# DATA ERRORS CONTROL IN THE MODULAR NUMBER SYSTEM BASED ON THE NULLIFICATION PROCEDURE

## Keywords:

computer system and components, modular number system, information control, modular arithmetic operations, zeroing procedure.## Abstract

A method for error control in the modular number system (MNS) based on the use of the zeroing procedure is proposed. Error control in the MNS is a non-positional operation and requires the development of special methods, designed to increase the efficiency of this procedure. This method is designed to verify the correct implementation of the computing process of computer systems and components. It is assumed that the error in one module remainder does not affect the residual values corresponding to other modules (bases) of the MNS. The essence of the method of error control is to use the procedure of pair number zeroing with the preliminary fetching of digits. This makes it possible to increase the efficiency of information control, presented in the modular number system. The practical significance of the results obtained is that, in comparison with the existing methods of error control in MNS, the error detection time is more than halved.## References

J. Wang, S. Ma, Z.-G. Yang and J. Hu, “A systemic performance evaluation method for residue number system,” Proceedings of the 2016 2nd IEEE International Conference on Computer and Communications (ICCC), Chengdu, 2016, pp. 321-325.

I.Ya. Akushskii and D.I. Yuditskii, Machine Arithmetic in Residual Classes, Sov. Radio, Moscow, 1968.

K. Phalakarn and A. Surarerks, “Alternative redundant residue number system construction with redundant residue representations,” Proceedings of the 2018 3rd International Conference on Computer and Communication Systems (ICCCS), Nagoya, 2018, pp. 457-461.

S. Wei and C. Jiang, “Residue signed-digit arithmetic and the conversions between residue and binary numbers for a four-moduli set,” Proceedings of the 2012 11th International Symposium on Distributed Computing and Applications to Business, Engineering & Science, Guilin, 2012, pp. 436-440.

V. Krasnobayev, A. Kuznetsov, S. Koshman, S. Moroz, “Improved method of determining the alternative set of numbers in residue number system,” in: Chertov O., Mylovanov T., Kondratenko Y., Kacprzyk J., Kreinovich V., Stefanuk V. (eds) Recent Developments in Data Science and Intelligent Analysis of Information. ICDSIAI’2018. Advances in Intelligent Systems and Computing, vol 836. Springer, Cham, pp. 319-328, 05 August 2018. DOI: 10.1007/978-3-319-97885-7_31.

A. Armand and S. Timarchi, “Low power design of binary signed digit residue number system adder,” Proceedings of the 2016 24th Iranian Conference on Electrical Engineering (ICEE), Shiraz, 2016, pp. 844-848.

A. Yanko, S. Koshman, V. Krasnobayev, “Algorithms of data processing in the residual classes system,” Proceedings of the 4th International Scientific-Practical Conference Problems of Infocommunications. Science and Technology (PIC S&T), Kharkiv, 2017, pp. 117-121.

S. Wei, “An RSA encryption implementation method using residue signed-digit arithmetic circuits,” Proceedings of the 2012 5th International Conference on BioMedical Engineering and Informatics, Chongqing, 2012, pp. 1299-1303.

A. Safari, J. Nugent and Y. Kong, “Novel implementation of full adder based scaling in residue number systems,” Proceedings of the 2013 IEEE 56th International Midwest Symposium on Circuits and Systems (MWSCAS), Columbus, OH, 2013, pp. 657-660.

G. Harman and I. E. Shparlinski, “Products of small integers in residue classes and additive properties of Fermat quotients,” International Mathematics Research Notices, vol. 2016, no. 5, pp. 1424-1446, Jan. 2016.

D. Younes and P. Steffan, “Efficient image processing application using residue number system,” Proceedings of the 20th International Conference Mixed Design of Integrated Circuits and Systems – MIXDES 2013, Gdynia, 2013, pp. 468-472.

V. Krasnobayev and S. Koshman, “A method for operational diagnosis of data represented in a residue number system,” Cybernetics and Systems Analysis, vol. 54, issue 2, pp. 336-344, 2018.

