Techniques for Raising the Remainder to a Power in the System of Residual Classes

Krasnobayev, Victor; Кuznetsov, Alexandr; Lokotkova, Irina; Кіян, Анастасія; Кузнецова, Тетяна

doi:10.1109/dessert50317.2020.9125049

Cited by 3 publications

(1 citation statement)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Thus, researches devoted to the development of a method for raising the residues of integers modulo an arbitrary SRC to the power of a natural number are relevant and important. However, the existing methods for implementing the modular operation of raising integers to a power [19] are not always applicable for their implementation in a negative numerical range. This is mainly due to the fact that there is no simple mathematical model [20] for the process of raising integers to an arbitrary power of a natural number in the SRC, both in positive and negative numerical ranges.…”

Section: Problem Statementmentioning

confidence: 99%

Mathematical Model of the Process of Raising Integers to an Arbitrary Power of a Natural Number in the System of Residual Classes

Yanko,

Kovalchuk

2023

TACS

View full text Add to dashboard Cite

It is known that the use of a non-positional number system in residual classes (SRC) in computer systems (CS) can significantly increase the speed of the implementation of integer arithmetic operations. The use of such properties of a non-positional number system in the SRC as independence, equality and low-bitness (low-digit capacity) of the residues that define the non-positional code data structure of the SRC provides high user performance for the implementation in the CS of computational algorithms consisting of a set of arithmetic (modular) operations. The greatest efficiency from the use of the SRC is achieved when the implemented algorithms consist of a set of arithmetic operations such as addition, multiplication and subtraction. There is a large class of algorithms and tasks (tasks of implementing cryptoalgorithms, optimization tasks, computational tasks of large dimension, etc.), where, in addition to performing integer arithmetic operations of addition, subtraction, multiplication, raising integers modulo and others in a positive numerical range, there is a need to implement the listed above arithmetic and other operations, in the negative numerical range. The need to perform these operations in a negative numerical range significantly reduces the overall efficiency of using the SRC as a number system of the CS. In this aspect, the lack of a mathematical model for the process of raising integers in the SRC in the negative numerical region makes it difficult to develop methods and procedures for raising integers to an arbitrary power of a natural number in the SRC, both in positive and negative numerical ranges. The purpose of the article is the synthesis of a mathematical model of the process of raising integers to an arbitrary power of a natural number in the SRC, both in positive and negative numerical ranges.

show abstract

Section: Problem Statementmentioning

confidence: 99%