For #120, that is roughly 58 days with 64 RTX 4090s, to solve
For #125, with 128 RTX 4090s, that would be around 163 days, to solve.
And those are running on some zero-point module free energy?
So you basically stored 500 billion DP 0, tames, basically just printing pubs and privs to a file, and now are offsetting 130s pub by random amounts, and looking for a collision?
No (to all of the questions). Have you looked at the 2**65 keyspace? It's 36893488147419103232.
BTW it only takes around 16 bytes / key to store hundreds of billions of tame kangaroos for 129 bit case.
Ofcourse I'm not simply "printing pubs and privs" to a text file, that's an over-simplification.
If you want some hints: the more keys a hash table has, the less space/key is required.
For the traditional Kangaroo algo, for 130, with DP 32, I need to find only 9 billion tames and 9 billion wilds to solve. So it sounds like you just stored random pubs and privs, because 500 billion tames, with a decent DP, would take a loooooong time.
Also, you need to perform roughly 2^66.05 "steps" for #130, that would be the average.
I think you are kidding with your 9 billion kangaroos. You are missing something critical about the underlying theory.
Otherwise, you can solve all puzzles with 2 kangaroos, if you wait a trillion years.
If you are so sure #120 / #125 were solved with existing software, did you also do the math about how many kangaroos would have been needed? At DP 0 /1 / 2 etc? Your times have no meaning without space complexity attached to them.
Lol, yeah, I do not think you understand the Kangaroo algo.
It's all laid out for you in various readings/papers.
I never said 9 billion kangaroos. Do you understand the algo? When I say "find" x amount of tames and wilds, it is referring to the points/distances found by each type of kangaroo. You store tame and wild points (Based on DP used) and distances, that are generated from the tame and wild kangaroos, hopping all around.
2^66.05 - 2^32 (DP size that I stated) = 2^34.05 stored DPs. 2^33.05 tames and 2^33.05 wilds. 2^33.05 = 8,892,857,981; so roughly 9 billion points and distances stored (tames and wilds) to solve, on average. Could be a little higher, could be a little lower. So no, I was not "kidding". And yes, my times are based on math, and the space complexity is what I said, roughly 9 billion points & distances per tame and wild, to solve. I can't give you exact amount of GBs required because each Kangaroo program stores points differently, different amount of bytes and different formats, binary vs plain text. One would need to calculate it based on their DP and how the points/distances are stored.
But yes, you could set out 2 kangaroos, 1 tame, and 1 wild, and eventually solve, in many many years, or you could get lucky and solve within minutes, hours, days.
I doubt whoever solved 120/125, if they used the kangaroo algo, set a DP of less than 28. They would have an enormous amount of DP overhead, that JLP explains well in his github:
DP overhead according to the range size (N), DP mask size (dpBit) and number of kangaroos running in paralell (nbKangaroo).
110 and 115 were both solved with DP 25. I know that during the 115 run, the grid sizes for the GPUs were choked down and another part of the code was reduced, to prevent a massive DP overhead. And when finally solved, I do believe total DPs stored (points w distances) was a smidge over the expected total of 2^33.55
