Etar, I write it one more time: you just OVERestimate your actual power.
You use "square root method", but count the whole range. It is not correct.
Your example with 5 rooms x 200 people each and only one David among them: if you ask the whole room you perform ONLY one operation, but not 200 operations. Yes, it is better not to ask every person in every room, but ask once per room. This is efficient way. But it does not mean that you actually ask everybody. This will be overestimation.
Most famous Square root methods:
- Baby-step Gian-step
- Pollard's Rho algorithm
- Pollard's kangaroo algorithm
Have a look this link as well:
https://www.embeddedrelated.com/showarticle/1093.php You guys are so smart here, I even feel awkward.
Then answer me 3 simple questions:
#1 Question .
Let's imagine and take for the fact that I have a RAM for storing 2 ^ 255 public keys
And I make a table of baby steps by this size.
Those it’s enough for me to take 2 Giant steps to break the entire range 2 ^ 256 in 1second.
What speed will I have in that case? If you answer 2hashes/s. I will call the orderlies and will laugh for a long time.

#2 Question .
For example, I have a very small table of baby's steps. Let it be 10 values. And I take 100 giant steps per second. What speed will be in this case?
#3 Question .
There are 2 factories that produce cars. The first factory does everything .. from wheels to the trunk and engine. And the second one does only large-assembly cars. The first plant will produce 100 cars per month. The second is also 100 cars.
Those due to the fact that the second factory does not make a car from atoms, but of large parts, we can’t say that it makes 100 cars a month?
