So I did some IBLT research (as posted to bitcoin-dev ) and I lazily used SHA256 to create both the temporary 48-bit txids, and from them to create a 16-bit index offset. Each node has to produce these for every bitcoin transaction ID it knows about (ie. its entire mempool), which is normally less than 10,000 transactions, but we’d better plan for 1M given the coming blopockalypse.
For txid48, we hash an 8 byte seed with the 32-byte txid; I ignored the 8 byte seed for the moment, and measured various implementations of SHA256 hashing 32 bytes on on my Intel Core i3-5010U CPU @ 2.10GHz laptop (though note we’d be hashing 8 extra bytes for IBLT): (implementation in CCAN)
- Bitcoin’s SHA256: 527.7+/-0.9 nsec
- Optimizing the block ending on bitcoin’s SHA256: 500.4+/-0.66 nsec
- Intel’s asm rorx: 314.1+/-0.3 nsec
- Intel’s asm SSE4 337.5+/-0.5 nsec
- Intel’s asm RORx-x8ms 458.6+/-2.2 nsec
- Intel’s asm AVX 336.1+/-0.3 nsec
So, if you have 1M transactions in your mempool, expect it to take about 0.62 seconds of hashing to calculate the IBLT. This is too slow (though it’s fairly trivially parallelizable). However, we just need a universal hash, not a cryptographic one, so I benchmarked murmur3_x64_128:
- Murmur3-128: 23 nsec
That’s more like 0.046 seconds of hashing, which seems like enough of a win to add a new hash to the mix.
I like data. So when Patrick Strateman handed me a hacky patch for a new testnet with a 100MB block limit, I went to get some. I added 7 digital ocean nodes, another hacky patch to prevent sendrawtransaction from broadcasting, and a quick utility to create massive chains of transactions/
My home DSL connection is 11Mbit down, and 1Mbit up; that’s the fastest I can get here. I was CPU mining on my laptop for this test, while running tcpdump to capture network traffic for analysis. I didn’t measure the time taken to process the blocks on the receiving nodes, just the first propagation step.
1 Megabyte Block
Naively, it should take about 10 seconds to send a 1MB block up my DSL line from first packet to last. Here’s what actually happens, in seconds for each node:
The packet dump shows they’re all pretty much sprayed out simultaneously (bitcoind may do the writes in order, but the network stack interleaves them pretty well). That’s why it’s 67 seconds at best before the first node receives my block (a bit longer, since that’s when the packet left my laptop).
8 Megabyte Block
I increased my block size, and one node dropped out, so this isn’t quite the same, but the times to send to each node are about 8 times worse, as expected:
Using the rough formula of
- Get a faster DSL connection. Though even an uplink 10 times faster would mean 1.1% orphan rate with 1MB blocks, or 8% with 8MB blocks.
- Only connect to a single well-connected peer (-maxconnections=1), and hope they propagate your block.
- Refuse to mine any transactions, and just collect the block reward. Doesn’t help the bitcoin network at all though.
- Join a large pool. This is what happens in practice, but raises a significant centralization problem.
- We need bitcoind to be smarter about ratelimiting in these situations, and stream serially. Done correctly (which is hard), it could also help bufferbloat which makes running a full node at home so painful when it propagates blocks.
- Some kind of block compression, along the lines of Gavin’s IBLT idea. I’ve done some preliminary work on this, and it’s promising, but far from trivial.
What happens if bitcoin blocks fill? Miners choose transactions with the highest fees, so low fee transactions get left behind. Let’s look at what makes up blocks today, to try to figure out which transactions will get “crowded out” at various thresholds.
Some assumptions need to be made here: we can’t automatically tell the difference between me taking a $1000 output and paying you 1c, and me paying you $999.99 and sending myself the 1c change. So my first attempt was very conservative: only look at transactions with two or more outputs which were under the given thresholds (I used a nice round $200 / BTC price throughout, for simplicity).
(Note: I used bitcoin-iterate to pull out transaction data, and rebuild blocks without certain transactions; you can reproduce the csv files in the blocksize-stats directory if you want).
