Вибір параметрів еліптичних кривих у задачах шифрування інформаційних потоків
Loading...
Date
2018
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
The analysis of information flow protection systems using the mathematical apparatus of elliptic curves (EC) was conducted in this paper on which basis the main advantages were established, namely, the speed and relatively small length of the key. It provides unique capabilities for building reliable and efficient cryptographic algorithms. Despite the significant advantages of EC in cryptographic information security systems, there are also some difficulties that hamper the practical use of EC in these systems. They are conditioned by the need for solving such urgent classes of tasks – providing a simple number of p – module for the conversion of groups of points of an elliptic curve, generating parameters and bases on the EC, finding the order of EC. Therefore, studies were conducted on the choice of parameters of the EC according to certain criteria, taking into account which can build information flow protection systems that will provide the necessary level of stability and security against unauthorized access. The theoretical foundations of cryptography on the basis of the mathematical apparatus of elliptic curves and the estimation of computational complexity of the methods of point exponentiation, which are basic in encrypting information flows in computer systems are presented. Based on the conducted studies, the graphs of the dependence of memory volume M of each method, depending on the width of the window w, when bit input parameters of the EC 200 bit and the time complexity. The latter points indicate a significant advantage of the method of maximum memory compared with the method of exponentiation at a fixed point, and in two cases, there is a slight decrease in computing resources approximately 1.25 times with an increase in the dimension of the window. It is also established that the method of exponentialization at a fixed point needs much less memory.
Description
Keywords
еліптична крива, криптографія, порядок еліптичної кривої, базові параметри, експоненціювання точок, дискретний логарифм, обсяг пам'яті, часова складність, просте число, модуль перетворень, elliptic curve, cryptography, order of elliptic curve, basic parameters, point exponentiation, discrete logarithm, memory volume, temporal complexity, simple number, module for the conversion