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Solving systems of linear algebraic equations in the complex application of homomorphic cryptographic transformations

Keywords:

A.K. Vishnevsky – Ph. D. (Eng.), Research Scientist, Peter The Great Military Academy of Strategic Rocket Forces (Moscow). E-mail: vishn.artem@yandex.ru V.V. Knyazev – Dr. Sc. (Eng.), Professor, Associate Professor, Peter The Great Military Academy of Strategic Rocket Forces (Moscow). E-mail: knzv.1961@yandex.ru


This paper presents an algorithm for computing ill-conditioned systems of linear algebraic equations with coefficients in a closed open distributed computing environment. The effect is achieved by the conversion coefficients in excess balances simple module using strong cryptographic algorithms used to select a pseudo-random sequence of simple modules. An additional effect of this algorithm is to reduce the conditioning systems of linear algebraic equations by representing the coefficients in the ring of integers, a limited module and a simple calculation error control through the use of simple mod-ules redundant. Also, estimates are obtained for reduction conditioning system of linear algebraic equations and complexi-ty of reverse recovery of the coefficients of linear algebraic equations.
References:

 

  1. Besekerskijj V.A., Popov E.P. Teorija sistem avtomaticheskogo upravlenija.Izd. 4‑e, pererab. i dop. SPb.: Professija. 2003. 752 s.
  2. Safonov V.V., Bogdanov JU.N., Zolotorev I.I.i dr. Sostojanie i osnovnye napravlenija razvitija bespilotnykh letatelnykh apparatov zarubezhnogo i otechestvennogo proizvodstva: analit. obzor. Voronezh: OVNI VAIU. 2012. 122 s.
  3. Bortovye sistemy upravlenija kosmicheskimi apparatami / Pod red. prof. A.S. Syrova. M.: Izd-vo MAI-PRINT. 2010. 304.
  4. Bondarev V.N. Napravlenija razvitija boevojj aviacii voenno-vozdushnykh sil // Oboronnyjj kompleks RF: sostojanie i perspektivy razvitija. 2014. № 4. S. 287−294.
  5. Tanenbaum EH., van Steen. M. Raspredelennye sistemy. Principy i paradigmy. SPb.: Piter. 2003. 877 s.
  6. Voevodin V.V., Voevodin Vl.V. Parallelnye vychislenija. SPb.: BKHV-Peterburg. 2002. 608 s.
  7. Gentry S., HaleviS. Implementing gentry’s fully-homomorphic encryption scheme. EUROCRYPT // ser. LectureNotesinComputerScience. Ed. K.G. Paterson. V. 6632. Springer. 2011. P. 129−148.
  8. Babenko L.K., Burtyka F.B., Makarevich O.B.i dr. Zashhishhennye vychislenija i gomomorfnoe shifrovanie // III Nacionalnyjj superkompjuternyjj forum (25−27 nojabrja 2014, g. Pereslavl-Zalesskijj). IPS imeni A.K. Ajjlamazjana RAN. 2014. URL:http://2014.nscf.ru/TesisAll/4_Systemnoe_i_promezhytochnoe_PO/01_141_ByrtikaFB.pdf.
  9. Trepacheva A.V. Kriptoanaliz gomomorfnykh kriptosistem na osnove polinomialnykh gomomorfizmov // Izvestija JUzhnogo federalnogo universiteta. Tekhnicheskie nauki. 2014. T. 158. № 9. S. 31−49.
  10. Makarevich O.B., Burtyka F.B. Zashhishhennaja oblachnaja baza dannykh s primeneniem gomomorfnojj kriptografii // Tez. dokl. 6‑jj Ross. multikonf. «Informacionnye tekhnologii v upravlenii» (ITU-2014). SPb. 2014. S. 567−572.
  11. ZHirov A.O., ZHirova A.O., Krendelev S.F. Bezopasnye oblachnye vychislenija s pomoshhju gomomorfnojj kriptografii // Bezopasnost informacionnykh tekhnologijj. 2013. № 1. S. 6−12.
  12. Burtyka F.B. Simmetrichnoe polnostju gomomorfnoe shifrovanie s ispolzovaniem neprivodimykh matrichnykh polinomov // Izvestija JUzhnogo federalnogo universiteta. Tekhnicheskie nauki. 2014. T. 158. № 9. S. 107−122.
  13. Bukhshtab A.A. Teorija chisel. M.: Prosveshhenie. 1966. 384 s.
  14. Kukushkin S.S. Teorija konechnykh polejj i informatika. T. 1. M.:Minoborony Rossii. 2003. 278 s.
  15. Finko O.A. Moduljarnaja arifmetika parallelnykh logicheskikh vychislenijj // Pod red. V.D. Maljugina. M.: Institut problem upravlenija im. V.A. Trapeznikova RAN; Krasnodar: Krasnodarskijj voen. institut. 2003. 224 s.  http://elibrary.ru/item.asp?id=23447304.
  16. SHnajjer B. Prikladnaja kriptografija. Protokoly, algoritmy, iskhodnye teksty na Si. M.: TRIUMF. 2003. 816 s.
  17. Alferov A.P., Zubov A.P., Kuzmin A.S.i dr. Osnovy kriptografii. M.: Gelios ARV. 2001. 480 s.
  18. Babash A.V., SHankin G.P. Kriptografija. M.: SOLON‑R. 2002. 512 s.

 

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