wumpus changed the topic of #bitcoin-wizards to: This channel is 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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<amiller>
okay so in generalized zero knowledge proofs, there is always a "simulate" function. The simulator takes in a random challenge, and it produces a (commitment, response) pair.
<amiller>
the simulator is essential to the proof that this is zero knowledge and reveals no *computationally useful* information about the secret
<amiller>
In the existing (before the AOS/borromean optimization) generalized-OR proofs, the simulator also tells you what to do for the secrets you *dont* have
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<amiller>
the design constraint here for a sound OR proof is that you have to force one of the commitments to be chosen independent of its challenge
<amiller>
which is done using hash functions, by having the challenge depend on the commitment
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<amiller>
okay so even given those constraints, it's pretty clear from the borromean signatures approach that the existing generic technique is inefficient
<amiller>
the high level idea is that N-1 of the challenges don't have to depend on their commitment (instead the commitment depends on the challenge, because of using "simulate"), but the *sum* of all the challenges has to depend on *all* the commitments, therefore at least one of the challenges has to depend on its commitment
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<amiller>
the high level idea above is the same in borromean and in the existing technique
<amiller>
but the existing technique does all that in the most obvious but dumb way
<amiller>
you generate a random challenge for the N-1 fake statements, then compute the commitment depending on those. Compute the real commitment using the witness. The *total* of the challenges is based on the hash of all the commitments, and so the final challenge is chosen by subtracting all the earlier-chosen challenges from this total... then *all* the challenges have to be included in the proof, which is needlessly inefficient
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<amiller>
Okay so to optimize the generic technique, so that we only have to include one random string in the proof, we only need to "pick" one random value, and then the rest are determined by applying hash functions to commitments and prior challenges
<amiller>
with that whole strategy in mind there's only one way to do it that seems to typecheck
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<gmaxwell>
18:32 < ryan-c``> I appear to have shamed brainwallet.org into shutting down.
<gmaxwell>
ryan-c: a darker interpertation: taking the site down makes it harder for people to sweep vulnerable brainwallets; meaning more coins sit around available for theft.
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<tromp_>
bitcoin is the ultimate password entropy educator
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* nsh
smiles
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