I do not argue that the keys from the puzzle were obtained randomly. What was this generator, bitwise, ekdska, super random, etc. irrelevant.
But here we go into the theory of probability. For example, if you get a random number from 1 to 100, then theoretically one kind of number, for example 3, can fall 10 times in a row. But it is theoretically. If in practice this happens, then it will be more like a generator failure. Another example. We create a million random numbers from 1 to 100. In theory, some numbers will turn out much more, and some much less. But in practice, the quantitative discrepancy will be no more than 10 percent on all numbers. That is, not entirely by accident.
From this we see that the numbers found have some rules or conditions. The number of set bits can be from 30 to 70 percent, a sequence of up to 8 identical bits in a row, the same rotation no more than 10 times, etc. The same rules can be chosen for the 8-decimal version and the 16-decimal representation. Repeating the same numbers, ladder, etc.
And applying these rules, we can discard most of the keys so as not to check them for correctness. Yes, there may be exceptions to the rules, but most should be subject to these rules.
This increases the speed of search. And you can start not with boundary values, but let's say averaged ones.
01 - 100%, 02 - 100%, 03 - 100%, 04 - 25%, 05 - 60%, 06 - 50%, 07 - 43%, 08 - 38%, 09 - 67%, 10 - 20%, 11 - 36%, 12 - 67%, 13 - 31%, 14 - 36%, 15 - 60%, 16 - 50%, 17 - 65%, 18 - 33%, 19 - 63%, 20 - 50%,
21 - 52%, 22 - 55%, 23 - 52%, 24 - 38%, 25 - 68%, 26 - 42%, 27 - 52%, 28 - 50%, 29 - 55%, 30 - 53%, 31 - 68%, 32 - 47%, 33 - 48%, 34 - 47%, 35 - 43%, 36 - 47%, 37 - 59%, 38 - 45%, 39 - 51%, 40 - 55%,
41 - 51%, 42 - 45%, 43 - 56%, 44 - 50%, 45 - 42%, 46 - 41%, 47 - 51%, 48 - 65%, 49 - 51%, 50 - 48%, 51 - 37%, 52 - 58%, 53 - 45%, 54 - 59%, 55 - 56%, 56 - 61%, 57 - 51%, 58 - 43%, 59 - 56%, 60 - 53%,
61 - 48%, 62 - 55%, 63 - 57%, 65 - 45%, 70 - 49%, 75 - 44%, 80 - 46%, 85 - 46%, 90 - 48%, 95 - 51%, 100 - 53%,
Sort, less than 50 and more than 50.
01 - 100%, 02 - 100%, 03 - 100%, 05 - 60%, 09 - 67%, 12 - 67%, 15 - 60%, 17 - 65%, 19 - 63%,
21 - 52%, 22 - 55%, 23 - 52%, 25 - 68%, 27 - 52%, 29 - 55%, 30 - 53%, 31 - 68%, 37 - 59%, 39 - 51%, 40 - 55%,
41 - 51%, 43 - 56%, 47 - 51%, 48 - 65%, 49 - 51%, 52 - 58%, 54 - 59%, 55 - 56%, 56 - 61%, 57 - 51%, 59 - 56%,
62 - 55%, 63 - 57%, 95 - 51%, 100 - 53%,
Count 35 Average 60,77%
04 - 25%, 07 - 43%, 08 - 38%, 10 - 20%, 11 - 36%, 13 - 31%, 14 - 36%, 18 - 33%,
24 - 38%, 26 - 42%, 32 - 47%, 33 - 48%, 34 - 47%, 35 - 43%, 36 - 47%, 38 - 45%,
42 - 45%, 45 - 42%, 46 - 41%, 50 - 48%, 51 - 37%, 53 - 45%, 58 - 43%,
61 - 48%, 65 - 45%, 70 - 49%, 75 - 44%, 80 - 46%, 85 - 46%, 90 - 48%,
Count 30 Average 41.43%
06 - 50%, 16 - 50%, 20 - 50%,
28 - 50%,
44 - 50%,
Count 5 Average 50% not used in calculation.
That is, the search can begin with a range from 41 to 61 percent.
And if we search for those already found with this range, then we will find 58 keys out of 71. That is more than 81 percent of the locations.
In this case, the search is performed in only 20 percent of the possible options, that is, 80 percent of the options recline !!!
If you have not found, increase the range, say up to 31 - 71, while also excluding options from 41 to 61 percent. Etc. Or we proceed to search for the next key.