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06:31 < kanzure> win 172
06:31 < kanzure> no
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16:40 < sanket1729> waxwing_, I know the intuition to prove it. But still did not find time to write things down. Basically, in an observable RO model we have access to queries made to the RO.
16:41 < sanket1729> Let Q be a taproot key of the form Q = P' + H(P' || S') for which we would like to find a collision. Imagine this is already on the blockchain
16:43 < sanket1729> We make subsequent queries to the observable RO of the form of P_i, which would output H(P_i || S''). The output of these should be indistinguishable from Random functions.
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16:44 < sanket1729> Now, we want to make the output this random function equal to a specific value (Q - P_i) which we have already committed. Note that the observable is coming in handy over here because we can use P_i in proof here.
16:45 < sipa> What property are you trying to prove?
16:45 < sipa> Taproot being secure probably needs a whole bunch of properies.
16:45 < sanket1729> And the probability that the output of this random function is same to the one value(Q - P_i) is negligble
16:46 < sanket1729> sipa: That once a taproot Q = P + H(P || S') is committed to the blockchain, It cannot be spent by any another combination apart from P, S'
16:46 < sipa> What if the private key to P is part of S?
16:49 < sipa> I think proving that the taproot function is a sound commitment is a very useful thing to prove, but it's not exactly the same as unforgeability of spends (which is much harder to model)
16:49 < sanket1729> You would still have to spend it via either P or S. And not some other P' and S2
16:49 < sanket1729> Yup, I am ignoring the information from script predicates.
16:51 < sipa> I was talking to real_or_random about this earlier, and I think it's useful to have a model where you treat the script as a commitment to a set of lists of public keys (including the empty list which would be trivially spendable).
16:51 < sipa> And take into account that the internal public key may be repeated in the script.
16:51 < sipa> And that the script may be empty.
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16:52 < sipa> And you try to prove unforgeability even when the attacker has access to an oracle that produces signatures for other paths than the one he has to forge.
16:53 < sipa> This ignores the fact that scripts can impose additional conditions, but it's easy to argue those don't interact with security.
16:54 < sipa> While it's somewhat harder to argue that Schnorr signatures being present inside the script don't interact with the internal pubkey.
16:54 < sanket1729> I think if we model it that way it is possible to prove something. Meaning, all scripts would have all spending condition which rely on pubkey
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16:56 < sipa> There are also privacy properties that may be useful; i.e. showing that f(P,s) = P + H(P||s)*G is a hiding commitment if P is a freshly generated key.
16:56 < sipa> s/i.e./e.g./
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