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15:21 < nicolagreco> a bit of a random question, but is there a way to prove that a snapshot of a state comes from a log of operations (without involving consensus)?
15:21 < nicolagreco> (I guess this is the proof of consistency that things like ethereum do)
15:23 < Taek> Naively you could require the log and then process the whole  thing
15:23 < Taek> this is basically what Bitcoin validation does
15:23 < Taek> If the rules of your log are simple, you could use a zk-snark
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15:24 < Taek> then you don't need to process the whole log yourself. Someone does, but once you have the proof from the snark, it's a lot faster to verify
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15:28 < kanzure> you can also do probabilistically checkable proofs, which are essentially zk-snarks... so..
15:28 < kanzure> you can also do public auditing with secure multiparty computation, but this is essentially multisig stuff
15:30 < kanzure> er... i don't know why i said auditing, i meant the audit log + verification stuff.
15:30  * nsh muses
15:31 < nsh> at best you can only prove up to convergence if more than one way to end at a given state
15:32 < nsh> e.g. with a chess transcript there could be arbitrary numbers of moves elided
15:33 < nicolagreco> (sorry all, I have forgot to say "efficient way to prove", meaning that it has to perform better than re-running the entire log)
15:33 < Taek> snarks can do that, but snarks require a lot of engineering
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15:34 < nsh> cut and choose is probably as good as you get with moonmaths
15:34 < nsh> *without
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15:43 < proslogion> that should depend on the nature of the operations
15:56 < nicolagreco> say it adding removing keys from a key value store (so only get and put ops)
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17:13 < maaku> nicolagreco: you can get SPV-level assurance with commitments to the current state
17:13 < maaku> also mimblewimble is non-pairing way to get the same, for a limited set of problems
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17:15 < amiller> using "cut-and-choose" directly over all the state updates is only good for showing that a large fraction of the steps are valid, not that the whole thing is valid
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17:18 < amiller> thats a pretty cool list of all the approaches though! i really like this channel still :)
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17:31 < bsm1175321> nicolagreco: does "log of operations" mean a sequential log?  If yes, then one can use any old hash function, combined with its "midstate".  This doesn't tell you how the midstate was arrived at, however.
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17:35 < nicolagreco> amiller: (hi!) where can I read more about cut-and-choose?
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17:36 < bsm1175321> One can also use a single Merkle tree, where the hash state is a path to the most recently added element, which includes the Merkle root, and enough information to update the Merkle root by adding one element.  This allows one to retain Merkle proofs about any other elements that were added prior to the most recent update.
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17:39 < amiller> nicolagreco, here's a nice paper explaining how cut-and-choose works in the setting of multi-party computation
17:39 < amiller> https://eprint.iacr.org/2008/049.pdf
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17:42 < bsm1175321> nicolagreco: A related idea is "incremental hash functions"  (google for more) https://eprint.iacr.org/2015/1028.pdf but after fooling with this paper for a while, I came to the conclusion that all their constructions are log(n) in the number of stored elements, and a Merkle tree (as described above) is simpler and has the same asymptotic scaling.
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18:33 < maaku> incremental hash functions provide a different engineering tradeoff
18:33 < maaku> as the size of the structure increases you tradeoff accuracy for constant-size state
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19:37 < bsm1175321> maaku: I think there's a very deep misunderstanding driven by Bloom filters.  What anyone actually cares about is false-positives.  Once you fix that, you end up with logarithmic scaling.  The additional parameter introduced is just confusing.
19:38 < bsm1175321> constant size is only possible by increasing the false-positive rate...
19:39 <@gmaxwell> the functions maaku is talking about do not have false positives, or admit efficient membership tests.
19:40 <@gmaxwell> (no false positives except in the cryptographic sense, which I assume you mean too when you say log scaling)
19:40 <@gmaxwell> They support efficient add and removal of members.
19:40 <@gmaxwell> e.g. useful for keeping a hash of your whole database, while you insert/remove/update records.
19:41 <@gmaxwell> and they have constant size state (state size depends on security, not number of elements)
19:42 <@gmaxwell> the 'dumb' and very very insecure simple version of those datastructure is a hash over items where the hash is the result of H(index_0||itemdata_0) ^ H(index_1||itemdata_1) ...
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