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Works of the Kiev school of theoretical cryptography

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This paper presents works of the Kiev school of theoretical cryptography that are carried out mainly during the last two decades in the fields of cryptographic methods of information security, cryptanalysis, and related mathematical disciplines.

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References

  1. I. N. Kovalenko, “On an algorithm of subexponential complexity for decoding heavily corrupted linear codes,” Dop. AN URSR, Ser. A, No. 10, 16–17 (1988).

  2. I. N. Kovalenko and M. N. Savchuk, “Some methods of decoding corrupted linear codes,” Data Registration, Storage, and Processing, 1, No. 2, 62–68 (1999).

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  14. A. N. Alekseychuk, “A probabilistic scheme of independent random elements distributed over a finite lattice. II. The method of lattice moments,” Cybernetics and Systems Analysis, No. 6, 824–841 (2004).

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  22. L. V. Kovalchuk, “Pseudoirreducible polynomials: Probabilistic irreducibility testing,” Cybernetics and Systems Analysis, No. 4, 610–616 (2004).

  23. M. N. Savchuk, “Some limit theorems in the scheme of equiprobable placement of particles by sets,” Teor. Veroyatn. Mat. Stat., No. 28, 122–130 (1983).

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  29. M. N. Savchuk and V. F. Sinyavskii, “On an algorithm for determination of moments of changing parameters of a Bernoullian sequence,” Probl. Upravlen. Inf., No. 1, 84–89 (1999).

  30. M. N. Savchuk, “Analysis of a method for improving characteristics of a random binary sequence,” Kibern. Vychisl. Tekhn., No. 118, 57–61 (1998).

  31. V. Sharapov, “Algorithm for testing random and pseudorandom sequences using contextual simulation,” in: Proc. Xth Anniv. Intern. Sci. Pract. Conf. “Information Security in Informational-Telecommunication Systems,” ChP “EKMO” and NITs “Tezis” of NTUU “KPI,” Kiev (2007), pp. 30–31.

  32. L. Koval’chuk and V. Bezditnyi, “Checking the independence of statistical tests destined for estimation of cryptographic properties of GPV,” Zakhyst Informatsii, No. 2 (29), 18–23 (2006).

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  39. S. A. Pometun, “On the number of Boolean functions with a given algebraic immunity,” Prikl. Radioelektronica, No. 3, 322–325 (2008).

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  41. A. N. Alekseychuk and R. V. Proskurovskii, “Lower bound of the probability of distinguishing between inner states of a combining gamma generator with nonuniform movement,” in: Legal, Normative, and Metrological Support of the Information Protection System in Ukraine, No. 2 (13), Kyiv (2006), pp. 159–169.

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  44. A. N. Alekseychuk, “Optimal balanced mappings in constructions of gamma generators with nonuniform movement of shift registers and protocols of transmission of keys along a tapped communication channel,” Registration, Storage, and Processing of Data, 10, No. 4, 47–56 (2008).

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  49. A. N. Alekseychuk and L. V. Kovalchuk, “Upper bounds of maximum values of average differential and linear characteristic probabilities of Feistel cipher with adder modulo 2m,” Theory of Stochastic Processes, 12 (28), Nos. 1–2, 20–32 (2006).

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  53. L. V. Koval’chuk, “Generalized Markov ciphers: Construction of an estimate of practical resistance to differential cryptanalysis,” in: Proc. MGU Conf. “Mathematics and Security of Information Technologies,” MTsNMO, Moscow (2007), pp. 595–599.

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  54. A. M. Alekseychuk, L. V. Koval’chuk, and S. V. Pal’chenko, “Cryptographic parameters of replacement units describing the resistance of GOST-like block ciphers to linear and differential cryptanalysis methods,” Zakhyst Informatsii, No. 2, 12–23 (2007).

  55. A. N. Alekseychuk, L. V. Koval’chuk, E. V. Skrynnik, and A. S. Shevtsov, “Estimates of practical resistance of the block cipher Kalina against differential linear cryptanalysis methods and algebraic attacks based on homomorphisms,” Prikladn. Radioelektronika, 7, No. 3, 203–209 (2008).

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  57. S. Vaudenay, “Decorrelation: A theory for block cipher security,” J. Cryptology, 16, No. 4, 249–286 (2003).

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  62. A. V. Fesenko, “Analysis of a public-key cryptosystem whose key is based on a piecewise linear image,” in: Proc. Xth Ann. Intern. Sci.-Pract. Conf. “Information Security in Informational-Telecommunication Systems,” ChP “EKMO” and NITs “Tezis” of NTUU “KPI,” Kiev (2007), pp. 32–33.

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  65. M. M. Savchuk and A. V. Fesenko, “Investigations of the possibility of using symmetric ciphers for construction of postquantum cryptographic protocols,” in: Proc. 6th Intern. Conf. “INTERNET–EDUCATION–SCIENCE–2008,” Vol. 2, UNIVERSUM–Vinnytsya, Vinnytsya (2008), pp. 411–412.

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  67. M. N. Savchuk and V. G. Sharapov, “Analysis of a method for testing random sequences that is based on context simulation,” Legal, Normative, and Metrological Support of the Information Protection System in Ukraine, No. 1(16), 82–89 (2008).

  68. M. N. Savchuk and V. G. Sharapov, “A multidimensional statistical test for binary sequences,” Legal, Normative, and Metrological Support of the Information Protection System in Ukraine, No. 1 (18), 65–72 (2009).

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  75. A. N. Alekseychuk and A. S. Shevtsov, “Upper estimates of imbalance of bilinear approximations for round functions of block ciphers,” Cybernetics and Systems Analysis, No. 3, 378–387 (2010).

  76. P. A. Endovitskii, “Refining the asymptotic approximation of the group size in the birthday paradox,” Cybernetics and Systems Analysis, No. 3, 518–522 (2010).

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Correspondence to M. N. Savchuk.

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Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 52–68, May–June 2010

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Savchuk, M.N. Works of the Kiev school of theoretical cryptography. Cybern Syst Anal 46, 386–404 (2010). https://doi.org/10.1007/s10559-010-9214-1

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