Manylion Llyfryddiaeth
| Teitl: |
МЕТОДИ ПОБУДОВИ ДОСКОНАЛОЇ ФОРМИ СИСТЕМИ ЗАЛИШКОВИХ КЛАСІВ НА МНОЖИНІ ЦІЛИХ КОМПЛЕКСНИХ ЧИСЕЛ. |
| Alternate Title: |
METHODS FOR CONSTRUCTING THE PERFECT FORM OF RESIDUE NUMBER SYSTEM ON THE SET OF COMPLEX INTEGERS. |
| Awduron: |
Алілуйко, А. М.1 aliluyko82@gmail.com |
| Ffynhonnell: |
Informatics & Mathematical Methods in Simulation / Informatika ta Matematičnì Metodi v Modelûvannì. 2024, Vol. 14 Issue 4, p324-334. 11p. |
| Termau Pwnc: |
*CHINESE remainder theorem, *NUMBER theory, *COMPLEX numbers, *PUBLIC key cryptography, *MODULAR arithmetic |
| Crynodeb: |
So much attention is paid to the tasks of increasing the speed of algorithms for performing modular arithmetic operations. The non-positional residue number system is quite promising for application in modern number theory, applied and computational mathematics, and asymmetric cryptography. This article is focused on the development of methods for finding a set of modules of a perfect-form residue number system in the domain of complex integers, which is an extension of the set of integers. A relevant problem has been solved: finding an arbitrary number of modules of the perfect form of an integer complex residue number system based on fractional transformations and factorization of the product of numbers. The use of this method allows for a significant reduction in computational complexity during arithmetic operations on complex numbers by parallelizing the computation process and converting numbers within the residue number system, eliminating the procedure of finding the inverse element modulo and multiplication by base numbers. Sets of three-module perfect form of the complex residue number system were obtained for the first time. Conditions have been determined for finding any number of modules of modified perfect form of a complex residue number system, with two of them are unknown. Examples of the application of the proposed methods for the perfect form of the residue number system are provided, in which all possible sets of complex modules are obtained for a given smallest module. Tabular values of the obtained modulus norms are presented and their graphical dependencies are analyzed. The results of the conducted research demonstrate that the proposed method significantly reduces the computational complexity of the Chinese Remainder Theorem by avoiding the operation of finding the inverse element modulo. The use of the proposed method for selecting modules that form a perfect form will increase the performance of computational systems operating within the residue number system. [ABSTRACT FROM AUTHOR] |
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| Cronfa ddata: |
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