Paying More Than 1 Person Under $1 (< 500000 Satoshi)
Here’s the result (against the current blocksize):
Let’s zoom in to the interesting part, first, since there’s very little difference before 220,000 (February 2013). You can see that only about 18% of transactions are sending less than $1 and getting less than $1 in change:
Paying Anyone Under 1c, 10c, $1
The above graph doesn’t capture the case where I have $100 and send you 1c. If we eliminate any transaction which has any output less than various thresholds, we’ll catch that. The downside is that we capture the “sending myself tiny change” case, but I’d expect that to be rarer:
This eliminates far more transactions. We can see only 2.5% of the block size is taken by transactions with 1c outputs (the dark red line following the block “current blocks” line), but the green line shows about 20% of the block used for 10c transactions. And about 45% of the block is transactions moving $1 or less.
Interpretation: Hard Landing Unlikely, But Microtransactions Lose
If the block size doesn’t increase (or doesn’t increase in time): we’ll see transactions get slower, and fees become the significant factor in whether your transaction gets processed quickly. People will change behaviour: I’m not going to spend 20c to send you 50c!
Because block finding is highly variable and many miners are capping blocks at 750k, we see backlogs at times already; these bursts will happen with increasing frequency from now on. This will put pressure on Satoshdice and similar services, who will be highly incentivized to use StrawPay or roll their own channel mechanism for off-blockchain microtransactions.
I’d like to know what timescale this happens on, but the graph shows that we grow (and occasionally shrink) in bursts. A logarithmic graph prepared by Peter R of bitcointalk.org suggests that we hit 1M mid-2016 or so; expect fee pressure to bend that graph downwards soon.
The bad news is that even if fees hit (say) 25c and that prevents all the sub-$1 transactions, we only double our capacity, giving us perhaps another 18 months. (At that point miners are earning $1000 from transaction fees as well as $5000 (@ $200/BTC) from block reward, which is nice for them I guess.)
My Best Guess: Larger Blocks Desirable Within 2 Years, Needed by 3
Personally I think 5c is a reasonable transaction fee, but I’d prefer not to see it until we have decentralized off-chain alternatives. I’d be pretty uncomfortable with a 25c fee unless the Lightning Network was so ubiquitous that I only needed to pay it twice a year. Higher than that would have me reaching for my credit card to charge my Lightning Network account :)
Disclaimer: I Work For BlockStream, on Lightning Networks
Lightning Networks are a marathon, not a sprint. The development timeframes in my head are even vaguer than the guesses above. I hope it’s part of the eventual answer, but it’s not the bandaid we’re looking for. I wish it were different, but we’re going to need other things in the mean time.
I hope this provided useful facts, whatever your opinions.
I used bitcoin-iterate and gnumeric to render the current bitcoin blocksizes, and here are the results.
My First Graph: A Moment of Panic
This is block sizes up to yesterday; I’ve asked gnumeric to derive an exponential trend line from the data (in black; the red one is linear)
That trend line hits 1000000 at block 363845.5, which we’d expect in about 32 days time! This is what is freaking out so many denizens of the Bitcoin Subreddit. I also just saw a similar inaccurate [correction: misleading] graph reshared by Mike Hearn on G+ :(
But Wait A Minute
That trend line says we’re on 800k blocks today, and we’re clearly not. Let’s add a 6 hour moving average:
In fact, if we cluster into 36 blocks (ie. 6 hours worth), we can see how misleading the terrible exponential fit is:
Clearer Graphs: 1 week Moving Average
So, not time to panic just yet, though we’re clearly growing, and in unpredictable bursts.
I’ve been trying not to follow the Great Blocksize Debate raging on reddit. However, the lack of any concrete numbers has kind of irked me, so let me add one for now.
If we assume bandwidth is the main problem with running nodes, let’s look at average connection growth rates since 2008. Google lead me to NetMetrics (who seem to charge), and Akamai’s State Of The Internet (who don’t). So I used the latter, of course:
I tried to pick a range of countries, and here are the results:
|Country||% Growth Over 7 years||Per Annum|
Countries which had best bandwidth grew about 17% a year, so I think that’s the best model for future growth patterns (China is now where the US was 7 years ago, for example).
