On Wed, Jun 19, 2013 at 10:39:04AM -0400, Alan Reiner wrote:
> On 06/19/2013 10:25 AM, Timo Hanke wrote:
> > Since you mention to use this in conjunction with the payment protocol,
> > note the following subtlety. Suppose the payer has to paid this address
> > called "destination": 
> >>    Standard Address ~ Base58(0x00 || hash160(PubKeyParent * Multiplier[i]) 
> >> ||
> >> checksum)
> > Also suppose the payee has spent the output, i.e. the pubkey
> > corresponding to "destination", which is PubKeyParent * Multiplier[i],
> > is publicly known. Then anybody can (in retrospect) create arbitrary
> > many pairs {PublicKeyParent, Multiplier} (in particular different
> > PublicKeyParent) that lead to the same "destination".
> >
> > Depending on what you have in mind that the transaction should "prove"
> > regarding its actual receiver or regarding the receiver's PubKeyParent,
> > this could be an unwanted feature (or it could be just fine). If it is
> > unwanted then I suggest replacing
> > PubKeyParent * Multiplier[i] by 
> > PubKeyParent * HMAC(Multiplier[i],PubKeyParent)
> > which eliminates from the destination all ambiguity about PubKeyParent.
> >
> > This modification would not be directly compatible with BIP32 anymore
> > (unfortunately), but seems to be better suited for use in conjunction
> > with a payment protocol. 
> >
> > Timo
> It's an interesting observation, but it looks like the most-obvious
> attack vector is discrete log problem:  spoofing a relationship between
> a target public key and one that you control.   For instance, if you see
> {PubA, Mult} produces PubB and you have PubC already in your control
> that you want to "prove" [maliciously] is related to PubB, then you have
> to find the multiplier, M that solves:  M*PubC = PubB.  That's a
> discrete logarithm problem.

Correct, for a given PubC in advance you can't create such a "malicious"
relation to PubB. You can only "reversely" construct new PubC from given

> I'm not as familiar as you are, with the available operations on
> elliptic curves, but it sounds like you can produce essentially-random
> pairs of {PubX, Mult} pairs that give the same PubB, but you won't have
> the private key associated with those public keys.  

Depends on who is "you". The arbitrary person who produces {PubX, Mult}
won't have the private key, but the person who knows the private key for
PubA will have it (assuming that PubB was computed from {PubA, Mult} in
the first place).

In the end, it all depends on your application. What proves enough for
one party doing repeated transactions with another may not suffice for a
third party doing auditing. On the other hand, ambiguity about PubA may
just as well be a wanted feature for deniability reasons.


Timo Hanke
PGP 1EFF 69BC 6FB7 8744 14DB  631D 1BB5 D6E3 AB96 7DA8

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