# Are there an infinity of public addresses for a wallet?

If I understand correctly a private 256-bit integer determines the curvature of an EC curve corresponding to your wallet and that 256-bit integer can be consider the "private key".

Now how many "public address(es)" are there corresponding to that particular wallet?

Is there just one public address or an infinity?

I've got a related question related to change: in typical bitcoin clients, when a change public address (I take it a change address is public, right?) is given, is that change address corresponding to the same wallet that the one where the bitcoin came from?

• I think these are known as 'collisions'. Commented Jan 14, 2014 at 19:38

A wallet contains a collection of keys, not just a single one.

Every private key has exactly one associated public key. Addresses are shortened forms of public keys (they're encoded hashes of the public key).

Change addresses are indeed public. Like every other address, the key for it is independent from the other keys in your wallet. Note that some clients send change back to one of the addresses the inputs were previously assigned to, in which case it's obviously the same key that is reused.

• can't upvote you because I miss one upvote to have 15 rep ^ ^ Commented Jan 14, 2014 at 19:49
• "Addresses are shortened forms of public keys (they're encoded hashes of the public key)." And there can be an infinity of shortened forms / public addresses for a single private key / public key? Commented Jan 14, 2014 at 19:57
• @bitcoin: No, there is only one. Commented Jan 14, 2014 at 20:05
• But bear in mind addresses are 160 bits. If there are 2^160 addresses and 2^256 public keys, there are 2^96 public keys per address!
– kaoD
Commented Jan 14, 2014 at 20:07
• @kaoD: could you expand a bit on the math behind that? Any 160 bit public address of the 2^160 can be used as a public address? Commented Jan 14, 2014 at 20:16