| --- Day changed Mon Dec 22 2014 | ||
| maaku | so the MMR structure (which rusty is calling a naive merkle array) is better than any considered alternatives after about 1M headers | 00:00 |
|---|---|---|
| maaku | also easier to implement, so yay | 00:00 |
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| gmaxwell | yep. sounds reasonable to me. | 00:02 |
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| maaku | petertodd: are there any existing implementations of merkle mountain ranges? | 00:12 |
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| petertodd | maaku: yup: https://github.com/opentimestamps/opentimestamps-client/blob/28333aacb9bf4551210d7ea6b94879b703b1ae51/opentimestamps/journal.py#L147 | 00:13 |
| maaku | petertodd: C++? | 00:14 |
| petertodd | nah | 00:14 |
| maaku | ok thanks | 00:14 |
| maaku | (Python will be useful too; I'll need both) | 00:14 |
| gmaxwell | maaku: when you were commenting before about the cpu cost, I thought you were thinking of the same data structure but backwards. (which might be more efficient because long jumps in the unbalanced portions end up being the shorter hashes) | 00:14 |
| petertodd | there's a on-disk version somewhere in there too... | 00:14 |
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| petertodd | the on-disk version is quite nice, as there's a very clear way to store all of the leaf hashes and inner hashes using the standard breadth first tree -> array mapping (forget what that's called exactly) works fine with sparse files too if you want to leave some of the data out | 00:16 |
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| petertodd | though there's non-trivial complexity in proving a number of statements about MMR's... so I wouldn't jump too quickly to using them without thinking through that stuff. (non-issue in timestamping) | 00:18 |
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| maaku | gmaxwell: not sure I parse what you mean by "but backwards" | 00:22 |
| gmaxwell | putting the genesis block at the most unbalanced position, e.g. the version that cannot be efficiently appended to. | 00:23 |
| maaku | petertodd: hate to sound naive, but it seems pretty straightforward, and most importantly its properties are holding up under experiment. | 00:23 |
| maaku | which properties are you talking about? | 00:23 |
| petertodd | maaku: I mean things like proving what index # a proof corresponds too | 00:23 |
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| gmaxwell | maaku: just things like making sure you don't have any cases of inner node / leif emulation and things like that. | 00:25 |
| petertodd | RFC6962's merkle tree is a fair bit more clear in that regard; I'm working on implementing a prunable/summable version of it | 00:25 |
| gmaxwell | petertodd: you might want to be mindful of the compression function input sizes, note that SHA224 has a nice property that two if its output fit in a single compression function input. | 00:26 |
| petertodd | remember that MMR's are basically RFC6962 but with a small decrease in proof length at the cost of another layer of complexity | 00:26 |
| petertodd | gmaxwell: yeah, I write code in Python :) | 00:27 |
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| petertodd | gmaxwell: I've done crazy low-level optimizations before, but am deeply skeptical of their place in security code | 00:28 |
| gmaxwell | Well there is no free lunch. Thats a pointless halving in performance, ... if the performance isn't needed, better to use a more costly hash function. :) | 00:29 |
| petertodd | a pointless halving of what may easily be 1% of the performance of your system... | 00:30 |
| gmaxwell | (and if one doesn't like SHA224, SHA512/256 is well specified and also has room for metadata in one compression function run, and SHA512 appears to have improved security margin in any case) | 00:30 |
| maaku | petertodd: the number of hashes involved here is significant | 00:31 |
| gmaxwell | petertodd: perhaps, actually checking hashtrees in bitcoin already shows up quite visibly in the profiles. If there were several other proof hashtrees we were carrying around sha256 would be the number one thing in verifying blocks with already cached signatures. | 00:31 |
| petertodd | which gets to my bigger point: if you're architecture for bitcoin is sufficiently poorly scaling that you care about this stuff, you're going down a bad path | 00:32 |
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| maaku | actually after re-reading the MMR doc, I don't think that's what rusty implemented at all | 00:32 |
| gmaxwell | petertodd: I don't agree, all these decisions scoot around the amount of deceneralization you can get for a given scaling level. They also have significance when you want to talk about extracting proofs for embedded devices (and for using inside other ZKP). | 00:33 |
