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The BBGKY Hierarchy of Quantum Kinetic Equations and Its Application in Cryptography

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Abstract

In this paper, a new encryption method based on statistical mechanics is proposed, which enables transmitting information without transmitting the encryption key after sending the information, and also makes it possible to determine its own transformation for each information cell. For these purposes, solutions of the Schrödinger equation (Lieb–Liniger model) and a hierarchy of quantum kinetic BBGKY equations with the delta-function potential are used.

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REFERENCES

  1. J. Daemen and V. Rijmen, The Design of Rijndael AES—The Advanced Encryption Standard (Springer, Berlin, 2002).

    MATH  Google Scholar 

  2. E. H. Lieb and W. Liniger, “Exact analysis of an interacting Bose gas. I: The general solution and the ground state,” Phys. Rev. 130, 1605–1616 (1963).

    Article  ADS  MathSciNet  Google Scholar 

  3. A. Shamir, R. L. Rivest, and L. M. Adleman, in Mental Poker, Ed. by D. A. Klarner (The Mathematical Gardner, Wadsworth, 1981), p. 37–43.

  4. N. N. Bogolyubov, Lectures on Quantum Statistics (Gordon and Breach, New York, 1967).

    Google Scholar 

  5. N. N. Bogolyubov and N. N. Bogolyubov, Introduction to Quantum Statistical Mechanics (Nauka, Moscow, 1984) [in Russian].

    MATH  Google Scholar 

  6. D. Ya. Petrina, Mathematical Foundation of Quantum Statistical Mechanics, Continuous Systems (Kluwer Academic, Dordrecht, 1995).

    Book  Google Scholar 

  7. M. Yu. Rasulova, “Cauchi problem for Bogolyubov kinetic equations. Quantum case,” Akad. Nauk Uzb. SSR, No. 2, 6–9 (1976) [in Russian].

    MathSciNet  Google Scholar 

  8. H. A. Bethe, “On the theory of metals. I. Eigenvalues and eigenfunctions of a linear chain of atoms,” Z. Phys. 71, 205–226 (1931).

    Article  ADS  Google Scholar 

  9. A. Craig, I. Tracy, and H. J. Widom, “The dynamics of the one-dimensional delta-function Bose gas,” Phys. A: Math. Theor. 41, 485204-6 (2008).

    Article  MathSciNet  Google Scholar 

  10. M. Yu. Rasulova, “The solution of quantum kinetic equation with delta potential and its application for information technology,” Appl. Math. Inf. Sci. 12, 685–688 (2018).

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Institute of Nuclear Physics, 100214, Ulugbek, Tashkent, Uzbekistan

    M. Yu. Rasulova

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  1. M. Yu. Rasulova
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Correspondence to M. Yu. Rasulova.

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Translated by G. Dedkov

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Rasulova, M.Y. The BBGKY Hierarchy of Quantum Kinetic Equations and Its Application in Cryptography. Phys. Part. Nuclei 51, 781–785 (2020). https://doi.org/10.1134/S1063779620040619

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  • DOI: https://doi.org/10.1134/S1063779620040619

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