ISSN 2071-8594

Russian academy of sciences


Gennady Osipov

A.H. Alhussain, V.L. Stefanuk Probability Properties of Splitting Procedure


The paper contains a probability analysis of information safety providing with data splitting method that has been proposed before by the present authors. The research was made in analogy to the Claude Shannon’s proof of perfect secrecy of gamming procedure under certain properties of gammas. The present paper shows that the probabilities of values obtained after splitting procedure have the required properties of independence and incompatibility. Due to this fact the paper concludes that our splitting procedure, followed by gamming one, remains absolutely safe. Besides, the paper provides a theorem on asymptotic safety of splitting alone as the splitting depth tends to infinity. Independently the present paper shows that the splitting procedure has certain advantages which differ it from traditional gamming, and which make it especially difficult to perform statistical recovery of the original text on the base of its content even in the case when real randomness is replaced with pseudorandom numbers.


numerical splitting, generalized splitting, gamming, pseudorandom numbers, GPRN, text semantics, absolute safety, asymptotic absolute safety.

PP. 49-57.


1. V.L.Stefanuk, A.H.Alhussain. 2016. Kontrol stepenju zashity informatsii methodom tselochislennogo rascheplenia [Control the Level of Protection the Information by the Usage of Integer Splitting]. Iskusstvenny Intellkt I Prinyatie Reshenii [Artificial Intelligence and Decision Making] 4:86-91.
2. Stefanuk V.L., Alhussain A.H.. 2016. Symmetrichnoe shifrovanie na osnove metoda rascheplenia [Symmetric ciphering based on splitting metod]. Estestvennye i technicheskie nauki [Natural and technical sciences] 93:3:130-133
3. V.L. Stefanyuk, A.H. Alhussain, Symmetric Encryption on the Вase of Splitting Method// Bulletin of PFUR, Series Mathematics, Information Sciences, Physics. 2016: 2: 53-61.
4. Shannon C. Communication theory of secrecy systems. Bell System Techn. J., 28: 4: 656-715, 1949.
5. Gorbunova A.V., Zaryadov I.S., Matyushenko S.I., Samyilov K.E., Shorgin S.Ya. 2015. Approximatsia vremeny otklika sistemy oblachnykh vychislenii [Response time approximation for cloud computing]. Informatsia i yeye primenenie [Information and its application], 9:3:32–38.
6. Basharin G.P., Samyilov K.E., Yarkina N.V., Gudkova I.A. 2009 Novyi etap razvitiya matematicheskoy teorii teletrafika [New stage of development of nathematical theory of teletraffic]. Avtomatica i telemechanika [Automation and Remote Control]. 12: 6–28.
7. Sevastianov L.A. The probability scheme of constructing the mathematical model of shadowed spattering. 2000// Comp. Phys. Comm., 130: 1-2: 41-46.
8. Romanets Yu.V., Tomofeev P.A., Shan’gin V.F. 1999. Zashita informatsii v komputernych systemach I setyach [Safety of information in computer systems and nets] // M: Radio i svyz’ [Moscow: Radio and Communication]. 328p.
9. Ryabko B.Ya., Phionov A.N. Osnovy sovremennoi kriptographii for specialistov v informacionnych technologiyach [The basis for modern cryptography for information technology specialists] // Moskva: Nauchnyi Mir [Moscow: Scientific World], 2004. 173p.
10. Salomaa A., Public-Key Criptography// N.Y.: Springer-Verlag, 1990. 318p.
11. José Luis Gómez Pardo, Introduction to Cryptography with Maple// Springer Science & Business Media, 2012. 706p.
12. Douglas R. Stinson, Cryptography: Theory and Practice, Third Edition// CRC Press, 2005. 616 p.
13. Mikhail J. Atallah, Algorithms and Theory of Computation Handbook//CRC Press, 1998. 1312p.
14. Serge Vaudenay, A Classical Introduction to Cryptography: Applications for Communications Security//Springer Science & Business Media, 2006. 336p.
15. M. Hazewinkel, Encyclopaedia of Mathematics: Coproduct-Hausdorff-Young Inequalities//Springer-2013. 963 p.