| petertodd | maaku: I'll take a wild guess he made RFC6962 instead... | 00:33 |
| maaku | looking at it now to compare | 00:33 |
| maaku | petertodd: the validation is incremental and cheap, but that doesn't mean we shouldn't care about performance to regenerate/revalidate the current state | 00:33 |
| petertodd | gmaxwell: if ZKP matters to you, specify that as an explicit requirement - ZKP can easily result in needs that *against* normal scaling requirements | 00:33 |
| maaku | or not be concerned about low power, embedded devices | 00:34 |
| petertodd | gmaxwell: +-50% differences don't interest me in the slightest | 00:34 |
| gmaxwell | Good for you. | 00:35 |
| petertodd | the #1 goal of this stuff needs to be to make it understandable and obvious. for instance replacing the easy to read SignatureHash() function with that horrendous class was a huge step backwards for people's understanding of how signature hashes actually work - I routinely have to tell people to look up the old copy when they ask me how sig hashes work | 00:35 |
| maaku | not everyone would agree. i'm going to leave it at that. | 00:36 |
| petertodd | gmaxwell: don't forget I've actually spent the majority of my career *way* in the other direction, creating stupidly resource constrained hardware - I've written thousands of lines of uC assembler, VHDL, etc. but the costs of that kind of development are horrendous | 00:37 |
| maaku | yes, rusty implemented rfc6963, in terms of tree structure at least | 00:39 |
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| maaku | an efficient serialization of standard bitcoin merkle trees with the right-hashes-elided trick might work too | 00:40 |
| maaku | (basically the same thing in terms of proof size) | 00:41 |
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| petertodd | right-hashes-elided trick? | 00:46 |
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| maaku | petertodd: what tiernolan has been posting about recently w.r.t merged mining | 00:47 |
| petertodd | maaku: where's this? | 00:48 |
| maaku | the observation that if you have a merkle tree of 2^n + 1 items, the right-most path could be fully elided by specifying the root left branch and the right most item | 00:48 |
| maaku | bitcoin-development, maybe 2 weeks ago? | 00:48 |
| maaku | he has a 2013 post on bitcointalk with an earlier version of it | 00:48 |
| petertodd | oh right, that one where they're collapsed | 00:48 |
| petertodd | pretty sure there's at least one earlier publication of that idea FWIW | 00:49 |
| maaku | sure, probably | 00:50 |
| maaku | petertodd: so what's the reasoning for 'bagging the peaks' in MMR vs an rfc6962 like construction? | 00:53 |
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| petertodd | maaku: makes inclusion proofs from most recent leafs to tip as cheap as possible (amortised) - but that's only relevant in timestamping | 00:54 |
| maaku | rfc6962 does that, no? | 00:55 |
| petertodd | not quite as cheaply, but it's so close I'm not sure the difference is worth the effort | 00:56 |
| petertodd | provind index # in rfc6962 is dead obvious for instance | 00:56 |
| petertodd | *proving | 00:57 |
| petertodd | btw another valuable thing to be able to do is prove T_{i+1} is a superset of T_i, or more generally, T_{i+j} is a superset of T_i | 00:59 |
| petertodd | actually, superset is the wrong term for this... sucession? ie, with tree T_i that commits to array A, I want to show that if I append item a_{i+2} I get tree T_{i+1} | 01:01 |
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| maaku | is there a succinct way of determining the depth of index i of an MMR with N nodes? | 01:03 |
| petertodd | of the top of my head I'm going to say probably not - wasn't a design requirement for what it was designed for | 01:04 |
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| rusty | maaku: so, I implemented "spv path back to N != 0", and tidied things up a a bit. | 02:45 |
| rusty | maaku: the supremacy of "optimal" is even clearer if you ask it to go back from block 5M to 5M-150. | 02:47 |
| rusty | array: proof hashes 142-732(403.4+/-2.6e+02) | 02:47 |
| rusty | optimal: proof hashes 33-101(63.4+/-29) | 02:47 |
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| rusty | maaku: sleep time for me. Latest variant pushed, w/ two new batching trees. | 03:12 |
| rusty | maaku: Back tomorrow, but I want to try optimizing the proof length directly rather than the path length. Maybe cache the "best" 128 blocks on the LHS of the tree, see if that wins... | 03:12 |
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| kanzure | adam3us: typos? anti-relay -> anti-replay | 12:09 |
