Method for Implementing the Arithmetic Operation of Addition in Residue Number System Based on the Use of the Principle of Circular Shift

Krasnobayev, Victor; Koshman, Sergеy

doi:10.1007/s10559-019-00179-8

Cited by 8 publications

(6 citation statements)

References 5 publications

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“…In low-level programming and computer architecture, integers are represented as sequences of bits. This representation allows for bitwise operations like shifting, masking, and logical operations [4], which are used in various applications such as data encoding, encryption, and optimization algorithms. Integers are often the subject of study in algorithm design and analysis.…”

Section:  Issn:2302-9285mentioning

confidence: 99%

“…Many algorithms and data structures are designed specifically to efficiently handle integer inputs or produce integer outputs. Overall, integer representation is fundamental in computer science and mathematics, serving as a cornerstone for data representation, numerical computations, and algorithmic problem-solving [4]. Integer representation has been exploited before for many different applications of computing such as encryption [5] and compression [6].…”

Section:  Issn:2302-9285mentioning

confidence: 99%

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Challenges in data representation for efficient execution of encryption operation

Afendee Mohamed,

Garba Shawai,

Almaiah

et al. 2024

Bulletin EEI

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Big number operation has always been a bottleneck to computer system as it imposes high demand on computing power. With a limited power available, operations such as exponentiation and multiplication involving large integer belonging to encryption process requires grave scrutiny. One way to address this issue is by replacing an original complex computation into a sequence of small computations that in the end produces the same results. This paper takes an evolutionary approach to survey numerous articles that have contributed to the advancement of integer representation. Numerous representations were proposed, those that come into play concentrated on reducing non-zero digits and limiting non-zero spacing other than allowing subtraction operation. A comparison was made to distinguish the properties of each method from the others. This detailed outlook can be a guide for identifying the correct representation to be chosen for implementation within specific application.

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Section:  Issn:2302-9285mentioning

confidence: 99%

Section:  Issn:2302-9285mentioning

confidence: 99%

Challenges in data representation for efficient execution of encryption operation

Afendee Mohamed,

Garba Shawai,

Almaiah

et al. 2024

Bulletin EEI

View full text Add to dashboard Cite

show abstract

“…The Chinese remainder theorem states that if we know the remainder of the Euclidean division of an integer n by several integers, we can uniquely determine the remainder of the division of n by the product of these integers, provided that the divisors are prime to each other [32][33][34][35]. CRT algorithm is used to convert from RNS to the binary system [36][37][38].…”

Section: Chinese Remainder Theorem (Crt)mentioning

confidence: 99%

An efficient image cryptosystem based on the residue number system and hybrid chaotic maps

Kari¹,

Ghomian

2023

Preprint

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This paper presents a new method for encrypting gray-scale digital images. The proposed method uses a combination of the residue number system and chaotic maps to avoid the complexities of high-dimensional chaotic maps and improve the security of encryption and processing speed. In this method, the image pixel coordinates confusion operation is performed by Arnold's cat map, and the pixel content diffusion step is performed in two phases. In the first phase, the contents of the image pixels are converted to the introduced {(r-1)a, rb, (r + 1)c} residue number system and stored in a matrix. At the same time, a chaotic system produces a combination of Sinusoidal and Logistic maps of chaotic sequences, and after quantization, they are converted into the introduced residue number system and stored in another matrix of the same size. In the second phase of diffusion, XOR operation is performed between these two matrices. The implementation results show that the use of the residue number system, in addition to improving the evaluation parameters, improves the processing time, and the average processing time for encryption is 0.15 seconds. Also, the uniform histogram, the entropy of about 8, and the correlation coefficient close to 0 of the encrypted images all demonstrate the high security of the proposed method.

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“…is based on the usage of structures of positional low-bit binary adders [4][5][6][7]. This approach provides a wide range of options for implementation of the structure of such adders.…”

Section: Introductionmentioning

confidence: 99%

Synthesis of Structure of the Adder by Module

Krasnobayev¹,

Koshman²,

Kovalchuk³

2021

CNCS

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The subject of the article is the study of the structure of low-bit binary adders for an arbitrary modulus of the residual class system (RCS). The purpose of this article is to develop an algorithm for synthesizing the structure of the adder of two residuals of numbers by an arbitrary value of the RCS module, by organizing inter-bit connections between the binary digits of the adder, the combination of which determines the structure of the adder modulo. Tasks: to investigate the possibility of performing the operation of addition of two residuals in RCS based on positional binary adders; to analyze the influence of additionally introduced interdigit connections into the positional binary adder on the value of the contents of this adder; to develop an algorithm for the synthesis of an adder by an arbitrary RCS module. Research methods: methods of analysis and synthesis of computer systems, number theory, coding theory in RCS. The following results were obtained. It is shown in the work that the introduction of additional interdigit connections in a positional binary adder allows changing the contents of this adder. The rules for the introduction of these additional links are formulated, on the basis of which an algorithm for the synthesis of an adder by an arbitrary RCS modulus is obtained. Specific examples of the synthesis of structures of binary adders for various values of the RCS modules are given. Conclusions. Thus, the paper proposes an algorithm for the synthesis of an adder by an arbitrary RCS module, which is based on the use of positional binary adders, by introducing additional inter-bit connections. The application of the considered algorithm expands the functionality of positional binary adders

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Method for Implementing the Arithmetic Operation of Addition in Residue Number System Based on the Use of the Principle of Circular Shift

Cited by 8 publications

References 5 publications

Challenges in data representation for efficient execution of encryption operation

Challenges in data representation for efficient execution of encryption operation

An efficient image cryptosystem based on the residue number system and hybrid chaotic maps

Synthesis of Structure of the Adder by Module

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