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.
Thank you for exhausting explanation!
I hope I understand correct both JLP and "cuda" BSGS work up to 256bit size search
Maybe you noticed I migrated JLP bsgs from curve k1 to r1. It was success. I started it for interval almost 256bit:
1000000000....0000000
EFFF.....................FFFFF
I know it will probably not succeed in this century but it is not impossible
I want to try to find private key for gr**npassI continue to work to migrate also Kangaroo256 to r1 curve but I was told by the author to wait a bit until he updates hastables (?)
Anyway, I migrated cpu part already just to see how is the behaviour of the code. I already reported him my findings, it is here on the forum