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.
Fully Homomorphic Encryption (FHE) permits processing information in the form of ciphertexts without decryption. It can ensure the security of information in common technologies used today, such as cloud computing, the Internet of Things, and machine learning, among others. A primary disadvantage for its practical application is the low efficiency of sign and comparison operations. Several FHE schemes use the Residue Number System (RNS) to decrease the time complexity of these operations. Converting from the RNS to the positional number system and calculating the positional characteristic of a number are standard approaches for both operations in the RNS domain. In this paper, we propose a new method for comparing numbers and determining the sign of a number in RNS. We focus on the even ranges that are computationally simple due to their peculiarities. We compare the performance of several state-of-art algorithms based on an implementation in C++ and relatively simple moduli with a bit depth from 24 to 64 bits. The experimental analysis shows a better performance of our approach for all the test cases; it improves the sign detection between 1.93 and 15.3 times and the number comparison within 1.55–11.35 times with respect to all the methods and configurations.
A smart city has a complex hierarchical communication system with various components. It must meet the requirements of fast connection, reliability, and security without data compromise. Internet of Things technology is widely used to provide connectivity and control solutions for smart sensors and other devices using heterogeneous networking technologies. In this paper, we propose a routing solution for Wireless Sensor Networks (WSN) and Mobile Ad hoc NETworks (MANET) with increasing speed, reliability, and sufficient security. Many routing protocols have been proposed for WSNs and MANETs. We combine the Secret Sharing Schemes (SSS) and Redundant Residual Number Systems (RRNS) to provide an efficient mechanism for a Distributed dynamic heterogeneous network Transmission (DT) with new security and reliability routing protocol (DT-RRNS). We analyze the concept of data transmission based on RRNS that divides data into smaller encoded shares and transmits them in parallel, protecting them from attacks on routes by adaptive multipath secured transmission and providing self-correcting properties that improve the reliability and fault tolerance of the entire system.
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