Research Article Open Access

New Collisions to Improve Pollard's Rho Method of Solving the Discrete Logarithm Problem on Elliptic Curves

Ammar Ali Neamah1
  • 1 University of Kufa, Iraq

Abstract

It is true that different approaches have been utilised to accelerate the computation of discrete logarithm problem on elliptic curves with Pollard's Rho method. However, trapping in cycles fruitless will be obtained by using the random walks with Pollard's Rho. An efficient alternative approach that is based on new collisions which are reliant on the values ai, bi to solve this problem is proposed. This may requires less iterations than Pollard's Rho original in reaching collision. Thus, the performance of Pollard's Rho method is more efficiently because the improved method not only reduces the number of mathematical operations but these collisions can also applied on previous improvements which reported in the literature.

Journal of Computer Science
Volume 11 No. 9, 2015, 971-975

DOI: https://doi.org/10.3844/jcssp.2015.971.975

Submitted On: 2 June 2015 Published On: 16 December 2015

How to Cite: Neamah, A. A. (2015). New Collisions to Improve Pollard's Rho Method of Solving the Discrete Logarithm Problem on Elliptic Curves. Journal of Computer Science, 11(9), 971-975. https://doi.org/10.3844/jcssp.2015.971.975

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Keywords

  • Pollard’s Rho
  • Elliptic Curve Discrete Logarithm
  • Alternative Collisions