New Collisions to Improve Pollard's Rho Method of Solving the Discrete Logarithm Problem on Elliptic Curves
This work addresses a computational bottleneck in cryptography, specifically for elliptic curve discrete logarithms, but appears incremental as it builds on prior improvements to Pollard's Rho.
The paper tackles the inefficiency of Pollard's Rho method for solving the discrete logarithm problem on elliptic curves by proposing an alternative approach based on new collisions, which reduces the number of iterations and mathematical operations compared to the original method.
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.