I wonder if wallet tools fundamentally and exclusively generate private keys in the 256 bit range. Or can it happen that such a tool generates a 103bit or 87bit private key when generating addresses/wallets?
Bitcoin private keys have exactly 256 bits. A private key with fewer would require that the remaining bits be set to something.
From a security perspective, there would be nothing inferior about the keys that are closer to 1, and nothing superior about the keys that are closer to 10.
I am not entirely sure that this is true. One might think that the keys from the lower range tend to be found much sooner than their counterparts further up. With the simple reason that most cracking tools and their developers naturally start counting at one and increment linearly. Only a small exception would come up with the idea to start counting at eg 30% of a range, or to start counting backwards, or randomly. As for the rest, I'm with you.
That is true. Brute force attempts that check a range generally prioritize ranges that are likely to have more use. Due to bugs or laziness, the low end of the 256-bit range probably deserves a higher priority. If the attempt assumes that
any key is equally likely, then there is no benefit to start at the beginning of the 256-bit range, but on the other hand, starting at 1 is as good as any number, so why not.
Thus, most brute force attempts checking a range start at 1, making the low end of the 256-bit range more vulnerable simply because it is the range checked most often.
On the other hand, since there are so many people already checking the low end, an attacker might want to choose a different range that does not have as much attention in order to avoid the competition.
In the end, a randomly generated private key is extremely unlikely to be in a range that any attacker is searching, so there is no practical reason to be concerned.
