If satoshi had to sign for the coinbase address to mine the block, we could verify he indeed did own the private keys and those blocks would be in the circulating supply instead of us not sure if they are really circulating or not.
That's not the case, because you can produce valid ECDSA signature without knowing the private key. Some examples:
https://bitcointalk.org/index.php?topic=5373858.0You cannot produce a signature for an arbitrary message of an arbitrary private key. You can produce an (arbitrary) signature, and arbitrary message and calculate the corresponding public key, and calculate the corresponding address to the public key.
Hard to follow that but since the idea requires the signature of a predetermined public key, you wouldn't be able to fake it correct?
One way we can allow some lower trust pool setups would be to allow multiple coinbase transactions and only one of the coinbase addresses have to be signed for. So for example we could still allow 100 person pools to exist by allowing there to be 100 coinbase addresses that split the block reward and the miner only has to sign for one of them.
Some interesting benefits to this would be:
Totally making botnets infeasible since the bot would have to know the private key to where the coins are going. Also mining slavery where some person or organization forces a person to mine against their will and give all proceeds to the bad guy. This would mean that slavery of this type is prevented because the miner would have to know the private key. This slavery could be in the form of government regulation as well.
You explain why your solution would not prevent botnets above. A coinbase transaction could send 1 satoshi to a private key distributed to all computers in a botnet, and the remainder to the botnet operator.
6.25 BTC / 100 is not 1 satoshi. Im not exactly sure how the coinbase address rules work currently but if using this idea it would have to be equally split between a defined number of addresses. Or you could say the signature needs to come from a coinbase address that gets at least 1% of the block reward and all the other addresses can get any amount desired. That would probably be ideal to give maximum flexibility.
Instead of the users having to trust the pool and the pool not having to trust the users; the user would not have to trust the pool as much and the pool would have to trust the user now instead.
Pool trustworthiness has largely not been a major issue in the bitcoin world. It is trivial for a miner to switch from one pool to another, and pools are generally expected to payout mining rewards on a frequent basis.
true but using that logic bank trustworthiness hasn't really been a big issue either. So many banks are competing for your money that they are incentivized to be trustworthy and the government insures your deposits right? The real value of this idea is preventing the 51% attack. How do you know the mega pool (which this method prevents) wouldn't be able to use your hashrate to someday attack the network? Breaking up the pools won't 100% guarentee that the same operator doesn't run the majority of the small pools but just like breaking up monopolies in the real world, it does usually work and makes it exponentially harder for it to happen.
Provable circulating supply. All the blocks satoshi mined might have gone to randomly generated public keys without private keys. If satoshi had to sign for the coinbase address to mine the block, we could verify he indeed did own the private keys and those blocks would be in the circulating supply instead of us not sure if they are really circulating or not.
The question as to if the coin produced via early blocks is not necessarily if satoshi (or whoever mined those blocks) controlled the private keys when the blocks were mined, the question is if satoshi controls the private keys associated with the output of the coinbase transactions today.
Satoshi did spend some of his coin that he mined, so it is reasonable to believe that he controlled all the private keys associated with the coinbase transactions of the blocks he mined at the time they were mined. Further, anyone mining any kind of coin will need to expand valuable resources to mine, so it would be illogical for someone to intentionally mine in a way that results in coinbase transactions being sent to addresses they (directly or via an agent) cannot spend from.
good points but for one satoshi did not need to expend valuable resources to mine because he was just doing it on a PC and was probably the only one mining. He could have been just doing it to secure the network and didn't save the private keys (after the test transaction to hal finney) so he wouldn't be tempted to spend them cause that would basically be a premine. We can never know if someone saves their private keys or not but we could know at least they have them saved temporarily to mine the block. We can be sure that no coins were mined directly to a legitimate (but hidden) burn address.