Skip to main content
SpringerLink
Log in

Design and Performance Comparison of Modular Multipliers Implemented on FPGA Platform

  • Conference paper
  • First Online:
Cloud Computing and Security (ICCCS 2016)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 10039))

Included in the following conference series:

Abstract

Modular multiplier is the most critical component in many data security protocols based on public key cryptography (PKC). To provide data security in many real time applications, a high performance modular multiplier is of utmost importance. Two techniques mostly used for high speed modular multiplication are Montgomery Modular Multiplication (MMM) and Interleaved Modular Multiplication (IMM). This paper presents radix-2 hardware implementation of the MMM and IMM methods with detailed performance analysis. The designs are implemented in Verilog HDL and synthesized targeting Xilinx Virtex-6 FPGA platform. Synthesized results indicate that the radix-2 MMM design is better in terms of computation time, FPGA slice area and throughput as compared to the radix-2 IMM design.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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

References

  1. IEEE standard specifications for Public-Key cryptography - amendment 1: Additional techniques. IEEE Std 1363a–2004 (Amendment to IEEE Std 1363–2000), pp. 1–167, September 2004

    Google Scholar 

  2. AbdelFattah, A.M., El-Din, A.M.B., Fahmy, H.M.: An efficient architecture for interleaved modular multiplication

    Google Scholar 

  3. Blakely, G.: A computer algorithm for calculating the product AB modulo M. IEEE Trans. Comput. C–32(5), 497–500 (1983)

    Article  Google Scholar 

  4. Bunimov, V., Schimmler, M., Tolg, B.: A complexity-effective version of Montgomery’s algorithm. In: Workshop on Complexity Effective Designs, ISCA 2002, May 2002

    Google Scholar 

  5. Ghosh, S., Mukhopadhyay, D., Chowdhury, D.: High speed Fp multipliers and adders on FPGA platform. In: 2010 Conference on Design and Architectures for Signal and Image Processing (DASIP), pp. 21–26, October 2010

    Google Scholar 

  6. Hankerson, D., Vanstone, S., Menezes, A.J.: Guide to Elliptic Curve Cryptography. Springer, Berlin (2004)

    MATH  Google Scholar 

  7. Javeed, K., Wang, X.: Efficient Montgomery multiplier for pairing and elliptic curve based cryptography. In: 2014 9th International Symposium on Communication Systems, Networks Digital Signal Processing (CSNDSP), pp. 255–260, July 2014

    Google Scholar 

  8. Javeed, K., Wang, X.: Radix-4 and radix-8 Booth encoded interleaved modular multipliers over general Fp. In: 2014 24th International Conference on Field Programmable Logic and Applications (FPL), pp. 1–6, September 2014

    Google Scholar 

  9. Javeed, K., Wang, X., Scott, M.: Serial and parallel interleaved modular multipliers on FPGA platform. In: 2015 25th International Conference on Field Programmable Logic and Applications (FPL), pp. 1–4, September 2015

    Google Scholar 

  10. Kelley, K., Harris, D.: Very high radix scalable Montgomery multipliers. In: 2005 Proceedings of the Fifth International Workshop on System-on-Chip for Real-Time Applications, pp. 400–404, July 2005

    Google Scholar 

  11. Koç, C., Acar, T., Kaliski Jr., B.S.: Analyzing and comparing Montgomery multiplication algorithms. IEEE Micro 16(3), 26–33 (1996)

    Article  Google Scholar 

  12. Koblitz, N.: Elliptic curve cryptosystems. Math. Comput. 48(177), 203–209 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  13. Miller, V.S.: Use of elliptic curves in cryptography. In: Williams, H.C. (ed.) CRYPTO 1985. LNCS, vol. 218, pp. 417–426. Springer, Heidelberg (1986)

    Google Scholar 

  14. Montgomery, P.L.: Modular multiplication without trial division. Math. Comput. 44(170), 519–521 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  15. Narh Amanor, D., Paar, C., Pelzl, J., Bunimov, V., Schimmler, M.: Efficient hardware architectures for modular multiplication on FPGAs. In: 2005 International Conference on Field Programmable Logic and Applications, pp. 539–542, August 2005

    Google Scholar 

  16. Rivest, R., Shamir, A., Adleman, L.: A method for obtaining digital signatures and public-key cryptosystems. Commun. ACM 21, 120–126 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  17. Shigemoto, K., Kawakami, K., Nakano, K.: Accelerating Montgomery modulo multiplication for redundant radix-64k number system on the FPGA using dual-port block rams. In: 2008 IEEE/IFIP International Conference on Embedded and Ubiquitous Computing, EUC 2008, vol. 1, pp. 44–51. IEEE (2008)

    Google Scholar 

  18. Sloan Jr., K.R.: Comments on a computer algorithm for calculating the product AB modulo M. IEEE Trans. Comput. 34(3), 290–292 (1985)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Electrical Engineering Department, COMSATS Institute of Information Technology Abbottabad, Abbottabad, Pakistan

    Khalid Javeed

  2. School of Electronic Engineering, Dublin City University, Dublin, Ireland

    Khalid Javeed, Daniel Irwin & Xiaojun Wang

Authors
  1. Khalid Javeed
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Daniel Irwin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xiaojun Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiaojun Wang .

Editor information

Editors and Affiliations

  1. University of Information Science and Technology, Nanjing, China

    Xingming Sun

  2. Michigan State University , EAST LANSING, Michigan, USA

    Alex Liu

  3. National Dong Hwa University , Shoufeng, Taiwan

    Han-Chieh Chao

  4. Purdue University , West Lafayette, Indiana, USA

    Elisa Bertino

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing AG

About this paper

Cite this paper

Javeed, K., Irwin, D., Wang, X. (2016). Design and Performance Comparison of Modular Multipliers Implemented on FPGA Platform. In: Sun, X., Liu, A., Chao, HC., Bertino, E. (eds) Cloud Computing and Security. ICCCS 2016. Lecture Notes in Computer Science(), vol 10039. Springer, Cham. https://doi.org/10.1007/978-3-319-48671-0_23

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-48671-0_23

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-48670-3

  • Online ISBN: 978-3-319-48671-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation