Geodesic
Description of non-endomorphic maximum perfect ciphers with two-valued plaintext alphabet
Prikladnaâ diskretnaâ matematika, no. 4 (2015), pp. 43-55.

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This paper deals with non-endomorphic perfect (according to Shannon) ciphers, which are absolutely immune against the ciphertext-only attacks in the case when plaintext alphabet consists of two elements. Matrices of probabilities of cipher keys are described in terms of linear algebra on the basis of Birkhoff's theorem (about the classification of doubly stochastic matrices). The set of possible values of a priori probabilities for elements in ciphertext alphabet of a perfect cipher is constructed.
Keywords: perfect ciphers, non-endomorphic ciphers, maximum ciphers, doubly stochastic matrices. 
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N. V. Medvedeva; S. S. Titov. Description of non-endomorphic maximum perfect ciphers with two-valued plaintext alphabet. Prikladnaâ diskretnaâ matematika, no. 4 (2015), pp. 43-55. http://geodesic.mathdoc.fr/item/PDM_2015_4_a3/

[1] Shennon K., “Communication theory of secrecy systems”, Raboty po Teorii Informatsii i ibernetike, Nauka Publ., Moscow, 1963, 333–402 (in Russian)

[2] Andreev N. N., Peterson A. P., Pryanishnikov K. V., Starovoytov A. V., “The founder of the national classified telephone”, Radiotekhnika, 1998, no. 8, 8–12 (in Russian)

[3] Zubov A. Yu., Perfect Ciphers, Gelios ARV Publ., Moscow, 2003, 160 pp. (in Russian)

[4] Stinson D. R., “A construction for authentication secrecy codes from certain combinatorial designs”, Proc. Crypto'87, Advances in Cryptology, 1998, 355–366 | MR

[5] De Soete M., “Some constructions for authentication-secrecy codes”, Proc. Crypto'87, Advances in Cryptology, 1998, 57–75 | MR

[6] Goldlewsky P., Mitchell C., “Key-minimal cryptosystems for unconditional secrecy”, J. Cryptology, 3:1 (1990), 1–25 | MR

[7] Alferov A. P., Zubov A. Yu., Kuzmin A. S., Cheremushkin A. V., Basics of cryptography, Gelios ARV Publ., Moscow, 2001, 480 pp. (in Russian)

[8] Babash A. V., Shankin G. P., Cryptography (protection aspects), SOLON-R Publ., Moscow, 2002, 512 pp. (in Russian)

[9] Brassar Zh., Modern Cryptology, POLIMED, Moscow, 1999, 176 pp. (in Russian)

[10] Stinson D. R., Cryptography: Theory and Practice, CRC Press, N.Y., 1995, 616 pp. | MR | Zbl

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

[12] Medvedeva N. V., Titov S. S., “On non-minimal perfect ciphers”, Prikladnaya diskretnaya matematika. Prilozhenie, 2013, no. 6, 42–44 (in Russian)

[13] Medvedeva N. V., Titov S. S., “Non-endomorphic perfect ciphers with two elements in plaintext alphabet”, Prikladnaya diskretnaya matematika. Prilozhenie, 2015, no. 8, 63–66 (in Russian)

[14] Gantmacher F. R., The Theory of Matrices, Chelsea Publ. Company, N.Y., 1959 | MR

[15] Nosov V. A., Sachkov V. N., Tarakanov V. E., “Combinatorial analysis (nonnegative matrices, algorithmic problems)”, J. Soviet Math., 29:1 (1985), 1051–1099 | DOI | MR | Zbl

[16] Converse G., Katz M., “Symmetric matrices with given row sums”, J. Combin. Theory Ser. A, 18:2 (1975), 171–176 | DOI | MR | Zbl

[17] Lewin M., “On the extreme points of the polytope of symmetric matrices with given row sums”, J. Combin. Theory Ser. A, 23:2 (1977), 223–231 | DOI | MR | Zbl

[18] Koontz M., “Convex sets of some doubly stochastic matrices”, J. Combin. Theory Ser. A, 24:1 (1978), 111–112 | DOI | MR | Zbl