Improving Pollard´s Rho attack on elliptic curve cryptosystems

We propose a method to speed-up Pollard´s Rho algorithm using cycle detection with stack on elliptic curves. The Pollard´s Rho using cycle detection with stack requires less time than Pollard´s Rho original in reaching collision and it is guaranteed to stop within the second loop through the cycle. In practice, our new rudimentary implementation of proposed method decreases the running time and the number of evaluations of the iteration function on the cost of the memory space used.