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03:35 < Dave_> hi
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08:37 < kanzure> https://bitcoin.stackexchange.com/questions/77751/can-spv-clients-offer-proof-of-absence-of-a-transaction/77764#77764
08:41  * nsh not quite unconvinced
08:41 < nsh> *convinced
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08:46 < nsh> "If you are not worried about revealing information, then you can commit to the set of data items in one Merkle tree, and to the frontier of that set in another Merkle tree. A frontier is the set of ancestors to all values that are not in the tree (note that this is about the same size as the size of the set itself). Then, in order to prove that a value is inside the set you work with the first tree, and in order to prove that it is not you work with
08:46 < nsh> the second tree. "
08:46 < nsh> - https://crypto.stackexchange.com/questions/31914/proof-of-non-membership-on-a-merkle-tree
08:47 < kanzure> for ordered trees wouldn't you just reveal both the neighbors that should be surrounding the expected member, and show that therefore the member is not there?
08:48 < nsh> only if the ordering is arithmetic i guess
08:48 < nsh> current topological ordering of txs wouldn't have that property
08:48 < nsh> or am i being stupid?
08:50 < nsh>  'ordered' vs. 'sorted' i guess
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09:34 < maaku> reveal the hashes of a block, and the midstate of the coinbase to prove it's the lowest level?
09:34 < maaku> That's not exactly SPV, but it's 100k of data instead of 2-4MB
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09:36 < maaku> nsh: I think the point is a commitment to an ordered tree is basically the same as the frontier except more useful, so what's the point of the frontier tree?
09:38  * nsh nods
09:39 < RubenSomsen> isn't client side filtering (neutrino) a way to prove non-inclusion?
09:39 < nsh> discussed here: https://gist.github.com/chris-belcher/eb9abe417d74a7b5f20aabe6bff10de0 "Sorted merkle tree as solution to issue #693 [of JoinMarket]"
09:40 < sipa> RubenSomsen: possibly, if it's committed
09:41 < RubenSomsen> I'd answer on stackexchange but my reputation is below 50 haha
09:43 < sipa> fix it.
09:43 < nsh> cf. https://crypto.stackexchange.com/questions/48594/homomorphic-set-hash-with-membership-proof  (perhaps bulletproofs answer/comment would fit here too)
09:43 < RubenSomsen> sipa: will do :)
09:44 < nsh> "Proofs of presence/absence require you to be able to remove the additive inverse from the mapping."
09:46 < sipa> nsh: sounds like cryprographic accumulators are the solution to that question
09:46  * nsh nods
09:48 < nsh> the statement by McElrath that trusted setup is required is no longer holds though
09:50 < nsh> this looks interesting too: https://kodu.ut.ee/~lipmaa/papers/lip12b/cl-accum.pdf  (secure accumulators w/o trusted setup from euclidean rings)
09:52 < nsh> (may not work for elliptic curves if no equivalent of extended euclidean algorithm)
09:53 < nsh> +efficient
09:57 < nsh> ((but there is: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.140.7944&rep=rep1&type=pdf ))
10:10 < nsh> "Therefore, the Extended Euclidean Algorithm can be used to decide whether an element of R/a is a unit and to compute its inverse if it is a unit." # is probably how you avoid needing trapdoor/TS
10:10 < nsh> - 2.5.1 Quotients of Euclidean Rings in https://user.math.uzh.ch/fontein/diplom-fontein.pdf
10:10 < nsh> (perhaps you can create a bulletproofs-like scheme using this property?)
10:11 < nsh> (or MW)
10:18 < nsh> (perhaps like this "More specifically,our system allows demonstrating the knowledge of a hash chain from the con-sidered secret leaf to the root in a zero-knowledge manner." - https://hal.inria.fr/hal-01314642/document )
10:19 < nsh> [W]e achieve: The first lattice-based ring signature with logarithmic signature size in the cardinality of the ring. So far, all suggested proposals have linear size in the number of ring members. – A  lattice-based  group  signature  with  much  shorter  public  key,  signature length, and weaker hardness assumptions than all earlier realizations."
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--- Log closed Wed Aug 29 00:00:53 2018