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It is true that different approaches have been utilised to accelerate the computation of discrete logarithm problem on elliptic curves with Pollardâs Rho method. However, trapping in cycles fruitless will be obtained by using the random walks with Pollardâ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 Pollardâs Rho original in reaching collision. Thus, the performance of Pollardâ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.

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

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