If bandwidth is the main centralization concern, you’ll want block growth below 15%. That implies we could jump the cap to 3MB next year, and 15% thereafter. Or if you’re less conservative, 3.5MB next year, and 17% there after.
Previously I discussed the use of IBLTs (on the pettycoin blog). Kalle and I got some interesting, but slightly different results; before I revisited them I wanted some real data to play with.
Finally, a few weeks ago I ran 4 nodes for a week, logging incoming transactions and the contents of the mempools when we saw a block. This gives us some data to chew on when tuning any fast block sync mechanism; here’s my first impressions looking a the data (which is available on github).
These graphs are my first look; in blue is the number of txs in the block, and in purple stacked on top is the number of txs which were left in the mempool after we took those away.
The good news is that all four sites are very similar; there’s small variance across these nodes (three are in Digital Ocean data centres and one is behind two NATs and a wireless network at my local coworking space).
The bad news is that there are spikes of very large mempools around block 352,800; a series of 731kb blocks which I’m guessing is some kind of soft limit for some mining software [EDIT: 750k is the default soft block limit; reported in 1024-byte quantities as blockchain.info does, this is 732k. Thanks sipa!]. Our ability to handle this case will depend very much on heuristics for guessing which transactions are likely candidates to be in the block at all (I’m hoping it’s as simple as first-seen transactions are most likely, but I haven’t tested yet).
The key revelation of the paper is that we can have a network of arbitrarily complicated transactions, such that they aren’t on the blockchain (and thus are fast, cheap and extremely scalable), but at every point are ready to be dropped onto the blockchain for resolution if there’s a problem. This is genuinely revolutionary.
It also vindicates Satoshi’s insistence on the generality of the Bitcoin scripting system. And though it’s long been suggested that bitcoin would become a clearing system on which genuine microtransactions would be layered, it was unclear that we were so close to having such a system in bitcoin already.
Note that the scheme requires some solution to malleability to allow chains of transactions to be built (this is a common theme, so likely to be mitigated in a future soft fork), but Gregory Maxwell points out that it also wants selective malleability, so transactions can be replaced without invalidating the HTLCs which are spending their outputs. Thus it proposes new signature flags, which will require active debate, analysis and another soft fork.
There is much more to discover in the paper itself: recommendations for lightning network routing, the node charging model, a risk summary, the specifics of the softfork changes, and more.
I’ll leave you with a brief list of requirements to make Lightning Networks a reality:
- A soft-fork is required, to protect against malleability and to allow new signature modes.
- A new peer-to-peer protocol needs to be designed for the lightning network, including routing.
- Blame and rating systems are needed for lightning network nodes. You don’t have to trust them, but it sucks if they go down as your money is probably stuck until the timeout.
- More refinements (eg. relative OP_CHECKLOCKTIMEVERIFY) to simplify and tighten timeout times.
- Wallets need to learn to use this, with UI handling of things like timeouts and fallbacks to the bitcoin network (sorry, your transaction failed, you’ll get your money back in N days).
- You need to be online every 40 days to check that an old HTLC hasn’t leaked, which will require some alternate solution for occasional users (shut down channel, have some third party, etc).
- A server implementation needs to be written.
That’s a lot of work! But it’s all simply engineering from here, just as bitcoin was once the paper was released. I look forward to seeing it happen (and I’m confident it will).
This is the third part of my series of posts explaining the bitcoin Lightning Networks 0.5 draft paper.
In Part I I described how a Poon-Dryja channel uses a single in-blockchain transaction to create off-blockchain transactions which can be safely updated by either party (as long as both agree), with fallback to publishing the latest versions to the blockchain if something goes wrong.
In Part II I described how Hashed Timelocked Contracts allow you to safely make one payment conditional upon another, so payments can be routed across untrusted parties using a series of transactions with decrementing timeout values.
Now we’ll join the two together: encapsulate Hashed Timelocked Contracts inside a channel, so they don’t have to be placed in the blockchain (unless something goes wrong).
