The Development of Probabilistic Algorithm of Monitoring a Result Correctness for Cloud Computing in Residue Number System

Author(s):  
Chervyakov Nikolai Ivanovich ◽  
Nazarov Anton Sergeevich ◽  
Babenko Mikhail Grigor'Evich ◽  
Garianina Anastasiia Igorevna ◽  
Abhishek Vaish
2021 ◽  
Vol 1715 ◽  
pp. 012052
Author(s):  
N Kucherov ◽  
E Kuchukova ◽  
A Tchernykh ◽  
V Kuchukov ◽  
M Babenko

2017 ◽  
Vol 8 (3) ◽  
pp. 189-200 ◽  
Author(s):  
Jean-Claude Bajard ◽  
Julien Eynard ◽  
Nabil Merkiche

Author(s):  
Mikhail Selianinau

AbstractIn this paper, we deal with the critical problem of performing non-modular operations in the Residue Number System (RNS). The Chinese Remainder Theorem (CRT) is widely used in many modern computer applications. Throughout the article, an efficient approach for implementing the CRT algorithm is described. The structure of the rank of an RNS number, a principal positional characteristic of the residue code, is investigated. It is shown that the rank of a number can be represented by a sum of an inexact rank and a two-valued correction to it. We propose a new variant of minimally redundant RNS, which provides low computational complexity for the rank calculation, and its effectiveness analyzed concerning conventional non-redundant RNS. Owing to the extension of the residue code, by adding the excess residue modulo 2, the complexity of the rank calculation goes down from $O\left (k^{2}\right )$ O k 2 to $O\left (k\right )$ O k with respect to required modular addition operations and lookup tables, where k equals the number of non-redundant RNS moduli.


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