DESIGN AND RESEARCH OF THE BEHAVIORAL MODEL FOR THE MODULAR REDUCTION DEVICE
DOI:
https://doi.org/10.31489/2020No1/151-156Keywords:
asymmetric crypto-algorithms, hardware encryption, modular reduction, behavioral model, design.Abstract
A behavioral model of the modular reduction device with optimal hardware costs was designed in CAD Quartus Prime Lite Edition. An algorithm of operation is implemented in the Verilog HDL language. A method is used where, at each step of the calculation, the value of either tripled, doubled, or single value of the module is subtracted from the most significant bits shifted to the left by two. Functional and timing modeling of the behavioral model algorithm using examples was carried out and the correctness of the algorithm was confirmed. The device circuit at the register transfer level (RTL) for the low-budget FPGA Cyclone VE 5CEBA4F23C7 from Altera is obtained. A timing analysis was performed using a time analyzer to determine the maximum clock frequency for the principal and behavioral models in various working conditions.
References
"1 Hars L., Joye M., Quisquater J. Long Modular Multiplication for Cryptographic Applications. Cryptographic Hardware and Embedded Systems. CHES 2004, Lecture Notes in Computer Science, 2004, Issue 3156, pp. 45 – 61.
Petrenko V.I., Sidorchuk A.V., Kuz'minov J.V. Device for generating remainder with arbitrary modulus: pat. 2368942 С2 Russian Federation. No. 2007124282/09; Publ. 27.09.2009, Bull. No. 27, 9 p.
Pankratova I.A. Number-theoretical methods of cryptography. Tomsk, Tomsk State University, 2009, 120 p.
Zakharov V.M., Stolov E.L., Shalagin S/V. Apparatus for generating remainder for given modulo: pat 2421781 С1 Russian Federation.No. 2009138613/08; Publ. 20.06.2011, Bull. No. 17, 9 p.
Kopytov V.V., Petrenko V.I., Sidorchuk A.V. Device for generating remainder from arbitrary modulus of numbe. Pat. 2445730 С2 Russian Federation. No.2010106685/08; Publ. 20.03.2012, Bull. No.8, 8p.
Skryabin I., Sahin Y.H. Support operations for encryption algorithms with public key and their implementation in the microprocessor Elbrus. 2013. Available at: www.myshared.ru/ slide/213088
Eran Pisek, Plano, T.X., Th.M. Henige, Dallas, T.X. Method and apparatus for efficient modulo multiplication: pat. No. 8417756 B2 United States. No.12/216,896; Publ. 09.04.2013, 12 p.
Aitkhozhayeva Y. Zh., Tynymbayev S.T. Aspects of hardware reduction modulo in asymmetric cryptography. Bulletin of National Academy of Sciences of the Kazakhstan. 2014, No. 5(375), pp. 88 – 93.
Markus Bockes, Munich (DE); Jurgen Pulkus, Munich (DE) Method for arbitrary-precision division or modular reduction: pat. 9042543 B2 United States. No. 13/885, 878; Publ. 26.05.2015, 12p.
Yu H., Bai G., Hao J., Wang C. Yap Efficient Modular Reduction Algorithm Without Correction Phase. Frontiers in Algorithmics. Lecture Notes in Computer Science, 2015, Vol. 9130, pp. 304 – 313.
Tynymbayev S.T., Aitkhozhayeva Y.Zh. The remainder generator by an arbitrary modulus of the number: pat. 30983 The Republic of Kazakhstan. No. 014/1450.1; Published 15.03.2016, 5 p.
Kovtun M., Kovtun V. Review and classification of algorithms for dividing and modulating large integers for cryptographic applications. 2017. Available at: http://docplayer.ru/30671408-Obzor-i-klassifikaciya-algoritmov-deleniya
Tynymbayev S.T., Aitkhozhayeva Y.Zh, Adilbekkyzy S. High speed device for modular reduction. Bulletin of National Academy of Sciences of the Republic of Kazakhstan. 2018, No. 6 (376), pp. 147 – 152.
Adilbekkyzy S. Aitkhozhayeva Y.Zh., Tynymbayev S.T. Modeling of the partial reminder former of the modular reduction device. Eurasian Union of Scientists. 2019, Vol. 6 (63), pp. 47 – 51.
Tynymbayev S.T., Aitkhozhayeva Y.Zh, Adilbekkyzy S., et al. Development and modeling of schematic diagram for the modular reduction device. Problems of Informatics, 2019, No. 4, pp.42 – 52.
Kramarov S.O., Mityasova O.Yu., Sokolov S.V., Tishchenko E.N., Shevchuk P.S. Cryptographic information security. Moscow: RIOR Publishing Center, 2018, 322 p.
"