Revision: Why Poon-Dryja Channels Work
Here’s half of a channel setup between me and you where I’m paying you 1c: (there’s always a mirror setup between you and me, so it’s symmetrical)
The system works because after we agree on a new transaction (eg. to pay you another 1c), you revoke this by handing me your private keys to unlock that 1c output. Now if you ever released Transaction 1, I can spend both the outputs. If we want to add a new output to Transaction 1, we need to be able to make it similarly stealable.
Adding a 1c HTLC Output To Transaction 1 In The Channel
I’m going to send you 1c now via a HTLC (which means you’ll only get it if the riddle is answered; if it times out, I get the 1c back). So we replace transaction 1 with transaction 2, which has three outputs: $9.98 to me, 1c to you, and 1c to the HTLC: (once we agree on the new transactions, we invalidate transaction 1 as detailed in Part I)
Note that you supply another separate signature (sig3) for this output, so you can reveal that private key later without giving away any other output.
We modify our previous HTLC design so you revealing the sig3 would allow me to steal this output. We do this the same way we did for that 1c going to you: send the output via a timelocked mutually signed transaction. But there are two transaction paths in an HTLC: the got-the-riddle path and the timeout path, so we need to insert those timelocked mutually signed transactions in both of them. First let’s append a 1 day delay to the timeout path:
Similarly, we need to append a timelocked transaction on the “got the riddle solution” path, which now needs my signature as well (otherwise you could create a replacement transaction and bypass the timelocked transaction):
Remember The Other Side?
Poon-Dryja channels are symmetrical, so the full version has a matching HTLC on the other side (except with my temporary keys, so you can catch me out if I use a revoked transaction). Here’s the full diagram, just to be complete:
Closing The HTLC
When an HTLC is completed, we just update transaction 2, and don’t include the HTLC output. The funds either get added to your output (R value revealed before timeout) or my output (timeout).
Note that we can have an arbitrary number of independent HTLCs in progress at once, and open and/or close as many in each transaction update as both parties agree to.
Keys, Keys Everywhere!
Each output for a revocable transaction needs to use a separate address, so we can hand the private key to the other party. We use two disposable keys for each HTLC, and every new HTLC will change one of the other outputs (either mine, if I’m paying you, or yours if you’re paying me), so that needs a new key too. That’s 3 keys, doubled for the symmetry, to give 6 keys per HTLC.
Adam Back pointed out that we can actually implement this scheme without the private key handover, and instead sign a transaction for the other side which gives them the money immediately. This would permit more key reuse, but means we’d have to store these transactions somewhere on the off chance we needed them.
Storing just the keys is smaller, but more importantly, Section 6.2 of the paper describes using BIP 32 key hierarchies so the disposable keys are derived: after a while, you only need to store one key for all the keys the other side has given you. This is vastly more efficient than storing a transaction for every HTLC, and indicates the scale (thousands of HTLCs per second) that the authors are thinking.
My next post will be a TL;DR summary, and some more references to the implementation details and possibilities provided by the paper.
 The new sighash types are fairly loose, and thus allow you to attach a transaction to a different parent if it uses the same output addresses. I think we could re-use the same keys in both paths if we ensure that the order of keys required is reversed for one, but we’d still need 4 keys, so it seems a bit too tricky.
In Part I, we demonstrated Poon-Dryja channels; a generalized channel structure which used revocable transactions to ensure that old transactions wouldn’t be reused.
A channel from me<->you would allow me to efficiently send you 1c, but that doesn’t scale since it takes at least one on-blockchain transaction to set up each channel. The solution to this is to route funds via intermediaries; in this example we’ll use the fictitious “MtBox”.
If I already have a channel with MtBox’s Payment Node, and so do you, that lets me reliably send 1c to MtBox without (usually) needing the blockchain, and it lets MtBox send you 1c with similar efficiency.
But it doesn’t give me a way to force them to send it to you; I have to trust them. We can do better.
Bonding Unrelated Transactions using Riddles
For simplicity, let’s ignore channels for the moment. Here’s the “trust MtBox” solution:
What if we could bond these transactions together somehow, so that when you spend the output from the MtBox transaction, that automatically allows MtBox to spend the output from my transaction?
