Fast Operation of Determining the Sign of a Number in RNS Using the Akushsky Core Function

Abstract

This article presents a study related to increasing the performance of distributed computing systems. The essence of fog computing lies in the use of so-called edge devices. These devices are low-power, so they are extremely sensitive to the computational complexity of the methods used. This article is aimed at improving the efficiency of calculations while maintaining an appropriate level of reliability by applying the methods of the Residue Number System (RNS). We are investigating methods for determining the sign of a number in the RNS based on the core function in order to develop a new, fast method. As a result, a fast method for determining the sign of a number based on the Akushsky core function, using approximate calculations, is obtained. Thus, in the course of this article, a study of methods for ensuring reliability in distributed computing is conducted. A fast method for determining the sign of a number in the RNS based on the core function using approximate calculations is also proposed. This result is interesting from the point of view of nebulous calculations, since it allows maintaining high reliability of a distributed system of edge devices with a slight increase in the computational complexity of non-modular operations.

Algorithm for Determining the Optimal Weights for the Akushsky Core Function with an Approximate Rank

“…This paper continues the research that was started in [1]. The work included a part of the study devoted to research related to the calculation of ACF.…”

“…In this paper, we continue the research described in the work [1]. In the presented work, a fast method for determining the sign of a number was developed based on the Akushsky Core Function (ACF).…”

“…Based on the method obtained, a performance study was conducted. The performance of the previous study was taken as a benchmark [1]. It also added the performance of calculating the positional characteristic without considering the calculation of weights, as well as the sets we offer.…”

“…If we consider Formula (4) critically, then we can note that determining the rank of a number is also a computationally complex and non-modular operation. However, in [1], our research group obtained a result from the calculation of the approximate rank of the required accuracy. The ACF itself is remarkable in that it allows you to determine the positional characteristics of the number represented in the RNS.…”

Privacy Preserving Epigenetic PaceMaker Stronger Privacy and Improved Efficiency

“…Despite this, due to the modulo operations inherent in our system, our value image range is confined to [0, N − 1], where N is the product of all primes used. Formally, for a given set of primes P, there exists two distinct integers, x and y, such that −N < y < 0 < x < N , yet x mod P = y mod P. To tackle this sign issue, we follow [6,31], and use an additional bit. This extra bit can be employed as a sign bit, ensuring that x mod P and y mod P possess unique representations.…”