scholarly journals Improved Modular Division Implementation with the Akushsky Core Function

Computation ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 9
Author(s):  
Mikhail Babenko ◽  
Andrei Tchernykh ◽  
Viktor Kuchukov
Keyword(s):  
Approximate Method ◽  
Chinese Remainder Theorem ◽  
Number System ◽  
Residue Number System ◽  
Division Algorithm ◽  
Incorrect Result ◽  
Core Function ◽  
Residue Number ◽  
Division Operation

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.

scholarly journals A Division Algorithm in a Redundant Residue Number System Using Fractions

2020 ◽  
Vol 10 (2) ◽  
pp. 695
Author(s):  
Nikolay Chervyakov ◽  
Pavel Lyakhov ◽  
Mikhail Babenko ◽  
Irina Lavrinenko ◽  
Maxim Deryabin ◽  
...  
Keyword(s):  
Chinese Remainder Theorem ◽  
Arithmetic Operation ◽  
Number System ◽  
Residue Number System ◽  
Experimental Simulation ◽  
Division Algorithm ◽  
Reverse Conversion ◽  
Base Extension ◽  
Mixed Radix Conversion ◽  
Residue Number

The residue number system (RNS) is widely used for data processing. However, division in the RNS is a rather complicated arithmetic operation, since it requires expensive and complex operators at each iteration, which requires a lot of hardware and time. In this paper, we propose a new modular division algorithm based on the Chinese remainder theorem (CRT) with fractional numbers, which allows using only one shift operation by one digit and subtraction in each iteration of the RNS division. The proposed approach makes it possible to replace such expensive operations as reverse conversion based on CRT, mixed radix conversion, and base extension by subtraction. Besides, we optimized the operation of determining the most significant bit of divider with a single shift operation of the modular divider. The proposed enhancements make the algorithm simpler and faster in comparison with currently known algorithms. The experimental simulation using Kintex-7 showed that the proposed method is up to 7.6 times faster than the CRT-based approach and is up to 10.1 times faster than the mixed radix conversion approach.

scholarly journals Computationally Efficient Approach to Implementation of the Chinese Remainder Theorem Algorithm in Minimally Redundant Residue Number System

2021 ◽  
Author(s):  
Mikhail Selianinau
Keyword(s):  
Chinese Remainder Theorem ◽  
Number System ◽  
Residue Number System ◽  
Computer Applications ◽  
Efficient Approach ◽  
Residue Modulo ◽  
Modern Computer ◽  
New Variant ◽  
Residue Number ◽  
Residue Code

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.

scholarly journals Zero-Aware Low-Precision RNS Scaling Scheme

Axioms ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 5
Author(s):  
Amir Sabbagh Molahosseini
Keyword(s):  
High Precision ◽  
Deep Neural Networks ◽  
State Of The Art ◽  
Chinese Remainder Theorem ◽  
Number System ◽  
Residue Number System ◽  
Scaling Factor ◽  
Improve Performance ◽  
High Area ◽  
Residue Number

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.

scholarly journals Data Hiding in Digital Image for Efficient Information Safety Based on Residue Number System

2021 ◽  
pp. 35-44
Author(s):  
Joseph B. Eseyin ◽  
Kazeem A. Gbolagade
Keyword(s):  
Digital Image ◽  
Chinese Remainder Theorem ◽  
Data Communication ◽  
Number System ◽  
Residue Number System ◽  
Least Significant Bit ◽  
Residue Number ◽  
Information Safety ◽  
Execution Speed ◽  
Almost All

The mass dispersal of digital communication requires the special measures of safety. The need for safe communication is greater than ever before, with computer networks now managing almost all of our business and personal affairs. Information security has become a major concern in our digital lives. The creation of new transmission technologies forces a specific protection mechanisms strategy particularly in data communication state.  We proposed a steganography method in this paper, which reads the message, converting it into its Residue Number System equivalent using the Chinese Remainder Theorem (CRT), encrypting it using the Rivest Shamir Adleman (RSA) algorithm before embedding it in a digital image using the Least Significant Bit algorithm of steganography and then transmitting it through to the appropriate destination and from which the information required to reconstruct the original message is extracted. These techniques will enhance the ability to hide data and the hiding of ciphers in steganographic image and the implementation of CRT will make the device more efficient and stronger. It reduces complexity problems and improved execution speed and reduced the time taken for processing the encryption and embedding competencies.

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