Here’s one way. You send me a riddle question to which nobody else knows the answer: eg. “What’s brown and sticky?”. I then promise MtBox the 1c if they answer that riddle correctly, and tell MtBox that you know.
MtBox doesn’t know the answer, so it turns around and promises to pay you 1c if you answer “What’s brown and sticky?”. When you answer “A stick”, MtBox can pay you 1c knowing that it can collect the 1c off me.
The bitcoin blockchain is really good at riddles; in particular “what value hashes to this one?” is easy to express in the scripting language. So you pick a random secret value R, then hash it to get H, then send me H. My transaction’s 1c output requires MtBox’s signature, and a value which hashes to H (ie. R). MtBox adds the same requirement to its transaction output, so if you spend it, it can get its money back from me:
Handling Failure Using Timeouts
This example is too simplistic; when MtBox’s PHP script stops processing transactions, I won’t be able to get my 1c back if I’ve already published my transaction. So we use a familiar trick from Part I, a timeout transaction which after (say) 2 days, returns the funds to me. This output needs both my and MtBox’s signatures, and MtBox supplies me with the refund transaction containing the timeout:
MtBox similarly needs a timeout in case you disappear. And it needs to make sure it gets the answer to the riddle from you within that 2 days, otherwise I might use my timeout transaction and it can’t get its money back. To give plenty of margin, it uses a 1 day timeout:
It’s fairly clear to see that longer paths are possible, using the same “timelocked” transactions. The paper uses 1 day per hop, so if you were 5 hops away (say, me <-> MtBox <-> Carol <-> David <-> Evie <-> you) I would use a 5 day timeout to MtBox, MtBox a 4 day to Carol, etc. A routing protocol is required, but if some routing doesn’t work two nodes can always cancel by mutual agreement (by creating timeout transaction with no locktime).
The paper refers to each set of transactions as contracts, with the following terms:
- If you can produce to MtBox an unknown 20-byte random input data R from a known H, within two days, then MtBox will settle the contract by paying you 1c.
- If two days have elapsed, then the above clause is null and void and the clearing process is invalidated.
- Either party may (and should) pay out according to the terms of this contract in any method of the participants choosing and close out this contract early so long as both participants in this contract agree.
The hashing and timelock properties of the transactions are what allow them to be chained across a network, hence the term Hashed Timelock Contracts.
Next: Using Channels With Hashed Timelock Contracts.
The hashed riddle construct is cute, but as detailed above every transaction would need to be published on the blockchain, which makes it pretty pointless. So the next step is to embed them into a Poon-Dryja channel, so that (in the normal, cooperative case) they don’t need to reach the blockchain at all.
[ Note for new readers: the mechanisms described here are from the original LN draft. These days instead of throwaway keys we use hash preimages for revocation, and output scripts are used for HTLCs, as per https://github.com/ElementsProject/lightning/blob/master/doc/deployable-lightning.pdf ]
I finally took a second swing at understanding the Lightning Network paper. The promise of this work is exceptional: instant reliable transactions across the bitcoin network. But the implementation is complex and the draft paper reads like a grab bag of ideas; but it truly rewards close reading! It doesn’t involve novel crypto, nor fancy bitcoin scripting tricks.
There are several techniques which are used in the paper, so I plan to concentrate on one per post and wrap up at the end.
Revision: Payment Channels
A Payment Channel is a method for sending microtransactions to a single recipient, such as me paying you 1c a minute for internet access. I create an opening transaction which has a $10 output, which can only be redeemed by a transaction input signed by you and me (or me alone, after a timeout, just in case you vanish). That opening transaction goes into the blockchain, and we’re sure it’s bedded down.
Then I send you a signed transaction which spends that opening transaction output, and has two outputs: one for $9.99 to me, and one for 1c to you. If you want, you could sign that transaction too, and publish it immediately to get your 1c.
Then a minute later, I send you a signed transaction which spends that same opening transaction output, and has a $9.98 output for me, and a 2c output for you. Each minute, I send you another transaction, increasing the amount you get every time.
This works because:
- Each transaction I send spends the same output; so only one of them can ever be included in the blockchain.
