Topic: [ANSWERED] Why is bitcoin proof of work parallelizable ? - page 2. (Read 4661 times)

To begin, the discussion and the reference to the proof-of-stakes thread, is very helpful to me. Thank you.


Agreed. I really guess we somehow got stuck in a misunderstanding, I might have caused.


Agreed. A sequential deterministic PoW does not do the job for the obvious reasons you are giving. We need both (randomization of block winners AND non-parallelizability) and I am curious how this can be done.

The issue I take is: A very high number of CPUs has a different effect for parallelizable PoWs than for non-parallelizable PoWs. (The "Bill Gates" attack).


We are reaching common ground. In my model, multiple computers do give more power to the network - but not due to the effect that a single PoW is solved faster in time. When we add computers to the network, the PoWs I am thinking of, must be adapted, as in normal Bitcoin. However, the effect is that the probabilities for finding a solution are rearranged not the overall time for solving a block.


I am thinking not of a currency-like application but on a replicated directory service kind of application. Since this is written from scratch, there is the chance to try different PoW systems without having to break the old algorithm (or mind sets of developers).

Thanx again for challenging my thoughts in the discussion. This is very fruitful.

Thanx, Gandalf, for your help. I still do not get it and plead guilty of having caused the misunderstanding.

But I still do not get it and would like to work it out.


Fine. Still with you. Assuming this.


No. Why should the number of blocks go down? I do not claim that they go down.

Maybe the misunderstanding is earlier. A non-parallelizable PoW means that the participants CANNOT collude on the PoW. Of course, they still can share their revenues, that is a completely different issue.

In current parallelizable PoW, all 4000 participants work by looking for a nonce with a specific property. For this goal, they test large numbers of candidate nonces. Every test has a certain success probability (determined by difficulty). Individual tests are, of course, independent of each other. Hence the PoW can be brute forced. This can be done in parallel. A block is found sooner or later, according to the Poisson process in place. So, the time to find a block follows and exponential distribution.

Now let us consider a strictly sequential, deterministic PoW (not as a suggestion for Bitcoin, but to see the difference). Here, a specific computational result must be obtained. To obtain this result, a large number of arithmetic operations must be performed in strict sequence. The number is adapted to the average speed of a single core CPU. The participant who reaches the result first wins the block. This cannot be done in parallel. However, it is always the participant with the fastest single core CPU, who wins the block. This is boring and not what we need. This is time lock cryptography and not exactly useful for Bitcoin.

Now let us consider a non-parallelizable PoW. Here, every participant must make a large number of sequential steps to reach a goal. However, contrary to the sequential, deterministic PoW, there are still random aspects, branching points in the computation. So it still depends on random choices of the participants, who will win the block (which is what we need). Of course, participants can still pool. Two participants will still get twice as many blocks in the long run. The block rate does not go down magically.

However now comes the crucial difference. Assume I have 2^256 participants, numbered 0, 1, 2, 3, ... How long will they need for the first block? In the current (parallelizable) PoW used in Bitcoin they need a few microseconds. Every participant uses his own number as nonce in the first round...and most likely one of them will produce a hash which is smaller than the current target value. In the non-parallelizable PoW I am thinking of, they will still need more or less 10 minutes as they should, since this corresponds more or less to the number of operations they have to do before they get a realistic chance for reaching the goal. However, since there is some variability, also a slower CPU with better random choices gets a chance.

This isn't about parallelizable vs. non-parallelizable computations. Performance in serial computations doesn't scale linearly with more computing cores, but this is irrelevant. This is about the process of block finding, which is why I asked if your system diverges fundamentally in the notion that blocks are something found once in a while by people on the network. If not then it's really "if Billy and Sally each have an apple, then that's two apples" math - if in a given scenario (not in distinct scenarios) two people find 1 block each, then both of them together finds 2 blocks. If a network of 4000 people find 4000 blocks per month, each finds on average 1 block per month. This isn't enough data to know the distribution (it's possible one person finds all 4000) but the best scenario is when each finds close to 1.

