New Collisions to Improve Pollard’s Rho Method of Solving the Discrete Logarithm Problem on Elliptic Curves
Ammar Ali Neamah
DOI : 10.3844/jcssp.2015.971.975
Journal of Computer Science
Volume 11, Issue 9
It is true that different approaches have been utilised to accelerate the computation of discrete logarithm problem on elliptic curves with Pollardâs Rho method. However, trapping in cycles fruitless will be obtained by using the random walks with Pollardâs 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 Pollardâs Rho original in reaching collision. Thus, the performance of Pollardâs 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.
© 2015 Ammar Ali Neamah. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.