Since the coordinator knows Charlie's coins, he can block him as soon as Alice joins.
This causes the attack to fail while also causing the attack to be detected by both Charlie and Alice.
And all those points you're making are complete garbage.
My points proved conclusively that coordinators are trustless. You can even use all 3 anti Sybil method together to prove there's no malicious coordinator:
- First, register your private coin to the coordinator.
If it's accepted, then there's no Sybil attack.- Second, ask your friend to register a coin to the same round.
If it's accepted, then you've confirmed for a second time that there's no Sybil attack.- Just to be absolutely sure, back out of the round during signing to check to see if the transaction was built to target you.
If the transaction is created, you've confirmed for a third time that there's no Sybil attack.