Advertisement

Attack Experiments on Elliptic Curves of Prime and Binary Fields

  • Ni Ni HlaEmail author
  • Tun Myat Aung
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 755)

Abstract

At the beginning the paper describes the basic properties of finite field arithmetic and elliptic curve arithmetic over prime and binary fields. Then it discusses the elliptic curve discrete logarithm problem and its properties. We study the Baby-Step, Giant-Step method, Pollard’s rho method and Pohlig–Hellman method, known as general methods that can exploit the elliptic curve discrete logarithm problem, and describe in detail attack experiments using these methods over prime and binary fields. Finally, the paper discusses the expected running time of these attacks and suggests the strong elliptic curves that are not vulnerable to these attacks.

References

  1. 1.
    Anoop, M.S.: Elliptic Curve Cryptography. http://www.infosecwriters.com/Papers/Anoopms_ECC.pdf
  2. 2.
    Hankerson, D., Menezes, A., Vanstone, S.: Guide to Elliptic Curve Cryptography. Springer press (2004)Google Scholar
  3. 3.
    Lidl, R., Niederreiter, H.: Introduction to Finite Field Arithmetic and their Applications. Cambridge University Press (1986)Google Scholar
  4. 4.
    Behrouz, A.: Forouzan, Cryptography and Network Security. McGraw-Hill press, International Edition (2008)Google Scholar
  5. 5.
    Liao, H.-Z., Shen, Y.-Y.: On the elliptic curve digital signature algorithm. Tunghai Sci. 8 (2006)Google Scholar
  6. 6.
    Karthikeyan, E.: Survey of elliptic curve scalar multiplication algorithms. Int. J. Adv. Netw. Appl. 04(02) (2012)Google Scholar
  7. 7.
    Washington, L.C.: Elliptic Curves: Number Theory and Cryptography. Discrete Mathematics and its Applications (Boca Raton). Chapman & Hall/CRC, Boca Raton, FL (2003)Google Scholar
  8. 8.
    Musson, M.: Attacking the elliptic curve discrete logarithm problem. Master Thesis of Science (Mathematics and Statistics) Acadia University (2006)Google Scholar
  9. 9.
    Rosen, K.H.: Discrete Mathematics and its Applications, Global Edition (2008)Google Scholar
  10. 10.
    Hla, N.N., Aung, T.M.: Implementation of finite field arithmetic operations for large prime and binary fields using java BigInteger class. Int. J. Eng. Res. Technol. (IJERT), 6(08) (2017)Google Scholar
  11. 11.
    Aung, T.M., Hla, N.N.: Implementation of elliptic curve arithmetic operations for prime field and binary field using java BigInteger class. Int. J. Eng. Res. Technol. (IJERT), 6(08) (2017)Google Scholar
  12. 12.
    Recommended Elliptic Curves for Federal Government Use, NIST (1999)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.University of Computer Studies, Yangon (UCSY)YangonMyanmar

Personalised recommendations