does a generated private key, provide 1 public key? I mean, the pair is generated practically at once? Then this only public key is used to create multiples “adresses” which will be used to make transactions?
Thank you a lot.
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Generally, it's one address per keypair. This is even true in deterministic wallets where you generate multiple keypairs based on a single seed. Remember that there are still multiple keypairs in this scenario. A private key is generated randomly (or deterministically from a seed), and then a public key is derived from it. After that, an address is derived from the public key.
However, it's not quite that simple. There are two different representations of elliptic curve public keys that bitcoin supports, meaning that you can generate two different address from the same private key...both of which can be claimed with that private key. Wallets generally only use a single public key format (usually compressed), so within a wallet, there's one private key to one public key to one address.
Also, there are different types of addresses (pay-to-public-key-hash, pay-to-script-hash, mainnet, testnet, etc...), which each could use the same public key to generate different addresses based on their corresponding prefix. This is why pay-to-public-key-hash addresses begin with '1' and pay-to-script-hash addresses begin with '3'. To my knowledge, no wallets will generate two types of addresses from the same public key. That would be similar to re-using addresses, and is generally considered to be a bad practice.