It also means that if in a given situation 4000 people find 4000 blocks, each finding about 1, then if I join in it would only be fair if I also find about 1 (or, more precisely, that each will now find 4000/4001).

Yes, with parallelizable PoW you can overwhelm the network given enough time and money. My contention is that non-parallelizable makes the problem worse, not better. With fully serial only the fastest one will do anything, so noone else will be incentivized to contribute his resources. So this one person can do the attack, and even if he's honest, it's only his resources that stand against a potential attacker (rather than the resources of many interested parties).

And there's no indication that some hybrid middle ground gives better results - to me it seems like more like a linear utility function where fully parallel is best and it gets worse the closer you make it to fully serial.

Also, I hold the position that security can be significantly improved using some form of proof-of-stake (basically a more methodical version of the hardcoded hashes).

See above. I think you're going the wrong way.

I'm still not completely sure what the requirements are, this whole discussion has been confusing to me. But yes, to me it seems that from a "back to basics" viewpoint a serial computation only makes it easier for one entity to dominate the blockchain, making the "better security" requirement impossible. Again, if multiple computers don't give more power over the network, it means the attacker doesn't have to compete against multiple computers, only against one.

You mean an alternative Bitcoin-like currency, or something that doesn't look anything like it? If the former I doubt this will be applicable, if the latter I can only speculate unless you give more details about the application.

The Bitcoin code progresses slowly, probably mostly because of the sophistication of the code, but I trust that all sufficiently good ideas will make it in eventually.

Let´s make it a bit easier: assume, as in Menis example, that 4000 blocks are found per month by individual participants, under the assumption that your non-parallelizable PoW is in operation. Assume further that all of these people just meet up and decide to share the revenue equally to smoothe out their income stream. According to what you have been arguing, the total number of blocks they find would go down to 1 purely due to the fact, that they are colluding in terms of revenue-sharing.
By definition 4000 blocks, will reduce to 1 by your formular magically devining social contracts?
Good luck with that line of argumentation...

My example is wrong, since an incorrect bounty is something a node can check on its own. If you replace the setting by a double spend, it should work.


Why?

It is characteristic of non-parallelizable PoWs that they do not scale in the way you describe. I believe we have a misunderstanding here.


Ok. Forget the pool as part of the argument here but think of parallel computing. The pool is a parallel computer.

The line of reasoning is about parallel computation and scalability of the PoWs.

With parallelizable PoWs, Bill Gates can buy as much computing power as he wants. He then changes a transaction in block 5 to his favour. Thanx to his computing power he easily can redo the entire block chain history since then. If the PoWs are, as I suggest, non-parallelizable, he simply cannot do better buy buying more computers. The only thing he can do is increase the clocking. By this, he can speed up his computation mabe by a factor of 5 or 10 - as opposed to buying more computers, where only money is his limit. So, non-parallelizable PoWs are an effective solution against this kind of attack.

(Yes, I know that the hashes of some 6 or so intermediate blocks are hardcoded in the bitcoin program and hence the attack will not work out exactly the way I described it - but this does not damage the line of reasoning in principle.)


I do not think that the "variance in block finding times" is the essential advantage, it is rather convergence speed to "longest chain" (I have no hard results on this but am currently simulating this a bit) and better resistence against attacks which involve pools parallel computers.


Trying to understand the argument. Do you think there is no PoW matching all the requirements? Care to give a hint why?

As to a potential usefulness: The concept is by now means "finished" but until now the discussion on the board proved very fruitful and helps to improve the system I am working on. This is for a different kind of block-chain application, so I am not expecting an impact for Bitcoin. Bitcoin is widely disseminated so I do not expect significant protocol changes to occur any time soon, especially by suggestions from outside the core team. 

