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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<nsh>
ty waxwing
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<nsh>
would you put stake a $<large number> on one-more DLP being sufficiently close in hardness to the primitive DLP over a given elliptic curve.
<nsh>
there are separation results and proofs of algebraic non-equivalence (but no practicable attacks that i'm aware of)
<nsh>
(despite an equivalence by extraction of schnoor signatures to DLP under the ROM)
<nsh>
for forgery at least
<andytoshi>
yes, i would bet on that
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<sipa>
also, the proof in our paper is sort of modular; if you (trivially) extend the protocol to have 3rd precommit phase like BN does, an analogous proof exists that only relies on DLP
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<sipa>
perhaps that should have been in a footnote somewhere
<nsh>
oh cool
<nsh>
i suppose there's very little chance that the loss factor would be worse than e.g the birthday attack on P2SH
<andytoshi>
nsh: link to separation between DL and OMDL? i'm curious about this, i see separations between one-more DH but not DL .. but maybe my google-fu is not strong enough
<nsh>
maybe misread diagonally and it doesn't apply
<andytoshi>
thanks
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<andytoshi>
heh, so, this gives a separation in the generic group model (actually more general than this, but the GGM is a special case) ... but in the generic group model, DL is hard, so.. :)
<andytoshi>
what the paper shows is that you can't break DL in the generic group model .. and if you're given an oracle that lets you break n discrete logs, then you can't break n+1
<andytoshi>
but the conclusion here is that if you break OMDL, you're either using a non-PPT algorithm (like a quantum computer) or you're exploiting specific properties of the group. my claim is that in either case, you can break DL, so in practice they're equivalent
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