yeah, it's based on an arcane construction, which i think was probably one of the key elements of Satoshi's original discoveries that enabled it to be what it is
the payment addresses have to be hashed to reveal, from the pubkey, which is made visible for the first time when you already have published the transaction
this address previously cannot be connected to the pubkey that is derived from the secret key that enables spending
so it's basically a case of you not being able to see ahead of time who might have that key, because you don't know what the key is, only the RIPEMD160 hash of the key, which is a shorter hash than the one used in the signature algorithm (the SHA256 hash of the transaction creates the txid which the signing key must sign on, using teh pubkey, related to the address that was derived from the pubkey by the recipient
it also includes an unusual construction where instead of getting one bit of true/false when verifying, you take the txid (transaction hash) and the signature of the spend transaction, and this gives you something that should be the pubkey, and this can be verified because the pubkey, fed into ripemd160 hash, generates the address specified as teh "out point" in the transaction
so you see, it creates a fog of war on the network that can't be broken, the address hashes are deliberately fully 116 bytes shorter than the hash of the txid and the pubkey so that's a LOT of security against reversing the hash function, 116 bits of security is pretty much still considered to be 1000 years of brute force prevention security for AES style encryption algorithms
nobody had put it all together in this way before, and even, Satoshi, i don't think he had the whole picture before he started on the project, but once he discovered it, the fate of bitcoin was sealed, it was the first time anyone had created a peer to peer cryptocurrency system that was invulnerable to any kind of cryptanalysis attack
this is also why i'm also very hostile to the ecash people, because Chaum's blinded signatures did not solve this problem, and Adam Back is definitely not Satoshi even though some of his ideas that he tried to implement were related, and even that famous NSA paper that describes about 90% of what bitcoin is, was missing critical things, and this irreversible hashing of pubkeys to addresses and teh use of signatures that only give the (maybe) pubkey means that once the spend has hit the p2p network, the holder is now done, you don't know who the two addresses are controlled by (spend and change) and you don't know which of those two is the spend, and you don't know whether they are even another person or not, it can never be known ahead of time where a bitcoin transaction is going to be spent and once it is, it's too late to catch them
