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 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 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.

EFFICIENT METHOD FOR DESIGNING MODULO {2n ± k} MULTIPLIERS

2014 ◽  
Vol 23 (01) ◽  
pp. 1450001 ◽  
Author(s):  
HECTOR PETTENGHI ◽  
SORIN COTOFANA ◽  
LEONEL SOUSA
Keyword(s):  
Efficient Method ◽  
State Of The Art ◽  
Number System ◽  
Residue Number System ◽  
The State ◽  
Experimental Results ◽  
Average Improvement ◽  
Residue Number

In this paper, an efficient method for designing memoryless modulo {2n ± k} multipliers is proposed, which can be used to compose larger residue number system (RNS) moduli sets. This technique includes a novel choice for the weights associated with the partial products of the inputs is used, which improves the performance of the resulting multipliers. Experimental results suggest that the use of this choice of input weights in the structure herein proposed, provides an average improvement of 36.3% in area-delay-product (ADP) in comparison with the related state-of-the-art. Furthermore, the structures presented in the state-of-the-art are also improved by 43.5% in ADP.

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.

RNS-to-Binary Converters for New Three-Moduli Sets {2k−3, 2k−2, 2k−1} and {2k+1, 2k+2, 2k+3}

2018 ◽  
Vol 27 (14) ◽  
pp. 1850224 ◽  
Author(s):  
P. S. Phalguna ◽  
Dattaguru V. Kamat ◽  
P. V. Ananda Mohan
Keyword(s):  
State Of The Art ◽  
Number System ◽  
Residue Number System ◽  
Hardware Requirement ◽  
Mixed Radix Conversion ◽  
Residue Number ◽  
Conversion Time

In this paper, mixed radix conversion (MRC)-based residue number system (RNS)-to-binary converters for two new three-moduli sets {2[Formula: see text], 2[Formula: see text], 2[Formula: see text]} and {2[Formula: see text], 2[Formula: see text], 2[Formula: see text]} which are derived from the moduli set {2[Formula: see text], 2[Formula: see text], 2[Formula: see text]} are presented. These have the advantage of having one modulus of the form 2[Formula: see text] or 2[Formula: see text] simplifying computations in one residue channel. The proposed reverse converters are evaluated and compared with state-of-the-art reverse converters proposed in literature for other three-moduli sets regarding hardware requirement and conversion time.

scholarly journals Robust and Fragile Medical Image Watermarking: A Joint Venture of Coding and Chaos Theories

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Atta Ur Rahman ◽  
Kiran Sultan ◽  
Dhiaa Musleh ◽  
Nahier Aldhafferi ◽  
Abdullah Alqahtani ◽  
...  
Keyword(s):  
Medical Image ◽  
Joint Venture ◽  
State Of The Art ◽  
Image Watermarking ◽  
Region Of Interest ◽  
Number System ◽  
Residue Number System ◽  
The Other ◽  
Residue Number ◽  
Hybrid Watermarking

A secure spatial domain, hybrid watermarking technique for obtaining watermark (authentication information) robustness and fragility of the host medical image (content integrity) using product codes, chaos theory, and residue number system (RNS) is proposed. The proposed scheme is highly fragile and unrecoverable in terms of the host image, but it is significantly robust and recoverable in terms of the watermark. Altering the medical image may result in misdiagnosis, hence the watermark that may contain patient information and organization logo must be protected against certain attacks. The host medical image is separated into two parts, namely, the region of interest (ROI) and region of noninterest (RONI) using a rectangular region. The RONI part is used to embed the watermark information. Moreover, two watermarks are used: one to achieve authenticity of image and the other to achieve the robustness against both incidental and malicious attacks. Effectiveness in terms of security, robustness, and fragility of the proposed scheme is demonstrated by the simulations and comparison with the other state-of-the-art techniques.

scholarly journals Neural network method for base extension in residue number system

2020 ◽  
Author(s):  
M. Babenko ◽  
E. Shiriaev ◽  
A. Tchernykh ◽  
E. Golimblevskaia
Keyword(s):  
Neural Network ◽  
Elliptic Curve ◽  
Chinese Remainder Theorem ◽  
Homomorphic Encryption ◽  
Computational Cost ◽  
Number System ◽  
Residue Number System ◽  
Pseudorandom Sequence ◽  
Base Extension ◽  
Residue Number

Confidential data security is associated with the cryptographic primitives, asymmetric encryption, elliptic curve cryptography, homomorphic encryption, cryptographic pseudorandom sequence generators based on an elliptic curve, etc. For their efficient implementation is often used Residue Number System that allows executing additions and multiplications on parallel computing channels without bit carrying between channels. A critical operation in Residue Number System implementations of asymmetric cryptosystems is base extension. It refers to the computing a residue in the extended moduli without the application of the traditional Chinese Remainder Theorem algorithm. In this work, we propose a new way to perform base extensions using a Neural Network of a final ring. We show that it reduces 11.7% of the computational cost, compared with state-of-the-art approaches.

scholarly journals An efficient implementation of the Chinese Remainder Theorem in minimally redundant Residue Number System

2020 ◽  
Vol 21 (2) ◽  
Author(s):  
Mikhail Selianinau
Keyword(s):  
Chinese Remainder Theorem ◽  
Number System ◽  
Residue Number System ◽  
Computer Applications ◽  
The Novel ◽  
Residue Modulo ◽  
Modern Computer ◽  
Residue Number ◽  
Novel Method ◽  
Redundant Residue Number System

The Chinese Remainder Theorem (CRT) widely used in many modern computer applications. This paper presents an efficient approach to the calculation of the rank of a number, a principal positional characteristic used in the Residue Number System (RNS). The proposed method does not use large modulo addition operations compared to a straightforward implementation of the CRT algorithm. The rank of a number is equal to a sum of an inexact rank and a two-valued correction factor that only takes on the values 0 or 1. We propose a minimally redundant RNS, which provides low computational complexity of the rank calculation. The effectiveness of the novel method is analyzed concerning conventional non-redundant RNS. Owing to the extension of the residue code, by adding the extra residue modulo 2, the complexity of rank calculation goes down from \(O(k^2)\) to \(O(k)\), where \(k\) equals the number of residues in non-redundant RNS.

scholarly journals New Adder-Based RNS-to-Binary Converters for the Moduli Set

2011 ◽  
Vol 2011 ◽  
pp. 1-7
Author(s):  
Kazeem Alagbe Gbolagade
Keyword(s):  
State Of The Art ◽  
Chinese Remainder Theorem ◽  
Digital Signal ◽  
Number System ◽  
Residue Number System ◽  
Hardware Complexity ◽  
Reverse Converter ◽  
Efficient Scheme ◽  
Cost Efficient ◽  
Two Hybrid

We investigate Residue Number System (RNS) to binary conversion, which is an important issue concerning the utilization of RNS numbers in Digital Signal Processing (DSP) applications. We propose two new reverse converters for the moduli set . First, we simplify the Chinese Remainder Theorem (CRT) to obtain a reverse converter that uses mod- operations instead of mod- operations required by other state-of-the-art equivalent converters. Next, we further reduce the hardware complexity by making the resulting reverse converter architecture adder based. Two hybrid Cost-Efficient (CE) and Speed-Efficient (SE) reverse converters are proposed. These two hybrid converters are obtained by combining the best state-of-the-art converter with the newly introduced area-delay efficient scheme. The proposed hybrid CE converter outperforms the best state-of-the-art CE converter in terms of delay with similar area cost. Additionally, the proposed hybrid SE converter requires less area cost with smaller delay when compared to the best state-of-the-art equivalent SE converter.

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