Abstract
Modular Division is an essential operation in RSA and ECC cryptosystem. Compared with other essential operations, modular division is most complicated and time-consuming operation. Its implementation performance has a great effect on the performance of relevant cryptosystem. Especially, when operand is large number (1024-bit or larger), the optimization of modular division performance is vital to improve the performance of whole cryptosystem. In this paper, we first propose a word-oriented modular division algorithm and then develop an efficient CSA implementation architecture. Experiment shows that the proposed architecture can get better performance than other architectures and the longer size of operand is, the better performance is. It is significant for modular division application.
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References
Brent, R., Kung, H.T.: Systolic VLSI arrays for linear-time GCD computation. In: Proceedings of the VLSI 1983, Amsterdam, pp. 145–154 (1983)
Chen, C., Qin, Z.: Efficient algorithm and systolic architecture for modular division. Int. J. Electron. 98(6), 813–823 (2011)
Chen, G., Bai, G., Chen, H.: A new systolic architecture for modular divsion. IEEE Trans. Comput. 56(2), 282–286 (2007)
Knuth, D.E.: The Art of Computer Programming. Addison-Wesley, Reading (1981)
He, Q., et al.: A weighted threshold secret sharing scheme for remote sensing images based on Chinese remainder theorem. Comput. Mater. Continua 58(2), 349–361 (2019)
Thapliyal, H., Ramasahayam, A., Kotha, V.K., Gottimukkula, K.: Srinivas, M.: Modified montgomery modular multiplication using 4:2 compressor and CSA adder. In: Third IEEE International Workshop on Electronic Design, Test and Applications, Kuala Lumpur, Malaysia, pp. 598–602, January 2006
Cui, J., Zhang, Y., Cai, Z., Liu, A., Li, Y.: Securing display path for security-sensitive applications on mobile devices. Comput. Mater. Continua 55(1), 17–35 (2018)
Kaihara, M., Takagi, N.: A hardware algorithm for modular multiplication/division. IEEE Trans. Comput. 54(1), 12–21 (2005)
Menezes, A.J., Vanstone, S.A., Oorschot, P.C.V.: Handbook of Applied Cryptography. CRC Press, Boca Raton (1997)
Stein, J.: Computational problems associated with Racah algebra. J. Comput. Phys. 1, 397–405 (1967)
Takagi, N.: A VLSI algorithm for modular division based on the binary GCD. IEICE Trans. Fundamentals E81-A, 724–728 (1998)
Wang, J.F., Lin, P.C., Chiu, P.K.: A staged carry-save-adder array for montgomery modular multiplication. In: IEEE Asia-Pacific Conference on ASIC, pp. 91–100. Grand Hotel, Taipei, August 2002
Park, Y., Choi, H., Cho, S., Kim, Y.G.: Security analysis of smart speaker: security attacks and mitigation. Comput. Mater. Continua 61(1), 81–101 (2019)
Zhang, Y.Y., Li, Z., Yang, L., Zhan, S.W.: An efficient CSA architecture for montgomery modular multiplication. Microprocess. Microsyst. 31(170), 456–459 (2007)
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Hu, X., Qin, Z., Liu, Y., Yang, Q. (2020). A Word-Oriented Modular Division Algorithm and Its Efficient Implementation Based on CSA. In: Sun, X., Wang, J., Bertino, E. (eds) Artificial Intelligence and Security. ICAIS 2020. Communications in Computer and Information Science, vol 1253. Springer, Singapore. https://doi.org/10.1007/978-981-15-8086-4_58
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DOI: https://doi.org/10.1007/978-981-15-8086-4_58
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