John M. Pollard: “Randomness in these algorithms is crucial for their functioning.”
Impress me a little. First, where is that citation?
Secondly, if you make claims, it is not our responsibility to prove you are wrong, but YOUR responsibility to prove you are right.
But I'll make an exception for you, it is your lucky day
So, how exactly do you use randomness in your Kangaroo understanding of how the algorithm works?
And how exactly you break the birthday paradox, and ruin the stuff entirely, let us understand what do you mean by "making the algorithm more deterministic" by "removing the randomness"? What randomness to remove in the first place? Where is that located, and how do you mess around with it, to be able to claim that you create determinism out of uncontrollable chaos?
By applying precomputation in the Kangaroo algorithm, greater efficiency is achieved because precomputed intermediate results are reused instead of recalculating them each time. This reduces the number of necessary operations and, consequently, the computation time.
However, by reducing the number of operations, the probability of collisions also decreases. This is because the birthday paradox is based on the probability that two elements in a large set will coincide. With fewer operations, there are fewer opportunities for collisions to occur.