Ok, you're definitely confused about the capabilities of someone with >50% of the hashing power. He cannot do things like put a 100BTC generation transaction per block. Such blocks are invalid and will be rejected by the network (particularly the nodes that actually accept bitcoins for goods and services). In other words, these will not be Bitcoin blocks - the rest of the network will happily continue to build the Bitcoin chain, while he enjoys his own isolated make-believe chain.

Does your system maintain the notion that each given block is found by some specific individual? If so, if 4 people find 4 blocks in 4 months, it means each person finds 1 block in 4 months, contrary to the premise that each person finds 1 block per month...

If it wasn't clear, in this example the intention was that the 4 people aren't all there is, there are 4000 more similar people each finding 1 block per month, for a total of 4000 blocks per month. So again, if 4 people find 1 block per month each, then between them they find 4 blocks per month.

Because the pool shouldn't be the one deciding what goes in a block. As was explained, a pool is essentially just an agreement to share rewards. Even in centralized pools (and like I said there are decentralized ones), all the operator needs is to verify that miners intend to share rewards, by checking that they find shares which credit the pool in the generation transaction. But everything else can be chosen by the miner.

This is a future fix, however - currently centralized pools do tell miners what to include in the block. But miners can still verify that they're building on the latest block, so they can detect pools attempting a double-spend attack (which is the main thing you can do with >50%).

Variance in block finding times is unwanted, but I think most will agree it pales in comparison to the other issues involved. Especially since there are basically two relevant timescales - "instant" (0 confirmations) and "not instant". The time for 10 confirmations follows Erlang(10) distribution which has less variance.

By all means you should pursue whatever research question interests you, but I expect you'll be disappointed both in finding a solution satisfying your requirements, and in its potential usefulness.

Come on man you are ignoring the entire concept of a reward.

A pool doesn't "get more" it isn't trying to get 2x.  It still gets x.  It simply gets x more consistently.

A better example would be a lottery (real world) pool.  In a lottery (lets ignore the lesser prizes) you either win nothing or you win a HUGE prize.  However the odds of you winning in each draw is so low that even if you played every day for the rest of your life you may never win.  Rather similar to the bitcoin lottery right?

So you and 19 friends get a great idea.  Instead of playing individually you pool your 20 tickets and if any ticket wins you SPLIT THE REWARD 20 ways. 

Has the lottery pool gained 2x?  No.  Do bitcoin pools gain 2x?  No.  In the long run (say 100 years of solid 24/7 mining) a solo miner and a pool miner (assuming same hardware, downtime, and fees) will earn the same amount.  They both earn X.  The only advantage of a bitcoin pool is reduced volatility. You reach the "long run" (where expected value and actual value converge) much quicker.

Any problem no matter how non-parallelizable can be pooled.  Each "miner" would work completely independent and if/when he "wins" he shares the reward with the rest of the pool.  That is unavoidable.  If you think the biggest risk to bitcoin is pools then your proposal does nothing about that (and creates a large number of new problems).

Thanx for your interestign reply.


No. I do not think that.


I completely agree.

Now suppose it is you and me and some 40 other guys with the same hash performance as you have in your example. Suppose I want to claim 100 BTC bounty for every block instead of the standard 50 BTC. Chances are next to 100% that I will manage. Since, on the avaerage, I am faster than you (and all the other guys combined), I will dominate the longest chain in the long run.


No. It is not my mission.


Why?

The perspective I am looking at is not the single block but the development of the block chain.

As soon as one of the four people found a block, this person broadcasts this block and the puzzles the other three had been working on becomes obsolete (at least that's my understanding on what the reference implementation does). Only a cheater would be interested in continuing to work on "his" version of the block; however, having lost the block in question, chances are getting higher that he will not manage to push "his" version of the next block.

Four people with a computer would rather find a total of 4 blocks in FOUR months - and these blocks would be the four blocks chained next to each other, ie a block chain of length 4.


How do you prevent a pool from pooling more than 50% of the hashability and then imposing its own understanding of Bitcoin upon the remaining nodes?


