Symmetric Cryptoalgorithms in the Residue Number System

Kasianchuk, Mykhailo; Yakymenko, Igor; Nykolaychuk, Yaroslav

doi:10.1007/s10559-021-00358-6

Cited by 9 publications

(8 citation statements)

References 18 publications

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“…The deduction system is a modular non-positional system for representing digits. In scientific circles, it is generally believed that this view is based on the Chinese remainder theorem, the calculations of Nicomachus from Gerasa, Euclid, and Euler, or even more ancient Aztec and Mayan calculus [5][6][7][8][9].…”

Section: Methodsmentioning

confidence: 99%

“…In the works of [7,8], for error correction in the RNS, the possibilities of non-linear codes (R-codes) were investigated. They have good corrective abilities, as well as comparative ease of construction for any given minimum code distance.…”

Section: Methodsmentioning

confidence: 99%

“…Correction of information by the L-code leads to a useful redundancy equivalent to redundancy. Therefore, from the point of view of ensuring the possibility of monitoring and correcting errors arising in the dynamics of the computational process, linear L-codes are the most attractive [5,7,8].…”

Section: Methodsmentioning

confidence: 99%

“…The correctly chosen encoding method is able to provide the greatest resistance to possible accidental distortions [4][5][6][7]. To do this, special processing of the received information is carried out, which in turn assumes to eliminate the interference introduced into it, clear the signal from errors and achieve compliance with what was sent from the transmitting end of the line [8][9][10][11]. Thus, during construction, geonavigation and geophysical exploration of operated wells, one of the problems is a large amount of field information that needs to be transmitted from a great depth via wireless communication channels.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Error Control Coding Algorithms in High Reliability Telemetry Systems

et al. 2022

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In the oil and gas industry, in the process of drilling support (geosteering) and well telemetry, there is a problem of transmitting reliable information via wireless communication channels. The quality of such communication, as a rule, suffers due to the presence of errors caused by interference. As the depth of the well increases, the problem becomes more extensive. In order to solve the problem, it is proposed to choose noise-resistant coding in the system of residual classes. This system parallelizes the execution of arithmetic operations, has corrective abilities and organically adapts to the neural network basis of intelligent field management. At the same time, there are constraining factors for the mass application of the RNS; for example, difficulties in implementing non-modular procedures, forward and reverse coding, and some difficulties in identifying and correcting errors. That is why the task of improving the RNS seems relevant not only for oil and gas complexes, but also for any digital signal processing applications focused on intelligent neural network management on the basis of non-positional computing. The material of the article is limited to the study of the noise immunity of linear codes of the deduction system and the development of algorithms for detecting and correcting errors.

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