Do you mean to say that bsgs algo gives you 100% information if key is or is not in s given range k1-k2?
Or you say bsgs would find private key even if k1 k2 interval is incorrect?
I had a closer look at JLP bsgs code (not cuda you speak about) and it seems there is no limit to 125 or 128 bit for search interval? Is bsgs by nature searching whole 256 bit range?
Apart from testing a program, meaning we know a key lies in a range we are using to test a program, to see if program works and can find the key that we know is in the range we are searching....
So if you are searching a range and do not know if the key you are searching for lies in the range, if you run the range with BSGS program, if the key is not found, then you know for 100% sure, that the key is not in that range. If you use JLP Kangaroo, you have to at least set the -m option to -m 6, if the program does not find the key, then you know with 99% sure, the key is not in the range.
BSGS will 100% tell you if the key is or is not in the range you are searching.
JLP BSGS is not limited to any bit range; meaning you can search in a 10 bit range or a 256 bit range.
Both programs search in the range you specify. If you specify a 64 bit range, that is what the program will search; if you specify a 256 bit range, that is what the program will search.