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<waxwing>
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<nsh>
The straightforward solution to this task requires the delivery of the blockchain, the verification of the proof of work it contains, and subsequently the examination of the last k blocks. It follows that the communication required to complete this task is linear in the length of the chain.
<nsh>
At First thought the above seems the best one can hope: a sublinear in the length of the chain solution to the problem will be susceptible to an attacker that, using precomputation, can fool the verifier.
<nsh>
Contrary to this intuition, we show that with a suitable modification to the current Bitcoin blockchain protocol (that incurs a single hash expansion in each block and gives rise to the notion of an interconnected blockchain) we can produce proofs of proof of work with sublinear complexity in the length of the chain hence enabling SPV to be performed much more efficiently
<nsh>
--
<bsm1175321>
That's the first I've heard of this. Not related to braids AFAICT but I've had the same idea before -- one can easily build log(height) proofs in such a manner.
* nsh
nods
<bsm1175321>
e.g. if you break the block height into its binary representation, one can have miners commit to the PoW header in not only the previous block, but 2,4,8,16,32... blocks ago as well. Seems best for SPV, as they state in the abstract.
<nsh>
right
<bsm1175321>
SPV in braids is something I need to give more thought to. But I've figured out the analog quantity to "block height" such that any algorithm applied on block height can be applied on a braid too.
<nsh>
oh?
<bsm1175321>
Yes I've posted some pictures here before of "cohorts", and the concept was in my talk too.
<bsm1175321>
one cohort is the analog of a bitcoin block.
<nsh>
the main niggle i have about your proposal so far, bsm1175321, is that i suspect it opens up a whole new class of network segmentation attacks that might be difficult to reason about in incentive terms
<nsh>
that's not pathological necessarily, but it worries me
<bsm1175321>
That's a reasonable worry, but I'd argue it's true for Bitcoin as well.
<nsh>
particularly in the network's vs. individual miner's view of cohort work
<bsm1175321>
Speaking of which, do you know of any good analysis of network segmentation attacks against bitcoin?
<nsh>
which depends on bead visibility which can be games much more easily than block visibility atm
<nsh>
i would ask gmaxwell probably
<nsh>
or kanzure
<nsh>
*gamed
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<nsh>
*partition attacks is probably the more received term
<bsm1175321>
I'd put a horizon on it -- after 100 blocks and the rewards have been allocated, new beads referencing something more than 100 cohorts ago would be disallowed. This effectively puts a time limit on a network split.
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<nsh>
hmm
<bsm1175321>
Well by allocating rewards proportional to difficulty, miners don't have to care about seeing the cohort network, because it doesn't affect their income.
<bsm1175321>
What do you mean "network vs. individual miner"?
<Eliel_>
nsh: could you expand a little on the segmentation attack thing. I somehow find myself unable to understand how it'd enable something that's not already possible.
<bsm1175321>
Eliel_: I can think of one where a miner creates a bead with a very old parent. This has the effect of merging cohorts across a long time period into a single cohort. I'm not sure what good that does the miner though, because his payout would be effectively zero.
<bsm1175321>
BTW this is one way to disallow such behavior. Below some payout threshold, with the proper incentive structure, discard beads which have zero payout.
* nsh
finishes watching talk before commenting further
<nsh>
maybe i'm just stupid
<bsm1175321>
nsh: I'm sure much of this is unclear. My own understand of cohorts has improved since I gave that talk.
<nsh>
(generally, however, it's not just particular miners with perverse strategies that we have to worry about. it's network adversaries who can manipulate large numbers of miners simultaneously)
* nsh
nods
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