Due to legal restrictions or restrictions related to companies' internal information policies, businesses often do not trust sensitive information to public cloud providers. One of the mechanisms to ensure the security of sensitive data in clouds is homomorphic encryption. Privacy-preserving neural networks are used to design solutions that utilize neural networks under these conditions. They exploit the homomorphic encryption mechanism, thus enabling the security of commercial information in the cloud. The main deterrent to the use of privacy-preserving neural networks is the large computational and spatial complexity of the scalar multiplication algorithm, which is the basic algorithm for computing mathematical convolution. In this paper, we propose a scalar multiplication algorithm that reduces the spatial complexity from quadratic to linear, and reduces the computation time of scalar multiplication by a factor of 1.38.

Ensuring reliable data storage in a cloud environment is a challenging problem. One of the efficient mechanisms used to solve it is the Redundant Residue Number System (RRNS) with the projection method, a commonly used mechanism for detecting errors. However, the error correction based on the projection method has exponential complexity depending on the number of control and working moduli. In this paper, we propose an optimization mechanism using a base extension and Hamming distance to reduce the number of calculated projections. We show that they can be reduced up to three times than the classical projection method and, hence, the time complexity of data recovery in the distributed cloud data storage.

Fog computing (FC) is a distributed architecture in which computing resources and services are placed on edge devices closer to data sources. This enables more efficient data processing, shorter latency times, and better performance. Fog computing was shown to be a promising solution for addressing the new computing requirements. However, there are still many challenges to overcome to utilize this new computing paradigm, in particular, reliability and security. Following this need, a systematic literature review was conducted to create a list of requirements. As a result, the following four key requirements were formulated: (1) low latency and response times; (2) scalability and resource management; (3) fault tolerance and redundancy; and (4) privacy and security. Low delay and response can be achieved through edge caching, edge real-time analyses and decision making, and mobile edge computing. Scalability and resource management can be enabled by edge federation, virtualization and containerization, and edge resource discovery and orchestration. Fault tolerance and redundancy can be enabled by backup and recovery mechanisms, data replication strategies, and disaster recovery plans, with a residual number system (RNS) being a promising solution. Data security and data privacy are manifested in strong authentication and authorization mechanisms, access control and authorization management, with fully homomorphic encryption (FHE) and the secret sharing system (SSS) being of particular interest.

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.

Homomorphic encryption (HE) is a promising solution for handling sensitive data in semi-trusted third-party computing environments, as it enables processing of encrypted data. However, applying sophisticated techniques such as machine learning, statistics, and image processing to encrypted data remains a challenge. The computational complexity of some encrypted operations can significantly increase processing time. In this paper, we focus on the analysis of two state-of-the-art HE matrix multiplication algorithms with the best time and space complexities. We show how their performance depends on the libraries and the execution context, considering the standard Cheon–Kim–Kim–Song (CKKS) HE scheme with fixed-point numbers based on the Microsoft SEAL and PALISADE libraries. We show that Windows OS for the SEAL library and Linux OS for the PALISADE library are the best options. In general, PALISADE-Linux outperforms PALISADE-Windows, SEAL-Linux, and SEAL-Windows by 1.28, 1.59, and 1.67 times on average for different matrix sizes, respectively. We derive high-precision extrapolation formulas to estimate the processing time of HE multiplication of larger matrices.

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.