I agree to the interpretation of the parallel PoW situation. I disagree with the interpretation of the non-parallelism situation - there is not yet a final proposal for a non-parallelizable PoW, so we do not know yet if this is a necessary consequence. However, I am grateful that you are pointing out this argument, since it is a possible problem. I will take this in consideration in my future work on this - it is a helpful objection.


Again you are raising an important aspect. The task thus is to see that two goals can be balanced: Linear scaling and small variance.

I agree that the Poisson process is a very natural solution here and prominently unique due to a number of it's characteristic features, such as independence, being memory and state less etc. A non-parallelizable PoW will certainly lose the state-less property. If we drop this part, how will the linear scaling (effort to expected gain) and the variance change? We will not have all properties of Poisson, but we might keep most of the others. The question sounds quite interesting to me.

There are standard techniques to solve the problem you pose in a decentralized system. The buzzwords here are secret splitting (the puzzle is not created by a single person but by many persons, none of which knows the entire secret), you might want to Google "coin flipping over the phone" or "how to play any mental game".

I do not know yet if these standard techniques are practically feasible in the Bitcoin setting. They might. They might be not. That's the thrill of research. :-)

I am not sure whether there are non-parallelizable puzzle schemes where this requirement can be relaxed. Thus, there may be another way out.

I think you're confused about how the so-called "Bitcoin lottery" works. You seem to think that if I have some system and you have a parallel system with x100 the power, then you will find all the blocks and I will find none, because you'll always beat me to the punch. But no, these are independent Poisson processes (tied only via occasional difficulty adjustments) with different rates, meaning that you will simply find 100 times the blocks I will. So over a period where 1010 blocks were found between us, about 1000 will be yours and 10 will be mine.

In other words, it scales linearly - the amount you get out is exactly proportional to what you put in.

If that's all you're after, mission is already accomplished.

But if you think your "non-parallelizable PoW" system should behave differently, let's say that in this system a person with a computer finds one block per month. Then four people with a computer each should find a total of 4 blocks per month, right?. So a person with 4 computers also finds 4 blocks per month, because the system can't know who the computers belong to (and if it can then it's not at all about a different computational problem, but about using non-computational cues in distributing blocks). So a person with a special 4-CPU system also finds 4 blocks, as does a person with a quad-core CPU.


And, once more - pools are not a security threat if implemented correctly. There's no reason the pooling mediator also has to generate the work. And, there are already peer-to-peer pools such as p2pool.


Edit: Parallelism means that an at-home miner can plug in his computer and contribute to security/receive rewards exactly in proportion to what he put in. Non-parallelism means his effect will depend in complicated ways on what others are doing and usually leave the poor person at a significant disadvantage (since others are using faster computers), which is the opposite of what you want.

Block finding follows a Poisson process, which means that the time to find a block follows the exponential distribution (where the variance is the square of the mean). The variance is high, but that's an inevitable consequence of the fair linearly scaling process.

If it pleases you, the variance of block finding times will probably be less in the transaction fees era.

To my current understanding this is just the other way round.

In Bitcoin, a single botnet can obtain so much hashing power as to take over the system, since it can parallelize the PoW.

In a completely non-parallelizable PoW (as FreeTrade pointed out recently and I just commented on), the fastest single processor takes over the system - but we have a perfect protection against a botnet take-over (because parallelization does not help).

In the concept I am thinking of right now, we should be able to combine the advantages of both worlds, depending on how we build the PoW (described in a bit more detail in my recent reply to FreeTrade).

This is a very important question and trying to answer this I am understanding the mechanism I want to design much better. Thank you for asking it!

The PoW system currently used in Bitcoin has the same problem. It solves this problem by offering an extremly large search space and a situation (hashing) where nothing can be said efficiently or systematically on how to find a good solution. Thus, the solution method is random parallelization of a brute force search. This solution method introduces a random element into the situation (which was not there from the beginning: the PoW task is not random).

So, parallelization introduces a random element here. If we now prevent parallelization completely and produce a PoW system which makes the solver work through a sequential number of deterministic steps, the fastest single core processing unit will win every block.

