High Radix Montgomery Multipliers for Residue Arithmetic Channels on FPGAs

  • Yinan Kong
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 86)

Abstract

This work targets an efficient Montgomery Modular Multiplier for use in the channels of a Residue Number System (RNS). It is implemented on FPGA and optimized by attempting and evaluating the high radix techniques of the Montgomery Algorithm. The usual correction shift step at the end is proved to be infeasible. The resulting multiplier achieves 15ns for a modular multiplication using high radix without correction shift.

Keywords

Montgomery Modular Multiplication the Residue Number System FPGA Digital Arithmetic Public-Key Cryptosystems 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Omondi, A., Premkumar, B.: Residue Number Systems – Theory and Implementation, ser. Advances in Computer Science and Engineering: Texts, vol. 2. Imperial College Press, UK (2007)CrossRefGoogle Scholar
  2. 2.
    Barraclough, S.R.: The Design and Implementation of the IMS A110 Image and Signal Processor. In: Proc. IEEE CICC, San Diego, pp. 24.5/1-4 (1989)Google Scholar
  3. 3.
    Bajard, J.C., Imbert, L.: A full RNS implementation of RSA. IEEE Trans. Comput. 53(6) (June 2004)Google Scholar
  4. 4.
    Parhami, B.: Computer Arithmetic – Algorithms and Hard-ware Designs. Oxford University Press, Oxford (2000)Google Scholar
  5. 5.
    Rivest, R.L., Shamir, A., Adleman, L.M.: A method for obtaining digital signatures and public-key cryptosystems. Communications of the ACM 21(2), 120–126 (1978)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Soderstrand, M.A., Jenkins, W., Jullien, G.: Residue number system arithmetic: Modern applications. Digital Signal Processing (1986)Google Scholar
  7. 7.
    Shand, M., Vuillemin, J.: Fast Implementations of RSA Cryptography. In: Proceedings 11th IEEE Symposium on Computer Arithmetic, pp. 252–259. IEEE Computer Society Press, Los Alamitos (1993)CrossRefGoogle Scholar
  8. 8.
    Montgomery, P.L.: Modular multiplication without trial division. Mathematics of Computation 44(170), 519–521 (1985)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Walter, C.D.: Still faster modular multiplication. Electronics Letters 31(4), 263–264 (1995)CrossRefGoogle Scholar
  10. 10.
    Takagi, N.: A Radix-4 Modular Multiplication Hardware Algorithm for Modular Exponentiation. IEEE Transactions on Computers 41(8), 949–956 (1992)CrossRefGoogle Scholar
  11. 11.
    Kouretas, I., Paliouras, V.: A low-complexity high-radix RNS multiplier. IEEE Transactions on Circuits and Systems Part I 56(11), 2449–2462 (2009)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Orup, H.: Simplifying quotient determination in high-radix modular multiplication. In: Proceedings of the 12th IEEE Symposium on Computer Arithmetic, pp. 193–199 (1995)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Yinan Kong
    • 1
  1. 1.Department of Electronic EngineeringMacquarie UniversityNorth RydeAustralia

Personalised recommendations