sipa changed the topic of #bitcoin-wizards to: This channel is for discussing theoretical ideas with regard to cryptocurrencies, not about short-term Bitcoin development | http://bitcoin.ninja/ | This channel is logged. | For logs and more information, visit http://bitcoin.ninja
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<RubenSomsen>
Question related to taproot, it is P = C + H(C||S)G. Can you also do P = C + H(S)G assuming you have already seen a signature proving C is a valid pubkey?
<arubi>
it's a bit slow here at times RubenSomsen, but idling here is rewarding enough :)
<RubenSomsen>
Thanks for the heads-up
<arubi>
cheers
<waxwing>
RubenSomsen, i understand the Q, but my counter-Q is, is there any reason you'd need to not use C in the hash?
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<RubenSomsen>
Well, I am exploring whether it is possible to commit to more than one hash in the pubkey
<kanzure>
merkle root of a hash tree?
<RubenSomsen>
And it is possible in the taproot way, but it requires revealing every S you commit to
<waxwing>
oh. but since the idea is to have S be validated against (in non-cooperative case), why would you do that?
<sipa>
RubenSomsen: if you use your construction you can't prove afterwards what the commitment was
<sipa>
you could just reveal P-H(S)G for any S
<RubenSomsen>
sipa: but for a different S you would not be able to sign with C, no?
<sipa>
when you reveal the script, no signature with C is required in taproot
<RubenSomsen>
I know, my question is specific to the assumption that a signature exists
<RubenSomsen>
and I understand that taproot specifically avoids that requirement
<sipa>
in that case, i believe it's secure
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<RubenSomsen>
So if we assume a schnorr 2-3 multisig, in MAST there would be three scripts: AB, AC, and BC (and perhaps also ABC)
<sipa>
RubenSomsen: andytoshi just told me IRL i'm an idiot, and you can still sign with C-H(S)G as keu, for any C and S
<sipa>
it's just offsetting the key
<RubenSomsen>
umm let me see if I follow
<sipa>
so we start from a real C and a real S
<sipa>
and compute P = C + H(S)G
<RubenSomsen>
yeah
<sipa>
which is the commitment
<sipa>
the private key for p is just c+H(S)
<sipa>
now i want to open this commitment for S'
<RubenSomsen>
right
<sipa>
so I reveal S', and verifiers will want to see S' and a signature with P-H(S')G, right?
<RubenSomsen>
yeah
<sipa>
so the private key for P-H(S')G is just p+H(S)-H(S')
<sipa>
ah, but this can only be done by those who know p
<sipa>
who can already sign anyway?
<sipa>
is that your point?
<RubenSomsen>
need a moment to process, hold on
<waxwing>
if you (jointly) can sign P then you can sign on any tweak, i don't think it's the signing part for which the C-inside-hash matters
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<RubenSomsen>
the private key for P-H(S')G is p-H(S'), no?
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<andyphoneshi>
rubensomsen yes
<RubenSomsen>
Thanks Andrew
<andyphoneshi>
waxwing the commitment to C gets you a precommitment to the script which avoids the need for a signature
<RubenSomsen>
Wasnt there a way to commit to a value that requires a signature as proof?
<andyphoneshi>
but if you have a signature, you can use this trick (or rather a variant where the pubkey just signs S' directly without being offset) you can get arbitrary delegation like this
<andyphoneshi>
rubensomsen unsure
<andyphoneshi>
what i just described is due to gmaxwell who explained it to me IRL, but hasn't yet written it up
<waxwing>
ok so it's like: if it were P=C+H(S), then when opening the commitment (to the network, which only checks that P = C + H(S)), you could open it to a different pair (C, S) easily
<waxwing>
i.e you want to make it S', just choose C' = C + H(S') - H(S)
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<RubenSomsen>
Yeah that is my understanding now too. Thanks for pointing out what I was missing, guys.
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<andyphoneshi>
waxwing to get taproot one of those hashes should have P in it, as revealing this does not require a sig and therefore can be done more efficiently
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<waxwing>
andyphoneshi, yes, i was just trying to get clear why it's not secure to do it without C in the hash (you meant C not P presumably)
<waxwing>
but thanks for clarifying the 'without signature' bit in your description, i'd kind of glossed over that when reading Greg's write up. it's a rather crucial point :)
<waxwing>
so i suppose the typical scenario being something like S is (timelock condition) (pubkey condition) so there's a sig, just not against P/C.
<andyphoneshi>
yeah
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<instagibbs>
i had the same exact confusion, thought I had figured out a way to commit to many different contingencies, later realized I had glossed over the actual point of p2ch :)
<instagibbs>
Well, you can, but you must reveal all of them at the same time
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