Geodesic
Constructions of non-endomorphic perfect ciphers
Prikladnaya Diskretnaya Matematika. Supplement, no. 13 (2020), pp. 51-54 Cet article a éte moissonné depuis la source Math-Net.Ru

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This work is dealing with constructions of Shannon perfect ciphers (which are absolutely immune against the attack on ciphertext, according to Shannon). Based on the equivalence relation on the set of keys, sufficient conditions are obtained for that the encoding tables of non-endomorphic (endomorphic) perfect ciphers do not contain Latin rectangles (squares). Key equivalence refers to the following: two different keys are equivalent in cipher-value $x_i$ if the cipher-value $x_i$ on these keys is encrypted to the same code designation. In this case, pairwise different keys $k_1, k_2, k_3,\ldots , k_{n-1}, k_n$ form a cycle of length $n$ if there is such a sequence of cipher-values that: 1) the neighboring cipher-values are different; 2) the keys $k_1, k_2, k_3,\ldots , k_{n-1}, k_n, k_1$ are sequentially equivalent in the corresponding cipher-values. If $n$ is an odd number, then the keys $k_1, k_2,\ldots , k_n$ form an odd-length cycle. It is proved that if the keys $k_1, k_2, \ldots , k_n$ form an odd-length cycle, then this encoding table does not contain Latin rectangles. Example of such constructions is given.
Keywords: perfect ciphers, endomorphic ciphers, non-endomorphic ciphers. 
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N. V. Medvedeva; S. S. Titov. Constructions of non-endomorphic perfect ciphers. Prikladnaya Diskretnaya Matematika. Supplement, no. 13 (2020), pp. 51-54. http://geodesic.mathdoc.fr/item/PDMA_2020_13_a14/

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

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

[3] Zubov A. Yu., Sovershennye shifry, Gelios ARV, M., 2003

[4] Medvedeva N. V., Titov S. S., “Analogi teoremy Shennona dlya endomorfnykh neminimalnykh shifrov”, Prikladnaya diskretnaya matematika. Prilozhenie, 2016, no. 9, 62–65

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

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

[7] Birkhoff G. D., “Tres observations sobre el algebra lineal”, Revista Universidad Nacional Tucuman. Ser. A, 5 (1946), 147–151 | MR | Zbl