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<nickler>
adiabat: Isn't your Discreet Log Contracts scheme vulnerable to pubkey cancellation? The oracle could for example set R to -Pub_A resulting in Pub_Ai = -h(i, R)*V such that the oracle alone can spend that output. Or Alice could set Pub_A to -s_i*G + x*G to spend the output without the oracle's involvement.
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<waxwing>
nickler: would the delinearlization thing fix it, i.e. you send to hash(P_A)P_A + s_iG (by 'it' i mean your second point)
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<instagibbs>
waxwing, the oracle should delinearize her R. It's a fixed number of pubkeys so I don't think you have to be worried about wagner-style attacks
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<nickler>
waxwing: Yes. And as instagibbs says you could make Pub_Ai = h(Pub_A)*Pub_A + H(s_i*G)*s_i*G.
<nickler>
instagibbs: The paper mentions the case of multiple oracles, so it's probably better to defend against Wagner attacks by additionally including all pubkeys in the hashes.
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<instagibbs>
The oracle(s) cannot delinearize against the players' pubkeys(since they don't know them), which makes me wonder if there's a secure way to combine players' pubkeys for some reason.
<instagibbs>
(sorry that came out fairly confused, I'll think it over instead)
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<instagibbs>
For clarity: You can have the oracles delinearize their pubkeys all together, then also have any smart contract participants do the same if they are doing pubkey combination as well.
<instagibbs>
results in just 2 H(...) values, so not vuln to wagners
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<adiabat>
nickler: hm, probably best to delinearize all the keys just to be on the safe side
<adiabat>
In the case of Alice / Bob, it's all interactive so they can sign with their pubkeys before adding in the oracle's signature point
<adiabat>
But yeah... why not save those signatures and multiply everything by a hash of all the pubkeys involved
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