Improved Modular Division Implementation with the Akushsky Core Function

The residue number system (RNS) is widely used in different areas due to the efficiency of modular addition and multiplication operations. However, non-modular operations, such as sign and division operations, are computationally complex. A fractional representation based on the Chinese remainder theorem is widely used. In some cases, this method gives an incorrect result associated with round-off calculation errors. In this paper, we optimize the division operation in RNS using the Akushsky core function without critical cores. We show that the proposed method reduces the size of the operands by half and does not require additional restrictions on the divisor as in the division algorithm in RNS based on the approximate method.

En-AR-PRNS: Entropy-Based Reliability for Configurable and Scalable Distributed Storage Systems

Storage-as-a-service offers cost savings, convenience, mobility, scalability, redundant locations with a backup solution, on-demand with just-in-time capacity, syncing and updating, etc. While this type of cloud service has opened many opportunities, there are important considerations. When one uses a cloud provider, their data are no longer on their controllable local storage. Thus, there are the risks of compromised confidentiality and integrity, lack of availability, and technical failures that are difficult to predict in advance. The contribution of this paper can be summarized as follows: (1) We propose a novel mechanism, En-AR-PRNS, for improving reliability in the configurable, scalable, reliable, and secure distribution of data storage that can be incorporated along with storage-as-a-service applications. (2) We introduce a new error correction method based on the entropy (En) paradigm to correct hardware and software malfunctions, integrity violation, malicious intrusions, unexpected and unauthorized data modifications, etc., applying a polynomial residue number system (PRNS). (3) We use the concept of an approximation of the rank (AR) of a polynomial to reduce the computational complexity of the decoding. En-AR-PRNS combines a secret sharing scheme and error correction codes with an improved multiple failure detection/recovery mechanism. (4) We provide a theoretical analysis supporting the dynamic storage configuration to deal with varied user preferences and storage properties to ensure high-quality solutions in a non-stationary environment. (5) We discuss approaches to efficiently exploit parallel processing for security and reliability optimization. (6) We demonstrate that the reliability of En-AR-PRNS is up to 6.2 times higher than that of the classic PRNS.

Zero-Aware Low-Precision RNS Scaling Scheme

Scaling is one of the complex operations in the Residue Number System (RNS). This operation is necessary for RNS-based implementations of deep neural networks (DNNs) to prevent overflow. However, the state-of-the-art RNS scalers for special moduli sets consider the 2k modulo as the scaling factor, which results in a high-precision output with a high area and delay. Therefore, low-precision scaling based on multi-moduli scaling factors should be used to improve performance. However, low-precision scaling for numbers less than the scale factor results in zero output, which makes the subsequent operation result faulty. This paper first presents the formulation and hardware architecture of low-precision RNS scaling for four-moduli sets using new Chinese remainder theorem 2 (New CRT-II) based on a two-moduli scaling factor. Next, the low-precision scaler circuits are reused to achieve a high-precision scaler with the minimum overhead. Therefore, the proposed scaler can detect the zero output after low-precision scaling and then transform low-precision scaled residues to high precision to prevent zero output when the input number is not zero.

An Enhanced Error Detection and Correction Scheme for Enterprise Resource Planning (ERP) Data Storage

In this research paper, a Redundant Residue Number System (n,k) code is introduced to enhance Cloud ERP Data storage. The research findings have been able to demonstrate the application of Redundant Residue Number System (RRNS) in the concept of Cloud ERP Data storage. The scheme contributed in addressing data loss challenges during data transmission. The proposed scheme also addressed and improved the probability of failure to access data compared to other existing systems. The proposed scheme adopted the concept of Homomorphic encryption and secret sharing whiles applying Redundant Residue Number System to detect and correct errors.The moduli set used is {2m, 2m + 1, 2m+1 - 1, 2m+1 + 1, 2m+1 + k, 22m - k, 22m + 1} where k is the number of the information moduli set used. The information moduli set is {2m, 2m + 1, 2m+1 - 1} and the redundant moduli is {2m+1 + 1, 2m+1 + k, 22m - k, 22m + 1}. The proposed scheme per the simulation results using python reveals that it performs far better in terms of data loss and failure to access data related concerns. The proposed scheme performed better between 41.2% for data loss to about 99% for data access based on the combination of (2, 4) and (2, 5) data shares respectively in a (k, n) settings.

Sign Detection and Signed Integer Comparison for the 3-Moduli Set {2^n±1,2^(n+k)}

Comparison, division and sign detection are considered complicated operations in residue number system (RNS). A straightforward solution is to convert RNS numbers into binary formats and then perform complicated operations using conventional binary operators. If efficient circuits are provided for comparison, division and sign detection, the application of RNS can be extended to the cases including these operations.For RNS comparison in the 3-moduli set , we have only found one hardware realization. In this paper, an efficient RNS comparator is proposed for the moduli set which employs sign detection method and operates more efficient than its counterparts. The proposed sign detector and comparator utilize dynamic range partitioning (DRP), which has been recently presented for unsigned RNS comparison. Delay and cost of the proposed comparator are lower than the previous works and makes it appropriate for RNS applications with limited delay and cost.

A New Approach to Detecting and Correcting Single and Multiple Errors in Wireless Sensor Networks

Transmission errors are commonplace in communication systems. Wireless sensor networks like many other communication systems are susceptible to various forms of errors arising from sheer noise, heat and interference in sensor circuitry and from other forms of distortions. Research efforts in WSN have attempted to guarantee reliable and accurate data transmission from a target environment in the midst of these unwanted exposures. Many techniques have appeared and employed over the years to deal with the issue of transmission errors in communication systems. In this paper we present a new approach for single and multiple error control in WSN relying on the inherent fault tolerant feature of the Redundant Residue Number System. As an off shoot of Residue Number System, RRNS's fault tolerant capabilities help in building robust systems required for reliable data transmission in WSN systems. The Chinese Remainder Theorem and the Manhattan Distance Heuristics are used during the integer recovery process when detecting and correcting error digit(s) in a transmitted data. The proposed method performs considerably better in terms of data retrieval time than similar approaches by needing a smaller number of iterations to recover an originally transmitted data from its erroneous form. The approach in this work is also less computationally intensive compared to recent techniques during the error correction steps. Evidence of utility of the technique is illustrated in numerical examples.

Determining the rank of a number in the residue number system

In this article, the formulation and proof of the theorem on the difference in the ranks of the numbers represented in the Residue Number System is carried out. A method is proposed that allows to reduce the amount of necessary calculations and increases the speed of calculating the rank of a number relative to the method for calculating the rank of a number based on the approximate method. To find the rank of a number in the method for calculating the rank of a number based on the approximate method, it is necessary to calculate n operations with numbers exceeding the modulus value; in the proposed method, it is necessary to calculate n·(n−1)/2 operations not exceeding the value of the module.