Skip to main content

Higher radix nonrestoring modular multiplication algorithm and public-key LSI architecture with limited hardware resources

  • Conference paper
  • First Online:
Book cover Advances in Cryptology — ASIACRYPT'94 (ASIACRYPT 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 917))

Included in the following conference series:

  • 216 Accesses

Abstract

Security applications to be installed in small size hardware such as cellular phones and smart cards need a small and practical LSI for key distribution or authentication. This paper describes an improved modular multiplication algorithm and LSI architecture for public-key schemes with the goal of limiting hardware resources. The algorithm, which employs higher radix arithmetic, eliminates the slow restoring which occurs in modular multiplication. The proposed architecture is based on the use of RAM and low operation frequency. The LSI is designed to calculate 512 bit modular exponentiation within 0.1 seconds at the frequency of 17 MHz. This requires only 13 Kgates and six 512bit RAMs.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. Bos and M. Coster: “Addition Chain Heuristics,” Advances in Cryptology-CRYPTO '89, LNCS 435, Springer-Verlag, pp.400–407, 1989

    Google Scholar 

  2. E.F. Brickell, D.M. Gordon, K.S. McCurley, and D.B. Wilson: “Fast Exponentiation with Precomputation (Extended Abstract),” Advances in Cryptology-EUROCRYPT '92, LNCS 658, Springer-Verlag, pp.200–207, 1992

    Google Scholar 

  3. A. Bosselaers, R. Govaerts, and J. Vandewalle: “Comparison of three modular reduction functions,” Advances in Cryptology-CRYPTO'93, LNCS 773, Springer-Verlag, pp.175–186, 1993

    Google Scholar 

  4. E. F. Brickell: “A Survey of Hardware Implementations of RSA,” Advances in Cryptology-CRYPTO'89, LNCS 435, Springer-Verlag, pp.368–370, 1989

    Google Scholar 

  5. E.F. Brickell: “A Fast Modular Multiplication Algorithm with Application to Two Key Cryptography,” Advances in Cryptology-CRYPTO'82, pp.51–60,Plenum, 1982.

    Google Scholar 

  6. W. Diffie and M.E. Hellman: “New Directions in Cryptography,” IEEE Transaction of Information Theory, vol. IT-22, no.6,pp. 644–654, Nov. 1976

    Google Scholar 

  7. S.R. Dusse and B.S. Kaliski Jr.: “A Cryptographic Library for the Motorola DSP56000,” Advances in Cryptology-EUROCRYPT'90, LNCS473, pp.230–244, Springer-Verlag, 1991

    Google Scholar 

  8. F. Hoornaert, M. Decroos,J. Vandewalle, and R. Govaerts: “Fast RSA-Hardware: Dream or Reality?” Advances in Cryptology-EUROCRYPT '88, LNCS 330, Springer-Verlag, pp.257–264, 1988

    Google Scholar 

  9. K.Hwang: Computer Arithmetic: Principles, Architecture and Design, John Wiley & Sons, 1979

    Google Scholar 

  10. K. Iwamura, T. Matumoto, and H.Imai: “High-Speed Implementation Methods for RSA Scheme,” Advances in Cryptology-EUROCRYPT'92, LNCS 658, Springer-Verlag, pp.221–238

    Google Scholar 

  11. P. Ivey, S. Walker, J. Stern, and S. Davidson: “An Ultra-High Speed Public Key Encryption Processor,” IEEE 1992 Custom Integrated Circuits Conference, 1992

    Google Scholar 

  12. D. E. Knuth: The Art of Computer Programming — Seminumerical Algorithms, vol.2, Addison — Westley, second edition, 1981.

    Google Scholar 

  13. H.Morita, C.H.Yang: “A Modular-Multiplication Algorithm Using Lookahead Determination,” IEICE Transaction of fundamentals, vol. E76-A, no.l, pp. 70–77, Jan. 1993

    Google Scholar 

  14. Y.Nakamura, K.Oguri, A.Nagoya, and R.Nomura: “A Hierarchical Behavioral Description Based CAD System,” Proceedings of IFIP EURO ASIC '90, pp.282–287, May. 1990

    Google Scholar 

  15. R.L. Rivest, A. Shamir, and L. Adleman: “A Method of Obtaining Digital signatures and Public Key Cryptosystems,” Comm. of ACM, vol. 21, no.2, pp. 120–126, Feb. 1978.

    Google Scholar 

  16. VLSI Technology, Inc. “VSC470 Library,” VSD13881, and “0.8-Micron Datapath Library (VCC4DP3),” VSD13940, 1992

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Josef Pieprzyk Reihanah Safavi-Naini

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Abe, M., Morita, H. (1995). Higher radix nonrestoring modular multiplication algorithm and public-key LSI architecture with limited hardware resources. In: Pieprzyk, J., Safavi-Naini, R. (eds) Advances in Cryptology — ASIACRYPT'94. ASIACRYPT 1994. Lecture Notes in Computer Science, vol 917. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0000448

Download citation

  • DOI: https://doi.org/10.1007/BFb0000448

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-59339-3

  • Online ISBN: 978-3-540-49236-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics