33

[9] Zubov A. Yu., “O ponyatii $\varepsilon$-sovershennogo shifra”, Prikladnaya diskretnaya matematika, 2016, no. 3(33), 45–52 | MR | Zbl