> BIP 32 already specifies how to use the first three tree levels:  M/i/j/k, 
> i~wallet, j~Internal/External, k~address.  The first level is actually 
> type-1 derived, and thus we cannot create an arbitrary number of them 
> without pre-computing them from the offline wallet.  So it's not "free" to 
> create new wallets unless we redefine how the levels work.

Initially I was thinking that you would share the public key and chain code 
from [m/i'/0] so that you can receive payments at [m/i'/0/k], for a unique 
value of 'i' for each receive chain.

For the case of generating new receive chains from a *watch-only* wallet, as 
you say, the options are to either keep a cache of PubKey/ChainCode for 
unused [m/i'] or simply increment 'j' past 1 for an existing [m/i'/j] -- the 
concept of 'internal/'external' and change addresses at Depth=2 don't make 
sense for handing out receive chains to lots of people anyway, and certainly 
BIP32 doesn't *require* 0 <= j <= 1.  So I think incrementing 'j' is the way 
to go here...

The "default" layout of BIP32 does NOT mean that implementations should not 
check for transactions with j > 1. That would be a useless constraint and 
obviously self-limiting. It might be helpful to add to the 'Compatibility' 
section some minimum expectations about how a wallet should be 'probed' when 
imported. If you don't feel completely free to monotonically increment 'j' 
to your hearts content to achieve major usability benefits, then I say BIP32 
could use some clarifying.

BTW - the spec calls for addition not multiplication now, so we should call 
it the 'Addend' not the 'Multiplier' :-)

> Do these extra wallet chains behave as different wallets, or sub-wallets?

They could, but they certainly don't need to!  A single-wallet 
implementation treats this merely as an address-generation algorithm, and 
does not expose any hierarchy to the user interface.  The user just 
“magically” gets the ability to send multiple payments to their contacts 
without immediately sacrificing their privacy 
(http://www.wired.com/wiredenterprise/2013/06/bitcoin_retai/). Everything 
goes into the same ledger, balance, coin pool, etc. Most of the code base is 
unaware BIP32 is even in use.

While it is *possible* to support separate ledgers, balances, etc. it is 
certainly not required, and you get all the benefits either way.

I think, since your proposal generates and receives payments into 
BIP32-style addresses, we both need similar underlying wallet code. The only 
difference is that you are passing the Kpar for [m/i'/0/k] and the *result* 
of CKD'((Kpar, cpar), k), and instead I proposed passing Kpar and cpar, and 
leaving 'k' out of it, letting the receive choose 'k'.

> For instance, maybe there's a benefit to using the same parent pubkey 
> across multiple services, as a form of identity.   If I don't want that, I 
> use your method.  If I do want that, I use my method.

I think it's a interesting idea using static public keys as a means for 
persistent identity and hence security from MitM. If you want a shared 
public key across multiple services we could just combine both ideas and get 
all the benefits, by making the data structure { ParentPubKey, Addend, 
ChainCode }:

   ParentPubKey: Public key of m/i' -- 33 bytes
   Addend: I[L]*G from CDK'(m/i', j) -- 33 bytes
   ChainCode: I[R] from CDK'(m/i', j) -- 32 bytes

All that remains secret is the ChainCode from [m/i'] -- and of course the 
private keys.  The ParentPubKey is a common value across multiple services, 
corresponding to user's identity rooted in [m/i'].  Each service gets their 
own 'j'.  ParentPubKey + Addend gives you the PubKey of [m/i'/j].  With the 
ChainCode, the receiver then can generate [m/i'/j/k] for monotonically 
increasing 'k'. Again, from the user perspective all transactions under 
[m/i'] can be presented in a single ledger, or not.

Anyway, fundamentally my feedback is if you are designing for persistent 
long-term relationships, you could build in a mechanism for generating 
address chains so you don't need any further communication after the initial 
exchange, and it need not complicate the wallet.


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