This article presents a study related to increasing the performance of distributed computing systems. The essence fog lies in use so-called edge devices. These devices are low-power, so they extremely sensitive computational complexity methods used. is aimed at improving efficiency calculations while maintaining an appropriate level reliability by applying Residue Number System (RNS). We invest...

This paper introduces a method for extracting the core of a Residue Number System (RNS) number within the RNS, this affording a new method for scaling RNS numbers. Suppose an RNS comprises a set of co-prime moduli, mi, with ∏mi = M. This paper describes a method for approximately scaling such an RNS number by a subset of the moduli, ∏mj = MJ ≈ √M, with the characteristic that all computations a...

Fully Homomorphic Encryption (FHE) permits processing information in the form of ciphertexts without decryption. It can ensure security common technologies used today, such as cloud computing, Internet Things, and machine learning, among others. A primary disadvantage for its practical application is low efficiency sign comparison operations. Several FHE schemes use Residue Number System (RNS) ...

in this paper, a new method is introduced for improving the efficiency of the residue number system, which uses both binary and residue representations in order to represent a number. a residue number system uses the remainder of the division in several different modules. conversion of a number to smaller ones and carrying out parallel calculations on these numbers greatly increase the speed of...

Residue Number Systems (RNS) are naturally considered as an interesting candidate to provide efficient arithmetic for implementations of cryptosystems such as RSA, ECC (Elliptic Curve Cryptography), pairings, etc. More recently, RNS have been used to accelerate fully homomorphic encryption as lattice-based cryptogaphy. In this paper, we present an RNS algorithm resolving the Closest Vector Prob...

In this paper, we present a high speed pairing coprocessor using Residue Number System (RNS) and lazy reduction. We show that combining RNS, which are naturally suitable for parallel architectures, and lazy reduction, which performs one reduction for more than one multiplication, the computational complexity of pairings can be largely reduced. The design is prototyped on a Xilinx Virtex-6 FPGA,...

The residue number system (RNS) has computational advantages for large integer arithmetic because of its parallel carry free, and high-speed arithmetic nature. However, magnitude comparison is a very complex operation for RNS. This paper presents a new comparison algorithm based on the modification of Mixed-Radix Conversion II technique. The new algorithm uses small modulo operations only and h...

Residue Number System is a numerical system which arithmetic operations are performed parallelly. One of the main factors that affects the system’s performance is the complexity of reverse converter. It should be noted that the complexity of this part should not affect the earned speed of parallelly performed arithmetic unit. Therefore in this paper a high speed converter for moduli set {2n-1, ...

Residue Number System is a numerical system which arithmetic operations are performed parallelly. One of the main factors that affects the system’s performance is the complexity of reverse converter. It should be noted that the complexity of this part should not affect the earned speed of parallelly performed arithmetic unit. Therefore in this paper a high speed converter for moduli set {2n-1, ...

In this paper, some of the main properties of various number systems such as the Double-Base Number System (DBNS), Fermat Number System (FNS), Residue Number System (RNS), Redundant Complex Number System (RCNS) and Complex Logarithmic Number System (CLNS) have been discussed. Also, the applications of these various number systems in the area of VLSI design, digital signal processing, finite imp...