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11:25 < vfP56jSe> The only place in Schnorr where we need a RNG is for generating a's right? And those aren't that bad because we can use hash of inputs as seed?
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12:07 < gmaxwell> vfP56jSe: yes, the hash of the entire input could be used as a randomizer for batch validation.
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12:44  * nsh wonders what part of the algorithm uses randomisation
12:45 < gmaxwell> 11:54:42 < vfP56jSe> So this way, we get the benefit of 1. Being able to sum the relevant scalars like "(-y*r1-w*r2)*C" 2. Use a
12:45 < gmaxwell>                      "multi-exponentiation" algorithm to calculate the sum of EC multiplications like "r1*A + (-x*r1)*B + (-y*r1-w*r2)*C + r2*D +
12:45 < gmaxwell>                      (-v*r2)*E"?
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12:46 < sipa> nsh: take the equations for verifying a single signature each, multiply each by a random scalar, add them together into a single equation
12:46 < nsh> ah
12:46 < gmaxwell> The signal signature equations look like   R_n = s_n G + e_n P_n
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12:47 < gmaxwell> If you don't randomize but just combine them (stick a Sigma of n on each term), then it's possible to cheat by adding additional false equations that cancel out the other false equations.
12:47 < gmaxwell> Randomization makes that infeasable.
12:47 < nsh> so the randomness frustrates 'padding' out a bad signature for want of a better term
12:47 < nsh> or wrapping maybe
12:48 < nsh> i suppose cancelling is fine
12:49 < gmaxwell> right, like you have some   R != sG + eP   (its false)  now you add another false signature that is just the negation of the first false signature... canceling it out. but combined they'd verify.
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12:49 < gmaxwell> If you seperately randomize each equation, they can't cancel anymore unless you successfully predicted the randomization.
12:49 < nsh> gotcha, ty
12:50 < gmaxwell> And if the randomization is either secret or derrived from a hash of all the inputs (a fiat shamir transform), you can't predict it.
12:50  * nsh nods
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13:22  * vfP56jSe nods, but is a bit late
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--- Log closed Fri Feb 08 00:00:43 2019