B. Cao, T. Srikanthan and Chip-Hong Chang, “Design of residue-to-binary converter for a new 5-moduli superset residue number system,” Proceedings of the 2004 IEEE International Symposium on Circuits and Systems (IEEE Cat. No.04CH37512), Vancouver, BC, 2004, pp. II-841.

K. Tao, L. Peng, K. Liang and B. Zhuo, “Irregular repeat accumulate low-density parity-check codes based on residue class pair,” Proceedings of the 2017 IEEE 9th International Conference on Communication Software and Networks (ICCSN), Guangzhou, 2017, pp. 127-131.

A. Rahman, M. T. Naseem, I. M. Qureshi and M. Z. Muzaffar, “Reversible watermarking using residue number system,” Proceedings of the 2011 7th International Conference on Information Assurance and Security (IAS), Melaka, 2011, pp. 162-166.

F. Barsi and P. Maestrini, “Error correcting properties of redundant residue number systems,” IEEE Transactions on Computers, vol. C-22, no. 3, pp. 307-315, March 1973.

D. K. Taleshmekaeil, A. Safari and Y. Kong, “Using one

hot residue number system (OHRNS) for digital image processing,” Proceedings of the 16th CSI International Symposium on Artificial Intelligence and Signal Processing (AISP 2012), Shiraz, Fars, 2012, pp. 064-067.

A. Kuznetsov, I. Kolovanova and T. Kuznetsova, “Periodic characteristics of output feedback encryption mode,” Proceedings of the 2017 4th International Conference Problems of Infocommunications. Science and Technology (PIC S&T), Kharkov, 2017, pp. 193-198.

M. Labafniya and M. Eshghi, “An efficient adder/subtracter circuit for one-hot residue number system,” Proceedings of the 2010 International Conference on Electronic Devices, Systems and Applications, Kuala Lumpur, 2010, pp. 121-124.

Yu.V. Stasev, A.A. Kuznetsov “Asymmetric code-theoretical schemes constructed with the use of algebraic geometric codes,” Cybernetics and System Analysis, no. 3, pp. 47-57, May-June 2005.

D. J. Guan and Y. Cheng, “Parity detection for some three-modulus residue number system,” Proceedings of the 2014 Ninth Asia Joint Conference on Information Security, Wuhan, 2014, pp. 76-81.

V. Krasnobayev, S. Koshman and A. Yanko, “The method of error detection and correction in the system of residual classes,” Computer Science and Cybersecurity, Issue 1(1), pp. 58–66, 2016.

A. Mirshekari and M. Mosleh, “Hardware implementation of a fast FIR filter with residue number system,” Proceedings of the 2010 2nd International Conference on Industrial Mechatronics and Automation, Wuhan, 2010, pp. 312-315.

S. Wei, “Fast signed-digit arithmetic circuits for residue

number systems,” Proceedings of the 2015 IEEE International Conference on Electronics, Circuits, and Systems (ICECS), Cairo, 2015, pp. 344-347.

E. B. Olsen, “RNS hardware matrix multiplier for high precision neural network acceleration: ‘RNS TPU’,” Proceedings of the 2018 IEEE International Symposium on Circuits and Systems (ISCAS), Florence, 2018, pp. 1-5.doi: 10.1109/ISCAS.2018.8351352

A. Hariri, K. Navi and R. Rastegar, “A simplified modulo (2n-1) squaring scheme for residue number system,” Proceedings of the International Conference on "Computer as a Tool" EUROCON 2005, Belgrade, 2005, pp. 615-618.

C. Fan and G. Ge, “A unified approach to Whiteman's and Ding-Helleseth's generalized cyclotomy over residue class rings,” IEEE Transactions on Information Theory, vol. 60, no. 2, pp. 1326-1336, Feb. 2014.

S. Jayashri and P. Saranya, “Reconfigurable FIR filter using distributed arithmetic residue number system algorithm based on thermometer coding,” Proceedings of the 2014 International Conference on Communication and Signal Processing, Melmaruvathur, 2014, pp. 1991-1995.