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| amiller | adam3us1, everyone meant "anti-replay", not "anti-relay", but you seem to be responding as though you read it as "anti-relay" | 13:06 |
| amiller | or maybe you didn't and it's a benign typo in either case | 13:07 |
| sipa | a proof-of-non-relay seems quite impossible :) | 13:08 |
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| gmaxwell | sipa: it's called quantum encryption? :P | 13:18 |
| sipa | Hey. No novel assumptions. | 13:18 |
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| rusty | maaku: OK, so I | 15:43 |
| rusty | 've implemented optimization-by-prooflen (rather than optimization by pathlen, then convert to proof). It does make a difference. | 15:44 |
| rusty | eg: (1M blocks, 100 runs): | 15:44 |
| rusty | optimal: proof hashes 315-2143(1031.7+/-5.6e+02) <- old result | 15:45 |
| rusty | prooflen-optimal: proof hashes 265-1719(818.2+/-4.4e+02) <- new result | 15:45 |
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| rusty | 20% smaller CSPV proofs, basically | 15:45 |
| sipa | how is the size of blocks relevant? | 15:45 |
| rusty | sipa: the size of the merkle proof, not the block... | 15:46 |
| sipa | ah, 1 million blocks, not 1 MB blocks; sure | 15:46 |
| sipa | rusty: i've previously implemented that too | 15:46 |
| sipa | i don't think i have that code anymore | 15:46 |
| rusty | sipa: cool! I'm playing with different topologies for the prevblock merkle. | 15:46 |
| sipa | trying to remember what structure i used | 15:47 |
| rusty | sipa: see https://github.com/rustyrussell/rusty-junkcode (particularly test-trees.c) | 15:47 |
| rusty | sipa: topology makes a big difference. But it was only last night I realized that optimizing SPV # blocks then converting to proof was kinda dumb. | 15:48 |
| rusty | sipa: so implemented that now instead of doing actual work :) | 15:48 |
| sipa | now, one interesting thing is that even a 'skiplist' with only a single reference back (in addition to the direct parent), with exponentially distributed distance back is enough to get within (iirc) a constant factor of optimal | 15:49 |
| rusty | sipa: Hmm, interesting! | 15:50 |
| rusty | sipa: how did you select distance back for block N? | 15:50 |
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| rusty | (I'm trying to parse "exponentially distributed distance back" with "single reference back"... and failing?) | 15:51 |
| sipa | so every block has two references back, its direct parent, and another | 15:52 |
| rusty | Yep, how do you select "another"? | 15:52 |
| sipa | that other is 50% of the time 2 back, 25% of the time 4 back, 12.5% of the 8 back, ... | 15:52 |
| rusty | sipa: ah, nice. Let me simulate that... | 15:53 |
| sipa | iirc it's something like 4x worse | 15:53 |
| * rusty continues to ignore that module bug email... | 15:53 | |
| sipa | https://github.com/bitcoin/bitcoin/blob/master/src/chain.cpp#L64-L73 <- this is a slightly more complex formula, used in bitcoin itself now | 15:53 |
| sipa | after trying a dozen functions or so, this one was the best | 15:53 |
| rusty | sipa: weird, I didn't know bitcoin had this already! | 15:55 |
| sipa | this is just an implementation detail, to speed up iterating chains | 15:55 |
| gmaxwell | rusty: totally different application, thats an in memory data structure used for node-internal blockchain management. | 15:55 |
| rusty | sipa/gmaxwell: thanks. | 15:56 |
| sipa | in cases where only the size of a proof and not the entire storage matters, this is definitely suboptimal | 15:56 |
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| sipa | but it's interesting that it's only a constant factor (but a significant one) worse | 15:56 |
| sipa | (iirc, again, this is just how i remember the numbers i saw - no formal proof or anything) | 15:56 |
| rusty | sipa: well, I'll code it up anyway, since I'm here. Plus, procrastination... | 15:57 |
| gmaxwell | the difference in the comitted structure is that you don't have free choice of where you go back unless you commit to all. So e.g. just a constant single backref would usually just not be accessible. | 15:57 |
| gmaxwell | When we were expirementing before I just used octave backrefs with the optimization that if an already included shorter backref was a better path to genesis, in the DP solution, I omitted it. But maaku pointed out that results in long paths to get to anything except genesis. | 15:59 |
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| phantomcircuit | sipa, any idea if that's just because of the current blockchain structure and not necessarily a constant optimum? | 16:03 |
| rusty | gmaxwell: my testing (using traversal from block 8M to block 8M-150, ie. ~back 1 day) indicates doing a breadth-first tree for that case is a real win. eg. average 48 hashes of proof vs. 252. But breadth-first trees aren't incrementally updatable. | 16:03 |
