From my experience, 64 jumps are better than 32 by about 2%, so better use 64 when possible. For symmetry methods you need at least 256 jumps.
Your idea is to have 2^32 jumps, right? It will take 240GB of RAM, so not suitable for GPUs. The end, sorry.
Thank's for your answer.I have other question:
I have studied bitcrack and kangaroo (From Jean-Luc Pons) in detail. In the Pollard method with only 2 heards, Pollard recommends using a jump formula of powers of 2. When I tried to understand the Van-Oorschot method of parallelization, I realized that if you double the amount of Kangaroos, you must double the jump size mean. This results in huge jumps for a big range and a big number of kangaroos if you use powers of 2. Do you recommend better selecting the jump size using random K's in a given interval?
Thanks
There are several ways to choose good jump sizes, I just use random sizes in some interval, check my sources for details. Also in my approach the average size of jumps does not depend on the number of kangs are used and it still works fine. There are not any known ways to improve K somehow by choosing jumps in some special way, all known good ways get same result, so it's not important what way you use.
I understand that you use a base magnitude for the jumps and add a random portion to make the jumps, in a different way for each of the 3 heards, I will study this in detail. I'm not able to find an implementation for batch inversion on your code, do you use batch inversion to speed up the computation of the inverses? I understand that in the Classic Pollard method, you can use this approach, computing the next point for a group kangaroo paths. This will make the cost for one inversion only 3 - 4 multiplications? Is that correct?