I. Gorbenko, A. Kuznetsov, M. Lutsenko and D. Ivanenko, “The research of modern stream ciphers,” Proceedings of the 2017 4th International Conference Problems of Infocommunications. Science and Technology (PIC S&T), Kharkov, 2017, pp. 207-210. DOI: 10.1109/INFOCOMMST.2017.8246381

S. Akhter, G. Raturi and S. Khan, “Analysis and design of residue number system based building blocks,” Proceedings of the 2018 5th International Conference on Signal Processing and Integrated Networks (SPIN), Noida, 2018, pp. 441-445.

K. Runovski, & H.-J. Schmeisser, “On the convergence of Fourier means and interpolation means,” Journal of Computational Analysis and Applications, vol. 6, issue 3, pp. 211-227, 2004.

S. Bondarenko, L. Bodenchuk, O. Krynytska and I. Gayvoronska, “Modelling instruments in risk management,” International Journal of Civil Engineering and Technology, vol. 10, issue 1, pp. 1561-1568, 2019.

V. Krasnobayev, S. Koshman and A. Yanko, “The method for real-time data control within the system of residue classes based on the consecutive nullification principle” Radioelectronic and Computer Systems, no. 1(81), pp. 57-68, 2017.

A. Molahosseini, F. Teymouri and K. Navi, “A new four-modulus RNS to binary converter,” Proceedings of 2010 IEEE International Symposium on Circuits and Systems, Paris, 2010, pp. 4161-4164 DOI: 10.1109/iscas.2010.5537592.

T. Singh, “Residue number system for fault detection in communication networks,” Proceedings of the 2014 International Conference on Medical Imaging, m-Health and Emerging Communication Systems (MedCom), Greater Noida, 2014, pp. 157-161.

L. Sousa, “Efficient method for magnitude comparison in RNS based on two pairs of conjugate moduli,” Proceedings of the 18th IEEE Symposium on Computer Arithmetic (ARITH'07), 2007, pp. 240-250. DOI: 10.1109/arith.2007.16.

R. Chornei, V. M. Hans Daduna, & P. Knopov, “Controlled Markov fields with finite state space on graphs,” Stochastic Models, vol. 21, issue 4, pp. 847-874, 2005. doi: 10.1080/15326340500294520

H. K Bello and K.A Gbolagade, “A MRC based RNS to binary converter using the moduli set {22n+1-1, 2n-1, 22n-1},” International Journal of Advanced Research in Computer Engineering & Technology (IJARCET), vol. 6, issue 7, July 2017.

A. H. Navin, A. S. Khashandarag, A. R. Oskuei and M. Mirnia, “A novel approach cryptography by using residue number system,” Proceedings of the 2011 6th International Conference on Computer Sciences and Convergence Information Technology (ICCIT), Seogwipo, 2011, pp. 636-639.

V. S. Veeravalli, “Modified residue codes based on residue number system as a fault tolerance scheme,” Proceedings of the IEEE Southeastcon 2009, Atlanta, GA, 2009, pp. 383-387.

B. P. Tkach, & L. B. Urmancheva, “Numerical-analytic method for finding solutions of systems with distributed parameters and integral condition,” Nonlinear Oscillations, vol. 12, issue 1, pp. 113-122, 2009. doi:10.1007/s11072-009-0064-6

J. Bajard, L. Didier and P. Kornerup, “An RNS Montgomery modular multiplication algorithm,” IEEE Transactions on Computers, vol. 47, no. 7, pp. 766-776, 1998. DOI: 10.1109/12.709376.

## Downloads

## Published

## How to Cite

*International Journal of Computing*,

*19*(2), 237-246. Retrieved from https://computingonline.net/computing/article/view/1767

## Issue

## Section

## License

International Journal of Computing is an open access journal. Authors who publish with this journal agree to the following terms:• Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.

• Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.

• Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.