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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<dr-orlovsky>
Sorry for a possible stupid question, but am I right that if we have 256-bit amounts, we can do Pedersen commitments w/o any range proofs & risking to have an inflation?
<dr-orlovsky>
*possibly
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<fluffypony>
dr-orlovsky: how would you do commitments without range proofs and still prevent inflation?
<dr-orlovsky>
Range proofs are required to demonstrate that the given value does not "overflow", i.e. it is not greater that the maximum allowed total supply, which, in case of bitcoin, is 64-bit. So range proofs used to verify that the amount behind the commitment is less than 64-bit value. If our amount are 256 bits, one can not construct a Pedersen commitment that will "overflow", so I assume range proofs are not needed in this case
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<dr-orlovsky>
I.e. if I'd like to show that a+b (inputs) - (x+y) (outputs) = 0, and a, b, x, y are 64-bit values, and use Pedersen commitments (which result in 256 bit values), I will convert a,b,x,y each into 256-bit integer (before constructing a commitment) and attach a range proofs that each of them is not greater than 2^64. If the original a,b,x,y are 256-bit integer, no reason to prove that they are <2^256
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<tromp_>
then you can trivially transfer a 1 sat input into two outputs of 2 sat and r-1 sats, where r is secp256k1 order, and spend forever from latter output
<tromp_>
ignoring overflow doesn't mean you eliminated it
<tromp_>
256 bit amounts simply make it impossible to detect overflow with rangeproofs
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<waxwing>
who invented modular arithmetic anyway? that was a mistake.
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<bsm1175321>
gmaxwell, andytoshi: FWIW, the last time I worked with Shamir shares, I did also build a consensus system. Each device (share) had to be online, able to verify commitments to shares, change share epochs (redistribution), etc.
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<bsm1175321>
Obviously, each share being online and adding a consensus system is a pretty serious design consideration.
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<bsm1175321>
But, if shareholders are capable of verifying each other, it solves a lot of problems...but it does imply a consensus system.
<bsm1175321>
<aside> Thursday's BitDevsNYC had a presenter claiming a "novel MPC multi-signature scheme" showing no details, with andytoshi and sipa in the audience... I could barely hold it together knowing the hard work those guys and others are putting into it, and the challenges...
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<dr-orlovsky>
tromp: yep, thanks for a sample case. But wouldn't 256-bits allow smaller range proofs, i.e. we need just to prove that for instance that a single (highest) bit is zero
<sipa>
dr-orlovsky: unfortunately no
<sipa>
in order to prove something about the top bit, you need to make a bit decompositiom first
<sipa>
and it's the bit decomposition that is expensive, counterintuitively
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<dr-orlovsky>
oh, I see. Ok, how many 256-bit numbers are there that are > p (i.e. Secp256k1/G order)? I assume not a lot, about 2^-127 of all possible values. So we may just "know" P=G*x and K=H*x for all x>p and exclude them at the program level
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<tromp>
you can limit rangeproofs to 48 bit, as 2^48 satoshi is over 13.4 % of all 21M bitcoin, but that doesn't save much space over 64 bit rangeproofs.
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