The BBGKY Hierarchy of Quantum Kinetic Equations and Its Application in Cryptography
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e BBGKY Hierarchy of Quantum Kinetic Equations and Its Application in Cryptography M. Yu. Rasulova* Institute of Nuclear Physics, Ulugbek, Tashkent, 100214 Uzbekistan *e-mail: [email protected] Received December 20, 2019; revised January 16, 2020; accepted January 29, 2020
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. DOI: 10.1134/S1063779620040619
1. INTRODUCTION One of the most urgent problems of our time is the security of information transfer. This can be seen even from the fact how much spam we receive every day by email. It is known that “Advanced Encryption Standard” [1], which is the basis of western information encryption, is based on such chaotic actions as permutation of cells, columns and matrix rows, which are the conversion of plaintext to ciphertext. These actions are random in nature and therefore do not provide complete confidentiality of information. Complete closeness of information can be provided if each information cell is closed using its own transformation. Such a complete set of transformations can be obtained by solving the equations for a function of N variables, where N is the number of cells. As known, there are very few exactly solvable equations for functions of N variables. One of the most reliable is the Lieb–Liniger model for describing the system of bosons interacting by means of delta-function potentials. This problem was first solved by Lieb and Liniger [2] and is known in the scientific literature as the Lieb–Liniger model. Another vulnerable point leading to the loss of information security is the process of the encryption key transmitting after sending encrypted information from the sender (Alice) to the recipient (Bob). This vulnerability can be eliminated if Alice and Bob have their own encryption keys. Researchers drew attention to the problem of having their own encryption keys long before the development of modern information technologies. Back in the early 30s of the twentieth century, an attempt to play poker at a distance between Professor Niels Bohr with his son, Heisenberg and other colleagues was unsuccessful, and a problem
arose for the players to have their own encryption keys. Only in the 80s of the 20th century, Adi Shamir [3] indicated a way to solve this problem. His method of solving the problem is often called a three-step protocol. It consists of the following steps. Alice encrypts the information with her encryption key and sends it to Bob. Bob encrypts the received information with his own encryption key and returns the information now under the two encryption keys back to Alice. Alice, having received this information, decrypts it with her
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