The addresses are the out points, there is usually 2 but there can be any number, and each of these addresses designate the spending key for next time. The signature itself, when combined with the hash of the transaction, reveals the public key the address is derived from, and thus proves the right of ownership.
The public key is hidden until the tx is lredy history. This means also that quantum computers don't matter so long as you don't reuse and continue to hold coins at the dress.
The signature logarithm is based on a specific number series that is derived from a tiny seed, which is too small to manipulate to back door it, meaning to hide numbers in it that allow multiple solutions. The other ones used in blockchins do not have this property.
The vulnerability that was discovered that led to segwit related to the ECDSA signatures, which llow a much larger set of other solutions that is referred to as malleability. Schnorr signatures, like used in nostr, and taproot, don't have this problem. They can also be used in the same way here the txid hash and signature reveal the public key, but lso make it easy to function like a keychain, creating a mechanism for encoding multiple codes tied to a single key, which can be used to represent the lternte pths of execution of a smart contract.
