Advertisement

A Fast Modular Multiplication Algorithm with Application to Two Key Cryptography

  • Ernest F. Brickell
Conference paper

Abstract

This paper presents an algorithm which will perform multiplication modulo C in [log2C] + 7 clock pulses.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    W. Diffie, and M. E. Hellman, “New directions in cryptography,” IEEE Trans. Inform. Theory, IT-22, 6 (Nov. 1976), 644–654.CrossRefGoogle Scholar
  2. 2.
    D. E. Knuth, The Art of Computer Programming, Vol. 2: Semi-numerical Algorithms, Addison-Wesley, Reading, MA (1969).Google Scholar
  3. 3.
    R. Merkte, and M. E. Hellman, “Hiding information and receipts in trapdoor knapsacks,” IEEE Trans. Inform. Theory, IT-24 (Sept. 1978), 525–530.CrossRefGoogle Scholar
  4. 4.
    M. J. Norris, and G. J. Simmons, “Algorithms for high-speed modular arithmetic,” Congressus Numeratium, Vol. 31 (1981), 153–163.Google Scholar
  5. 5.
    S. Pohlig, and M. E. Hellman, “An improved algorithm for computing logarithms in GF(p) and its cryptographic significance,” IEEE Trans. Inform. Theory, IT-24 (Jan. 1978), 106–110.CrossRefGoogle Scholar
  6. 6.
    R. Rivest, A. Shamir, and L. Adleman, “A method for obtaining digital signatures and public-key cryptosystems,” Commun. ACM, 21, 2 (Feb. 1978), 120–126.CrossRefGoogle Scholar
  7. 7.
    R. W. Roberts, National Bureau of Standards, “Encryption algorithm for computer data encryption,” Federal Register, Vol. 40, No. 52 (March 17, 1975 ), 12134–12139.Google Scholar
  8. 8.
    J. E. Robertson, “A deterministic procedure for the design of carry-save adders and borrow-save subtractors,” University of Illinois, Dept. of Computer Science, Report No. 235 (July 1967).Google Scholar
  9. 9.
    F. A. Rohatsch, “A study of transformations applicable to the development of limited carry-borrow propagation adders,” Ph.D. Thesis, University of Illinois, Urbana, IL (June 1967).Google Scholar
  10. 10.
    C. S. Wallace, “A suggestion for a fast multiplier,” IEEE Trans. Elec. Comp., EC-13 (Feb. 1964), 14–17.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1983

Authors and Affiliations

  • Ernest F. Brickell
    • 1
  1. 1.Sandia National LaboratoriesAlbuquerqueUSA

Personalised recommendations