Can I just try sweeping this key? 0000000000000000000000000000000000000000000000000000000000000003
Is this something that an attacker can actually attempt to use, to try sweeping such randomly created keys (eg. as brute force) ?
Yep! You can sweep that key, it's a valid private key as it is within the range of 1 to (approx.) 1.15*10^77. But you
mustn't. Attackers can easily brute-force such private keys. In-fact, any manually written private key isn't safe because humans are worst random generator. They are always tend to go for patterns which make the keys predictable.
I meant, one can generate such private keys "hoping" it will match an existing one then he/she can sweep it into a new wallet, eg. like an attacker would do.
You can always start with a good randomly generated private key then do some random changes using that initial key as seed. Is there any protection for such attempts?
Still I don't understand why uniqueness is not ensured by design, one centralized mirrored server could track all transactions queue.
People are winning lottery from time to time...from those cases when people are complaining about stolen funds, are they really sure it was their fault of just the current design?