Elliptic Scalar Multiplication Using Point Halving

  • Erik Woodward Knudsen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1716)


We describe a new method for conducting scalar multiplication on a non-supersingular elliptic curve in characteristic two. The idea is to replace all point doublings in the double-and-add algorithm with a faster operation called point halving.


Elliptic Curve Elliptic Curf Scalar Multiplication Point Doubling Normal Basis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Morain, F., Olivos, J.: Speeding up computations on an elliptic curve using addition-subtraction chains. Theoretical Informatics and Applications 24(6), 531–544 (1990)zbMATHMathSciNetGoogle Scholar
  2. Zhang, C.N.: An improved binary algorithm for RSA. Computers and Mathematics with Applications 25, 15–24 (1993)zbMATHCrossRefGoogle Scholar
  3. Standard Specifications for Public Key Cryptography, Annex A. Number Theoretic Background. IEEE Standards Department (August 20, 1998)Google Scholar
  4. Koblitz, N.: CM-Curves with Good Cryptographic Properties. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 279–287. Springer, Heidelberg (1992)Google Scholar
  5. Meier, W., Staffelbach, O.: Efficient Multiplication on Certain Nonsupersingular Elliptic Curves. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 333–344. Springer, Heidelberg (1993)Google Scholar
  6. Muller, V.: Fast Multiplication on Elliptic Curves over Small Fields of Characteristic Two. Journal of Cryptology, 219–234 (1998)Google Scholar
  7. Silverman, J.: The arithmetic of Elliptic Curves. Graduate Texts in Mathematics, vol. 106. Springer, Heidelberg (1986)Google Scholar
  8. Cohen, G., Lobstein, A., Naccache, D., Zemor, G.: How to Improve an Exponetiation Black-box. Technical Report AP03-1998, Gemplus’ Corporate Product R&D Division Google Scholar
  9. Muller, V.: Efficient Algorithms for Multiplication on Elliptic Curves TI-9/97,1997, Institut fur theoretische InformatikGoogle Scholar
  10. Menezes, A.J.: Elliptic Curve Public Key Cryptosystems. Kluwer Acedemic Publishers, Dordrecht Google Scholar
  11. Schroeppel, R., Orman, H., O’Malley, S., Spatscheck, O.: Fast Key Exchange with Elliptic Curve Systems. In: Coppersmith, D. (ed.) CRYPTO 1995. LNCS, vol. 963, pp. 43–56. Springer, Heidelberg (1995)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Erik Woodward Knudsen
    • 1
  1. 1.De La Rue Card Systems 

Personalised recommendations