004.75

Residual number system, Chinese remainder theorem, distributed data storage, reverse transformation methods, secure data storage systems.

The methods of conversion from the residual number system to the decimal number system based on the classical Chinese remainder theorem (CRT) and its improvements CRT I, CRT II are considered in this paper. Analytical dependences of the time complexity of the specified methods are analyzed and constructed. As the result of carried out investigation, it is established that CRT II is characterized by greater efficiency compared to the other methods mentioned above. Examples of the implementation of direct and reverse conversion of RNS based on the application of CRT , CRT I, CRT II are given.

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12. Akushskyj Y. Ja., Judyckyj D.Y. Mashynnaja aryfmetyka v ostatochnykh klassakh. M.: Sov. radyo. 1968. p. 460.
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14. Karpinski M., Rajba S., Zawislak S., Warwas K., Kasianchuk M., Ivasiev S., Yakymenko I. A Method for Decimal Number Recovery from its Residues Based on the Addition of the Product Modules. Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications (IDAACS–2019): Proceedings of the 10th International Conference. 2019. V.1. p.13–17.

1. Mather T., Kumaraswamy S., and Latif S. Cloud security and privacy: an enterprise perspective on risks and compliance. O’Reilly Media, Inc., 2009.
2. LI, Baiyu; Micciancio, D. On the security of homomorphic encryption on approximate numbers. Proc. of 40th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Advances in Cryptology, EUROCRYPT 2021 – 2021, Part I, pp. 648-677, June 2021.
3. Li, W., Yang, Y., Yuan, D. A Novel Cost-Effective Dynamic Data Replication Strategy for Reliability in Cloud Data Centres. In Proceedings of the 2011 IEEE Ninth International Conference on Dependable, Autonomic and Secure Computing, Sydney, NSW, Australia, 12–14 December 2011, pp. 496–502.
4. Huang, C., Simitci, H., Xu, Y., Ogus, A., Calder, B., Gopalan, P., Li, J., Yekhanin, S. Erasure coding in windows azure storage. In Proceedings of the 2012 USENIX Annual Technical Conference (USENIXATC 12), Boston, MA, USA, 13–15 June 2012, pp. 15–26.
5. Kar A., Sur K., Godara S., Basak S., Mukherjee D., Sukla A. S., ... & Choudhury, R. Secuirity in cloud storage: An enhanced technique of data storage in cloud using RNS. In 2016 IEEE 7th Annual Ubiquitous Computing, Electronics & Mobile Communication Conference (UEMCON). 2016, October; pp. 1-4.
6. Yatskiv V., Tsavolyk T., Yatskiv N. The Correcting Codes Formation Method Based on the Residue Number System. Conference Proceedings of 14 th International Conference The Experience of Designing and Application of CAD Systems in Microelectronics (CADSM-2017) 21-25 February 2017 Polyana-Svalyava, Ukraine, 2017, pp. 237-240.
7. Schoinianakis D. Residue arithmetic systems in cryptography: a survey on modern security applications. Journal of Cryptographic Engineering, 10 (3), 2020, pp.249-267.
8. Yatskiv, V., Kulyna, S., Yatskiv N., Kulyna H. Protected Distributed Data Storage Based on Residue Number System and Cloud Services. Proc. of 10th International Conference on Advanced Computer Information Technologies, ACIT 2020 - 2020, pp. 796–799.
9. Omondi A.R., Premkumar A.B. Residue Number Systems: Theory and Implementation; World Scientific: Singapore, 2007.
10. Mohan, A. Residue Number Systems. Theory and Applications; Springer International Publishing: Cham, Switzerland, 2016.
11. Yuke Wang, Residue-to-Binary Converters Based On New Chinese Remainder Theorems. IEEE Transactions on Circuits and Systems – II: Analog and Digital Signal Processing, vol. 47, No. 3, March 2000, pp. 197–205.
12. Akushskyj Y. Ja., Judyckyj D.Y. Mashynnaja aryfmetyka v ostatochnykh klassakh. M.: Sov. radyo. 1968. p. 460.
13. Papachristodoulou, L. Fournaris, A.P. Papagiannopoulos, K. Batina, L. Practical Evaluation of Protected Residue Number System Scalar Multiplication. IACR Trans. Cryptogr. Hardw. Embed. Syst. 2018, 2019, pp. 259–282.
14. Karpinski M., Rajba S., Zawislak S., Warwas K., Kasianchuk M., Ivasiev S., Yakymenko I. A Method for Decimal Number Recovery from its Residues Based on the Addition of the Product Modules. Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications (IDAACS–2019): Proceedings of the 10th International Conference. 2019. V.1. p.13–17.