- I can’t publish them, since they need your signature and I don’t have it.
- At the end, you will presumably publish the last one, which is best for you. You could publish an earlier one, and cheat yourself of money, but that’s not my problem.
Undoing A Promise: Revoking Transactions?
In the simple channel case above, we don’t have to revoke or cancel old transactions, as the only person who can spend them is the person who would be cheated. This makes the payment channel one way: if the amount I was paying you ever went down, you could simply broadcast one of the older, more profitable transactions.
So if we wanted to revoke an old transaction, how would we do it?
There’s no native way in bitcoin to have a transaction which expires. You can have a transaction which is valid after 5 days (using locktime), but you can’t have one which is valid until 5 days has passed.
So the only way to invalidate a transaction is to spend one of its inputs, and get that input-stealing transaction into the blockchain before the transaction you’re trying to invalidate. That’s no good if we’re trying to update a transaction continuously (a-la payment channels) without most of them reaching the blockchain.
The Transaction Revocation Trick
But there’s a trick, as described in the paper. We build our transaction as before (I sign, and you hold), which spends our opening transaction output, and has two outputs. The first is a 9.99c output for me. The second is a bit weird–it’s 1c, but needs two signatures to spend: mine and a temporary one of yours. Indeed, I create and sign such a transaction which spends this output, and send it to you, but that transaction has a locktime of 1 day:
Now, if you sign and publish that transaction, I can spend my $9.99 straight away, and you can publish that timelocked transaction tomorrow and get your 1c.
But what if we want to update the transaction? We create a new transaction, with 9.98c output to me and 2c output to a transaction signed by both me and another temporary address of yours. I create and sign a transaction which spends that 2c output, has a locktime of 1 day and has an output going to you, and send it to you.
We can revoke the old transaction: you simply give me the temporary private key you used for that transaction. Weird, I know (and that’s why you had to generate a temporary address for it). Now, if you were ever to sign and publish that old transaction, I can spend my $9.99 straight away, and create a transaction using your key and my key to spend your 1c. Your transaction (1a below) which could spend that 1c output is timelocked, so I’ll definitely get my 1c transaction into the blockchain first (and the paper uses a timelock of 40 days, not 1).
So the effect is that the old transaction is revoked: if you were to ever sign and release it, I could steal all the money. Neat trick, right?
A Minor Variation To Avoid Timeout Fallback
In the original payment channel, the opening transaction had a fallback clause: after some time, it is all spendable by me. If you stop responding, I have to wait for this to kick in to get my money back. Instead, the paper uses a pair of these “revocable” transaction structures. The second is a mirror image of the first, in effect.
So the first output is $9.99 which needs your signature and a temporary signature of mine. The second is 1c for
meyou. You sign the transaction, and I hold it. You create and sign a transaction which has that $9.99 as input, a 1 day locktime, and send it to me.
Since both your and my “revocable” transactions spend the same output, only one can reach the blockchain. They’re basically equivalent: if you send yours you must wait 1 day for your money. If I send mine, I have to wait 1 day for my money. But it means either of us can finalize the payment at any time, so the opening transaction doesn’t need a timeout clause.
Now we have a generalized transaction channel, which can spend the opening transaction in any way we both agree on, without trust or requiring on-blockchain updates (unless things break down).
The next post will discuss Hashed Timelock Contracts (HTLCs) which can be used to create chains of payments…
Notes For Pedants:
In the payment channel open I assume OP_CHECKLOCKTIMEVERIFY, which isn’t yet in bitcoin. It’s simpler.
I ignore transaction fees as an unnecessary distraction.
We need malleability fixes, so you can’t mutate a transaction and break the ones which follow. But I also need the ability to sign Transaction 1a without a complete Transaction 1 (since you can’t expose the signed version to me). The paper proposes new SIGHASH types to allow this.
[EDIT 2015-03-30 22:11:59+10:30: We also need to sign the other symmetric transactions before signing the opening transaction. If we released a completed opening transaction before having the other transactions, we might be stuck with no way to get our funds back (as we don’t have a “return all to me” timeout on the opening transaction)]