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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<waxwing>
Alanius, perhaps you can answer this other question i had; why is knowledge soundness defined in terms of the extractor specifically getting *two* transcripts for the same commitment? That's clearly right for Schnorr (extracts the secret), but for protocols in general would not more than 2 sometimes be required?
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<BitDigiNet>
Anyone else looking for GPU ?
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<Alanius>
waxwing: you are absolutely right, some protocols need more transcripts for extraction than just two
<Alanius>
I know of a generalized notion called n-special-soundness which guarantees witness-extractability from 2^n transcripts
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<Alanius>
The notion is treated properly in this paper: https://doi.org/10.1007/s10623-014-0009-7 (unfortunately I don't know of a version that's not behind a pay wall) "Extended security arguments for signature schemes"
<waxwing>
Alanius, perhaps i can generate 2^n fake versions of the paper
<Alanius>
other papers (including an earlier version of the one I just cited) generalize special soundness for 2n+1 pass protocols in such a way that extractability is guaranteed from 1+n transcripts but I am skeptical those notions can correctly capture the requirement. The intuition is that there are n points where the transcripts can start to diverge and you might need the entire tree to extract.
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<waxwing>
thanks for explaining a bit; i'm finding the maze of definitions in this field quite hard to get on top of ... in the book i previously mentioned, knowledge soundness is just defined as relating to 2 transcripts and that's it (19.4). guess it's just context dependent.
<Alanius>
the definitions are maybe not fuzzy per se but certainly not consistent across papers even from the same author
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<waxwing>
right, not fuzziness, just lots of them, more like.
<Alanius>
I must say I admire the bravery of boneh and shoup for deciding once and for all what the right definitions are
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<Alanius>
Having said that, I do find their choice of definitions odd. They don't mention special soundness but define knowledge soundness as that property that is elsewhere called special soundness.
<Alanius>
I always thought that knowledge soundness was a more general notion, identical to witness-extractability, and referring to the existence of polynomial-time witness extractor who upon black-box interaction with the prover (or forger) can extract the witness. This more general notion boils down to special soundness in the specific case of sigma protocols.
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* waxwing
struggles to remember what 'special' meant, but only remembers it in the context of special HVZK
<Alanius>
special soundness: given two accepting transcripts with the same first message but a different second one, it's possible to get the witness