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<zmanian>
What is difference between Scalar, Field and Group arithmetic on Elliptic Curve group? Trying to figure out if my impressions are correct...
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<andytoshi>
zmanian: the field is the field over which the curve is defined (by the equation y^2 = x^3 + 7). it is integers mod 2^255 - 2^23 - 877 i think
<andytoshi>
zmanian: the group is the actual elliptic curve group whose elements are points on the curve
<andytoshi>
zmanian: the group has prime order so it is cyclic, meaning isomorphic to the integers mod N for some prime N. scalar arithmetic is the integers mod N
<andytoshi>
oh, fyi i'm talking specifically about secp256k1 here, things are actually a bit more general
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<gmaxwell>
I wish abstract algebra were[D[D[D taught in highschools in the US. According to anime it's taught in grade school in japan. :P
* kanzure
updates his understanding of gmaxwell to have sourced >1% of facts from anime
<kanzure>
blame is really good manga, btw
<gmaxwell>
hahah. I'm not really a big anime fan. more than a decade ago I had a girlfriend that was... and it's hard to work in technology without knowing more than a few. :)
<gmaxwell>
(What I was actually thinking about there was the number theory in Puella Magi; there is some scene with fermats little theorm or CRT or something)
<copumpkin>
gmaxwell: I got it as an option in my IB course
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<zmanian>
andytoshi: Thanks. Clears things up. I was confused if the field or the group was isomorphic to the integers mod n
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<bramc>
So I'm working on a merkle set data structure
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<kanzure>
cool. details?
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<bramc>
kanzure, there's a mix of good features and things I'm not going to be implementing in the first version
<kanzure>
what are the things you will be skipping?
<bramc>
The biggest features are that it clumps things together in memory to avoid cache misses and supports batch updates to reduce the amount of wasteful hash recalculation it's doing, both of which have the potential to be massive improvements under some circumstances
<bsm117532>
Could you provide a link for "Merkle Set"? I can imagine by analogy but have never heard of this...
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<kanzure>
bramc: maybe there's some tricks here where you can setup the delta update algorithm to be biased towards being really good at the type of update frequency that natural data (e.g. extracted from its designer looking at blockchain data) that the data structure would be used for.
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<bramc>
The things which will be missing in the first version: It will be in Python instead of C, it won't be benchmarked and optimized, it will be implemented to preallocate all memory it might use up front instead of doing dynamic malloc, it won't do background maintenance, it won't support giving up space if the set gets smaller, it's a set and not a dictionary
<bramc>
kanzure, My goal is to make something which is format compatible with what maaku's already written but much more performant and with fewer external dependencies
<bramc>
bsm117532 Not a standard data structure. It's a set which keeps the merkle root of its contents up to date, specifically for use in maintaining utxo roots
<kanzure>
hm what is background maintenance
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<bramc>
There's some rebalancing of the tree which is moderately expensive which can be done in the background so that the updates are always fast
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<bramc>
On the other hand, waiting until the last moment to do rebalancing is more space efficient.
<bramc>
Likewise, I'm making it defended against malicious content trying to make it inefficient, and some expense to average lookup time on non-malicious content, but also being more space efficient again.
<bramc>
Obviously it won't be production ready with the list of things left to do, but the idea is to get the ideas down and easy for other people to pick up and maintain.
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<nwilcox>
Was bramc talking about a UTXO state commitment tree, perchance?
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<bramc>
nwilcox, Yes I was
<nwilcox>
Cool. Do you have a public design or code?
<bramc>
nwilcox, No I'm still in the design phase, I think I mostly have the basics sorted out and hope to start coding shortly.
<bramc>
I'm not giving the blow by blow on my design iteration because it's a lot of unnecessary detail which leads nowhere except for the parts I'll eventually keep
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<bramc>
The intention is for other people to have actual code to play with as soon as possible, which of course means that that code won't be even vaguely production ready
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<phantomcircuit>
bramc, have you seen the utxo commitments which commit to the set but not the individual members of the set?
<phantomcircuit>
ie XOR all the things together and commit to that
<phantomcircuit>
it's nice in that it doesn't have any scaling issues
<bramc>
phantomcircuit, That's horribly busted, you can easily construct collisions
<phantomcircuit>
it's not in that it's useless for spv clients
<phantomcircuit>
bramc, yeah i described it incorrectly
<phantomcircuit>
find and ask sipa :)
<bramc>
I will, but the whole point of this is to fix spv. Well, that and allow for nodes to not have a complete history
<instagibbs>
hopefully soon questions about utxo commitment strategies are replied to with "read the wiki" rather than "find Bob and ask" ;)
<ryan-c>
anyone know of a publicly available tool that will find the shortest path of transactions between two addresses?
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<bramc>
instagibbs, Things are still under construction. Much better documentation will of course be necessary for a real extension to get added.
<phantomcircuit>
bramc, i actually view the fixing of spv clients as less important then fixing the full node download issues
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<bsm117532>
Could UTXO commitments assist in sharding the blockchain?
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<CodeShark>
has anyone tinkered with sharding using STXO/MMR commitments?