same public key

[davout]

You can't double money in bitcoin.

Yes you can, happened back in march

[davout]

ok, so having the same adress means actually the same private key.

No, to be precise it is not the case.

[DeathAndTaxes]

In other words if Alice has a wallet that contains the address xyz and Bob has a wallet that contains the same address xyz
both have the same private key?

(And thus all individual addresses of Alice and Bob can be signed with their own or the other one's private key?)

Well it is slightly more complex.  It is possible that Alice and Bob have different private keys which produce the same address because addresses are a hash of the public key.  If that happens (essentially 0% chance) either private key can sign a transaction to spend coins sent to the address in question.

[DannyHamilton]

The pub is derived from the priv, so if you had the pub you would also have the priv.

More than one private key can technically result in the same bitcoin address.

Therefore, if you have the same private key then you have the same address, but if you have the same address, you don't necessarily have the same private key.

In other words if Alice has a wallet that contains the address xyz and Bob has a wallet that contains the same address xyz
both have the same private key?

(And thus all individual addresses of Alice and Bob can be signed with their own or the other one's private key?)

Not necessarily, but they both have a private key that will create a valid signature for spending bitcoins that are associated with address xyz.  Not all individual addresses, only address xyz.

ok, so having the same adress means actually the same private key.

That makes sense.

Thank you!

No, having the same private key means having the same address.  Having the the same address does not necessarily mean having the same private key, but as long as you have a private key that is a valid private key for the address you are able to spend the bitcoins at that address.

[elements]

Ok, so in other words: if the private keys are different but the addresses are the same that means that only the amount assigned to that address (balance on that particular address) can be spent by both parties NOT the total amount of the wallets of each party. Correct?

[DannyHamilton]

Ok, so in other words: if the private keys are different but the addresses are the same that means that only the amount assigned to that address (balance on that particular address) can be spent by both parties NOT the total amount of the wallets of each party. Correct?

Correct.  Also, if the private keys ARE the same, that means that only the amount assigned to that address (balance on that particular address) can be spent by both parties NOT the total amount of the wallets of each party.

It doesn't matter if the private keys are the same or not.  It only matters if the private keys result in the same address.

[elements]

But if the private keys are the same, doesn't that also mean that they will create the same "universe" of public keys?

What I mean is this: if you create a new wallet it has one address and the private key. When you create new addresses for that wallet all derive from the same private key. If two private keys are identical won't they eventually create the same addresses? (Whether they show in your address book or not (yet))?

[DannyHamilton]

But if the private keys are the same, doesn't that also mean that they will create the same "universe" of public keys?

It was never stated, but I've been working off the assumption that we are talking about the Bitcoin-Qt wallet.  The Bitcoin-Qt wallet does not use a deterministic algorithm for generating bitcoin private keys or addresses.  Every new address is generated completely at random and has no mathematical association with any of the other addresses or private keys in the wallet.

What I mean is this: if you create a new wallet it has one address and the private key. When you create new addresses for that wallet all derive from the same private key.

No.  Regardless of the wallet you are using, each address has it's own private key.  When you create new addresses for the wallet, the wallet creates a new private/public key pair, and then computes the address from this new keypair.  In a deterministic wallet (such as Electrum), a deterministic algorithm is used to generate the next private key in the sequence instead of generating a random private key, but it is still a new private key.

If two private keys are identical won't they eventually create the same addresses? (Whether they show in your address book or not (yet))?

A private key only has one address associated with it.  (Well technically two, but that's due to the difference between the address that you get when you use a compressed public key and the one you get with an uncompressed public key)  If two private keys are identical, the address they create will be the same.

[DeathAndTaxes]

But if the private keys are the same, doesn't that also mean that they will create the same "universe" of public keys?

What I mean is this: if you create a new wallet it has one address and the private key. When you create new addresses for that wallet all derive from the same private key. If two private keys are identical won't they eventually create the same addresses? (Whether they show in your address book or not (yet))?

There is no such thing as a "universe of private keys".  Your wallet contains 1 private key for each public key (and address).

There are deterministic wallets which use a seed to produce multiple addresses but the seed isn't the private key.  The seed allows one to create multiple private keys (one private key for each address) from a single seed.

You likely are (incorrectly) assuming a wallet has only one single private key for all the addresses. If your wallet has 1000 addresses you have 1,000 unique private keys.

[DannyHamilton]

D&T,

You're getting slow.

 

[elements]

Thank you both for the clarification. Your assumptions were correct: a) I was referring to the Qt client and b) I thought there was just one private key from which all public keys derived.

Learned something! Thanks again!

[DeathAndTaxes]

D&T,

You're getting slow.

 

Yeah I am slipping in my old (forum) age.

[justusranvier]

There are deterministic wallets which derive all the private keys from a 256 bit root key and a 256 bit chain code for a total  of 512 bits of entropy.

The odds of a collision that would allow an attacker to derive the entire sequence of private keys is even more unpossible than finding one of the 2⁹⁶ private keys whose public key generates the same hash as a known bitcoin address.

[leijurv]

ok, so having the same adress means actually the same private key.

That makes sense.

Thank you!

However, there could be a RIPEMD-160 hash collision of two different ECDSA pubkey point. That would have two different privkeys with one pubkey.

[davout]

However, there could be a RIPEMD-160 hash collision of two different ECDSA pubkey point. That would have two different privkeys with one pubkey.

Re-read yourself :-)

[jackjack]

I want to repeat something:

An address corresponds to around 2^96 (around 8e28) different private keys

[kokjo]

However, there could be a RIPEMD-160 hash collision of two different ECDSA pubkey point. That would have two different privkeys with one pubkey.

their would be 2 keypairs, where the hash of the public keys would be equal.

keypair A: (Apub, Apriv)
keypair B: (Bpub, Bpriv)

Apub != Bpub and Apriv != Bpriv

BUT!!!!!

hash(Apub) == hash(Bpub)

[leijurv]

However, there could be a RIPEMD-160 hash collision of two different ECDSA pubkey point. That would have two different privkeys with one pubkey.

their would be 2 keypairs, where the hash of the public keys would be equal.

keypair A: (Apub, Apriv)
keypair B: (Bpub, Bpriv)

Apub != Bpub and Apriv != Bpriv

BUT!!!!!

hash(Apub) == hash(Bpub)

Yes. However, that would mean that the bitcoin address itself would be the same. Funds sent to that bitcoin address could be spent by either private key; the txout script only checks the hash of the pubkey key, not the public key itself.

[Remember remember the 5th of November]

You can't double money in bitcoin.

Yes you can, happened back in march

Really? Is there more information on this?

[davout]

Really? Is there more information on this?

March's fork.