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12:32 < adam3us> so waxwing and i were talking about whether one can actually have both perfect binding & binding :)
12:33 < adam3us> my argument was well, you could in theory prove the remaining coins have not inflated.
12:33 < adam3us> with binding but the spent coins in this block with blinding proofs
12:33 < adam3us> eg do a coinjoin like elgamal/borrowmean proof of coins spent in the block not overflowing
12:33 < waxwing> binding and hiding :) (let's go with hiding rather than blinding because binding and blinding are .. indistinguishable :) )
12:34 < adam3us> and per coin pedersen or bulletproof coins.
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12:34 < adam3us> ok. too much terminology. binding joint elgamal proof of joined coins in block
12:34 < adam3us> an hiding proofs with pedersen or bulletproofs per coin.
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12:35 < adam3us> then post QC you don't have to take evasive action, even with sudden onset, the failure mode is the QC attacker learns the sum of the coins spent in a block only.
12:35 < adam3us> and can not do hidden inflation. the elgamal proof would need to go in the block and be verified
12:36 < adam3us> (i thought this up sometime last year, just was something related waxwing an i were chatting about at the lisbon conf?)
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12:37 < waxwing> yeah i have no idea about the feasibility of these kind of ideas really, but the hope would be to create a scenario where a break results *only* in loss of hiding for the aggregate of coins in a block say, no chance of hidden inflation (e.g. elgamal for aggregate), no chance of revelation of individual coins in individual txs.
12:37 < waxwing> gonna try to read real_or_random 's switch commitments paper again because it seems highly relevant :)
12:38 < adam3us> it does imply coinjoin / key aggregation / mimble wimble like coordination.
12:38 < adam3us> which is a bit of an inconvenience and question mark how well that works given the way people transact at present.
12:39 < adam3us> also i'm not sure if you weren't careful that the multi-party part proofs might leak information. i guess ultimately you can do secure MPC but that's bandwidth expensive
12:39 < waxwing> yes i'd guess a relative non-starter if there is no way to remove full interactive processing (like a coinjoin case).
12:39 < adam3us> (leak info when attacked by a QC attacker)
12:40 < adam3us> bitcoin kind of needs that for more coinjoins tho. but this would have a worse failure mode if you do not achieve full block aggregation
12:41 < waxwing> yeah, true, there's a more positive way to look at it i guess
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12:48 < adam3us> anyway i'm not sure how practical but it's interesting to think about ways to have binding & hiding simultaneously in a restricted way, because conventional summary was they are fundamentally incompatible.
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12:50 < waxwing> yes i think logically incompatible in a single commitment, but wiggle room if you're prepared to commit to two different things as here :)
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14:34 < adam3us> waxwing: well, how about this: you know the sum of all other coins as every CT transaction must add.
14:36 < adam3us> could you not single handedly prove a elgamal commitment (binding) that the sum of all other coins, plus your outputs=the sum of allcoins with binding as that proof has a known answer that you don't care could be revealed by QC: the total number of mined coins
14:37 < adam3us> (minus your inputs). and then prove with perfect hiding that your individual outputs don't wrap. if you could pull that off: QC poses no risk.
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14:44 < waxwing> 'sum of all other coins' - you mean the fees right? everything else balances to zero. i mean, i'm assuming ins are CT and outs are CT. i guess it's more complicated in mixed case.
14:51 < adam3us> you can correct for non CT stuff by just subtracting it (immature outputs, fees)
14:51 < adam3us> before the proof part.
14:51 < adam3us> waxwing: no i mean all CT encrypted coins in circulation minus all cleartext ones
14:53 < adam3us> say you have two inputs B,C and spending them to D,E clear text fees F, now you make a hiding proof that B+C=D+E+F
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14:54 < adam3us> and A is sum of all other CT coins in the blockchain excluding B,C, A=sum(all)-B-C-T
14:54 < adam3us> where T is sum of clear text coins
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14:55 < adam3us> now make a binding proof that A+B+C=sum(all)-T
14:57 < adam3us> for sum(all)-T=xG+vH we know v because it's public, v=current coin issuance-t. (T=tG)
14:59 < waxwing> yes; so is your idea, that just one person/entity needs to do this, say, per block?
14:59 < adam3us> S=sum(all)-T, you don't know x from S=xG+vH as that info is spread across all users of CT
14:59 < adam3us> i am thinking you do it per transaction yourself without joining at block-level
15:00 < adam3us> so there are n+1 proofs for an n output transaction. n hiding proofs and one binding proof that the total coin suply is preserved
15:01 < waxwing> (i think you meant T=tH btw)
15:01 < adam3us> question is can you make that proof without knowing x
15:02 < adam3us> yes
15:02 < adam3us> (the x from S)
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16:26 < adam3us> hmm andytoshi (afk but on other comms) thinks the problem is if there are two coins excluded, then with QC one can be negative
16:27 < adam3us> and if there is one coin excluded, then obviously there is no ambiguity because the coin supply is known and the binding elgamal commitment reveals the sum of the values in it, so can be subtracted revealing the hiding amount by elimination
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--- Log closed Mon Jan 28 00:00:03 2019