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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<cnnx>
can someone suggest a source that has a good selection of asic hardware?
<cnnx>
in north america
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<kanzure>
"a signature is zero knowledge argument of knowledge that you know the private key"
<kanzure>
but doesn't this require knowledge of the public key??
<kanzure>
oops one too many question marks
<Alanius>
proof of knowledge refers to the existence of an extractor machine
<Alanius>
wait, nevermind
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<Alanius>
in the case of zero-knowledge based signature schemes, the public key is usually a known function of the secret key; so obtaining the public key from the secret key is trivial
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<kanzure>
ok, so the argument is that it's still zero knowledge since you don't learn anything about the private key (even though you learn which signatures it has made, if you see the signature)
<kanzure>
?
<Alanius>
yeah, but that can only hold in the random oracle as far as I know
<Alanius>
because the whole clue of zero-knowledge is that a simulator can generate the entire transcript without knowledge of the secret; if you want to make it non-interactive you have to enable the simulator to program the random oracle to give the right responses to certain queries
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<Alanius>
if you instantiate the random oracle with a hash function (unprogrammable) you can obviously tell simulated transcripts from authentic ones; but for the security argument, modeling the hash function as a programmable random oracle is good enough
<Alanius>
zero-knowledge means there exists a simulator that can generate valid transcripts without the secret that are indistinguishable from authentic; indistinguishable can only be defined with respect to distinguishers who in the random oracle model only have oracle access, which explains why the distinguisher cannot tell the reprogramming has occurred
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<adlai>
what do you mean by 'unprogrammable'? i assume any function is computable... you mean the instantiation is unique each time around?
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<Alanius>
the random oracle responds with random values to each query, but always the same response to the same query as long as you're in the same experiment; the simulator (whose existence may be required for a crypto proof, for instance) can use this to its advantage: by presenting the simulated algorithm with a view of the random oracle that is identical except for a select few query-response pairs
<sipa>
tl;dr: "programmable" is a technical term with a specific meaning in security proofs
<Alanius>
yes, that ^^
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<Alanius>
the key point that makes the proof work is that the simulated algorithm has no clue it's dealing with a fake random oracle; but the "programmed" query-response pairs are enough to enable the simulator generate zk proof transcripts, or invert rsa, or do whatever seemingly impossible task
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<Alanius>
the hash function is obviously the same each time round; but the proof models the hash function by a random oracle which is different each time around because it is drawn uniformly at random from the set of all discrete functions that map to the given output space
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