Skip to main content

A Word-Oriented Modular Division Algorithm and Its Efficient Implementation Based on CSA

  • Conference paper
  • First Online:
Artificial Intelligence and Security (ICAIS 2020)

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Brent, R., Kung, H.T.: Systolic VLSI arrays for linear-time GCD computation. In: Proceedings of the VLSI 1983, Amsterdam, pp. 145–154 (1983)

    Google Scholar 

  2. Chen, C., Qin, Z.: Efficient algorithm and systolic architecture for modular division. Int. J. Electron. 98(6), 813–823 (2011)

    Article  Google Scholar 

  3. Chen, G., Bai, G., Chen, H.: A new systolic architecture for modular divsion. IEEE Trans. Comput. 56(2), 282–286 (2007)

    Article  MathSciNet  Google Scholar 

  4. Knuth, D.E.: The Art of Computer Programming. Addison-Wesley, Reading (1981)

    MATH  Google Scholar 

  5. 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)

    Article  Google Scholar 

  6. 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

    Google Scholar 

  7. 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)

    Google Scholar 

  8. Kaihara, M., Takagi, N.: A hardware algorithm for modular multiplication/division. IEEE Trans. Comput. 54(1), 12–21 (2005)

    Article  Google Scholar 

  9. Menezes, A.J., Vanstone, S.A., Oorschot, P.C.V.: Handbook of Applied Cryptography. CRC Press, Boca Raton (1997)

    MATH  Google Scholar 

  10. Stein, J.: Computational problems associated with Racah algebra. J. Comput. Phys. 1, 397–405 (1967)

    Article  Google Scholar 

  11. Takagi, N.: A VLSI algorithm for modular division based on the binary GCD. IEICE Trans. Fundamentals E81-A, 724–728 (1998)

    Google Scholar 

  12. 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

    Google Scholar 

  13. 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)

    Article  Google Scholar 

  14. 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)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Zhongping Qin .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

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

Download citation

  • DOI: https://doi.org/10.1007/978-981-15-8086-4_58

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-15-8085-7

  • Online ISBN: 978-981-15-8086-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics