A Method for Arithmetic Comparison of Data Represented in a Residue Number System

Krasnobayev, Victor; Yanko, Alina; Koshman, Sergеy

doi:10.1007/s10559-016-9809-2

Cited by 61 publications

(18 citation statements)

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“…A . For this, by the values 3 1, 2 k = we define the desired value Thus, we get two code words: (1) (3, 3, 7, 7) A = and (2) (3, 1, 7, 7) A = .…”

Section: We Correct the Numbermentioning

confidence: 99%

“…Volume 34, Number 4, 2019 64 inverted, i.e. 2 3 a = , which through the second decoder in binary code is fed to the first input of the second adder, the second input of which receives the value The input of the device receives the corrected number (see Тable 2) (11, 001, 0111) A = . a = Thus, the error correction algorithms in the SRC with mutual in pairs non-simple bases make it relatively easy to implement a procedure for detecting and correcting onetime errors [4].…”

Section: Volume 34 Number 4 2019 61mentioning

confidence: 99%

“…The sum, difference, and product of any vectors of a linear code are code words. In this case, non-code words cannot be associated with any natural numbers [2]. We show that error correction in the SRC with the help of L-codes leads to hardware redundancy equivalent to reservation.…”

Section: Introductionmentioning

confidence: 96%

“…It is enough to define the diagonal elements of the matrix G and add one value 1 n a , i.e. It is easy to check that with such values of ij a , it is possible to establish not only the fact of code word distortion, but also to determine the number of the distorted residue [2]. In order to determine the necessary and sufficient conditions for correcting one-time errors using L-codes, the following theorem was formulated and proved.…”

Section: Introductionmentioning

confidence: 99%

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The implementation of L-codes in the system of residual classes

Yanko¹,

Krasnobayev²,

Martynenko³

2019

FARPLSS

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The possibilities of R-codes for error correction in the system SRC are being intensively investigated. This is due to the simplicity of the structure of R-codes and good corrective capabilities, as well as the comparative simplicity of their construction for any given minimum code distance. It is important and interesting to consider the so-called linear codes (L-codes) in the SRC. In the literature, L-codes are described qualitatively rather than quantitatively. Until now no one has researched in depth the properties of systems of residual classes, whose bases are not mutually prime numbers. Such a system also has certain corrective properties, which makes it necessary to assess the possibility and feasibility of using such systems to improve the reliability of computer systems and components. Therefore, this important and promising issue is considered in this article.

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“…A . For this, by the values 3 1, 2 k = we define the desired value Thus, we get two code words: (1) (3, 3, 7, 7) A = and (2) (3, 1, 7, 7) A = .…”

Section: We Correct the Numbermentioning

confidence: 99%

Section: Volume 34 Number 4 2019 61mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The implementation of L-codes in the system of residual classes

Yanko¹,

Krasnobayev²,

Martynenko³

2019

FARPLSS

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“…Складність завдань, які вирішуються сучасними системами і засобами обробки цілочисельної інформації (ЗОІ), обумовлює до них підвищені вимоги щодо якості обробки інформації [1][2][3][4][5][6][7][8]. Рішення широкого кола складних обчислювальних задач вимагає (наприклад, реалізація асиметричних криптографічних алгоритмів, оптимізація обчислень в теорії сигналів та шумостійке кодування [4,[8][9][10][11], реалізація симетричних крипто-примітивів [12][13][14][15][16][17][18] та багато іншого [19][20][21][22]) значних обсягів розрахунків, які проводяться в реальному часі функціонування ЗОІ.…”

Section: вступunclassified

Mathematical model of the process of tabular’s implementation of the operation algebraic multiplication in the residues class

Краснобаєв¹,

Зуб²,

Reshetniak³

et al. 2019

Computer Science and Cybersecurity

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Based on the properties of the class of residues in the article, a mathematical model of the process of tabular implementation of modular multiplication was synthesized, for both positive and negative numerical ranges of information processing by means of integer information processing. This model is recommended for practical application in the development of methods and algorithms for rapid processing of cryptographic information. Finding ways to simplify the structure of the table operating device integer information processing has led to the need to improve the mathematical model, methods and algorithms for modular operations, which increase the efficiency of the use of table arithmetic in the class of residues. A feature of the implementation of this model is the possibility of reducing the number of equipment operating device integer information by reducing the (50-70)% of logical elements "And" in the nodes of the table permanent storage device, directly implement the operation of modular multiplication by arbitrary mi module residual class. This is possible by using the symmetry properties of the aibi (mod mi) implementation table of the modular multiplication operation.

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