Yesterday, I read in detail about the giant baby steps algorithm.
I had heard about him before, but did not delve into the gist of it.
This algorithm is very similar to the one I use.
So you have use this algorithm which is in O(sqrt(n)) for both memory and time where n is the size of the range.
Starting with an offset does not prevent to use this algorithm.
That means that the key rate (or group operation) you announced is wrong.
Do not waste time in solving the above problem, solving it will just prove that you have correctly implemented this known algorithm.
About speed, read above. Yes, an algorithm is used that minimizes the use of resources. But this does not mean that they do not need to be taken into calculation of speed. The total number of keys that are processed will not decrease. It’s just that they are processed by comparison, not by adding a point.