| rusty | sipa: um, crazy idea. What if you select from the "best" blocks (ie. largest backskip) rather than just using exponential choice? | 16:06 |
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| * rusty needs more coffee... | 16:08 | |
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| rusty | sipa: OK, so single backlink can fare really badly. eg. my "seed=0" case for 1M hashes has some lucky jumps, so you get ~400 hashes for proof to genesis if you encode the whole tree. 583401 hashes for the single random-exponential backlink. | 16:37 |
| rusty | sipa: of course, that could be terribly unlucky. Running with 100 different seeds now. | 16:38 |
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| sipa | rusty: is that the optimal path? | 16:43 |
| sipa | rusty: also, see the code in bitcoin i linked you to | 16:43 |
| rusty | sipa: yep, taking the backlink if dist < overkill. | 16:44 |
| sipa | rusty: that doesn't guarantee optimality | 16:44 |
| rusty | sipa: s/taking/considering/. | 16:44 |
| sipa | you need dynamic programming to find the optimal solution | 16:44 |
| sipa | and for random exponential links, that probably matters a lot | 16:44 |
| rusty | sipa: yeah, already doing that. Of course, may have a bug :) | 16:45 |
| sipa | ideally, finding the optimal path would mean just eager matching | 16:45 |
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| rusty | sipa: distribution looks correct. AFAICT the solution just sucks. It makes it exponentially harder to get lucky. Perhaps reversing it and making it 50% jump of N, 25% jump of N/2.... | 16:52 |
| sipa | rusty: see the code i linked you to! | 16:54 |
| rusty | sipa: sure, I'll try that next. | 16:55 |
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| sipa | it's made so that further backlinks are likely to very quickly hit other far backlinks | 16:55 |
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| sipa | maybe just random backlinks without structure isn't enough | 16:55 |
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| rusty | sipa: running more tests. Reversing (ie. 50% jump-to-genesis) did slightly better on average, much better on best case. Bitcoin variant is remarkably consistently bad, 500796-515705(509877+/-3e+03). | 17:05 |
| rusty | sipa: in summary, I'm not convinced that there's a constant factor in this case. | 17:06 |
| sipa | eh? | 17:06 |
| sipa | i have trouble reading your numbers :) | 17:06 |
| rusty | sipa: sorry, that's min - max ( mean +/0 stddev) | 17:06 |
| sipa | what unit? | 17:06 |
| rusty | sipa: number of hashes to get from block 999,999 to 0. Assuming 1 hash requires for each backlink (ie. assuming prev and another are merkled). | 17:07 |
| sipa | it should be around 150 or so | 17:07 |
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| rusty | sipa: Maybe. See https://github.com/rustyrussell/rusty-junkcode | 17:10 |
| rusty | sipa: it's pretty easy to reason about why the exponential backlink didn't work. Your chances of jumping back N are 1/N^2. | 17:11 |
| sipa | yeah, i agree | 17:12 |
| sipa | rusty: GetSkipHeight gives the height to jump to, not how far to jump back | 17:12 |
| rusty | sipa: hence backjump = i - GetSkipHeight(i) | 17:12 |
| sipa | ah, yes! | 17:12 |
| sipa | sorry | 17:13 |
| rusty | sipa: I'm sure there are dumb errors, but hopefully they're better hidden than that :) | 17:13 |
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| sipa | rusty: why the rng in the decision loop? | 17:17 |
| rusty | sipa: you referring to -1ULL / isaac64_next_uint64(&isaac) ? | 17:18 |
| sipa | yes | 17:18 |
| rusty | sipa: I pick a random u64 as my "block hash", and 0xFFFF.... as my target. | 17:18 |
| sipa | ah | 17:19 |
| rusty | sipa: hence -1ULL / random() => amount I can skip backwards. | 17:19 |
| sipa | right | 17:19 |
| sipa | yeah, if you can't always jump back, i'm sure this solution is worthless | 17:19 |
| sipa | sorry, i shouldn't have brought it up here | 17:19 |
| sipa | it's interesting, but it's a very different problem | 17:19 |
| rusty | sipa: hey, it was fun! | 17:19 |
| sipa | iirc i experimented with just all powers of 2 backwards | 17:20 |
| sipa | which needs a way smaller tree, so fewer hashes per link to use in the proof | 17:20 |
| sipa | and eager selection when jumping back (as far as you can) | 17:21 |
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| rusty | sipa: I did that for pettycoin, too. Eager selection was a large factor worse than a real shortest calc though. | 17:24 |
| sipa | possibly, yes | 17:24 |
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| maaku | so I added an MMR estimator to rusty's code, and it does worse than rfc6962 | 22:54 |
| maaku | i'm a bit surprised about that | 22:54 |
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