Thus, we must reintroduce a random element in the PoW. Possibly, there are two construction elements for building a PoW: Two tasks could be chained one-after-the-other (leading to non-parallelizable work) or combined (leading to parallelizable work). Currently Bitcoin uses only ONE of these construction elements. Using ONLY the other one is a clear fail (as FreeTrade just pointed out). Using BOTH mechanisms could lead to a new, different PoW.

The question is: Would there be advantages when using a different PoW?

In addition to the ones outlined in my above posts, I see one more: Currently the time for solving a PoW is distributed according to a Poisson distribution (Satoshi describes the consequences of this in his paper). We have a parameter (difficulty) where we can tune the mean of this distribution, but we cannot independently tune the variance of the distribution (with Poisson it will always be equal to the mean). With a different PoW system we will be able to obtain different distribution shapes (possibly with a smaller variance than Poisson). This could make the entire system more stable. Certainly it will impact the Bitcoin convergence behaviour. For the end user the impact might be a higher trust in a block with smaller waiting times.

From the discussion I realize that I did not properly describe my core goal. It is not about mining or increasing revenue or making them more predictable. It is rather about undstanding the implications of the current choice improving the stability and speed of statistical convergence of the longest chain.  The discussion here thus far was very helpful and enables me to rephrase my thoughts, hopefully in a better way.

In a non-parallelizable PoW, we will have, say, 1.000.000 processing units all competing individually for a block. Some are faster, some are slower, but they do not differ so widely in performance. Every processing unit corresponds to a single processor (no parallelization advantage for a GPU or a multi core; however a single person might own several competing processing units, which might sit on a single die or a single GPU or several racks).

In a parallelizable PoW we will have a much smaller number of processing units competing for a block. Many of the former units will cooperate by the mere fact that they are sitting inside of a GPU and are parallelizing their work. Other units are even stronger, since they form pools. Moreover, we see a big variance in performance (ranging from the Celeron miner to the 100 racks x 4 high end GPU x 256 GPU processing cores miner).

Now, how do these two worlds compare?

1) In the parallelizable world it is POSSIBLE to form a processing unit which has more than 50% of the hashing power. You simply buy as many GPUs as necessary and that's it. In the non-parallelizable world this is not possible. The best you can do is to overclock your single core or to build specific SHA processor.

2) As a result of (1), the distribution of processing power in the two cases are very much different and thus the two algorithms will definitely behave differently.

Current state: I am trying to understand this difference. My (yet unproven) mathematical guts feeling is, that the convergence in the non-parallelizable setting is better (I am referring to the thoughts very informally described on pages 7 and 8 of Satoshi's white paper) and the system is more robust against some forms of attacks. I do not have a completely thought through concept yet.

The discussion here is very helpful for this. Thank you!

The original paper from 1996, Rivest, Shamir, Wagner (see above) provides some nice real-world examples here.

1 woman needs 9 months to give birth to a baby. So 2 women will have twice the power and will need 4.5 months to produce a baby.

A bus full of passengers stands in the desert. They ran out of gasoline. The driver discovers that the next gas station is 50 miles away. This is no problem, since there are 50 passengers on the bus. They will just split the task and every passenger will walk his share of 1 mile.

The examples show that there are tasks where you do not get 2X power by doing Y twice. In my above posting there are references to mathematical examples in the literature.

Another tiny problem, all nonparallelizable puzzle schemes proposed so far require the puzzle creator to keep a secret from the puzzle solver. How exactly do you do that in a decentralized system?

THAT IS THE ONLY ADVANTAGE POOLS HAVE NOW.

Each miner in the pool is working Independently. A pool with 1000 miners has absolutely no advantage over a pool with 10 or a solo miner (1). At its most basic level a pool is simply an agreement to "share" the reward.  No work gets shared, only the reward.    If a pool of 10,000 miners mines 5 million shares and then one miner finds the solution.  Essentially the other 9,999 miners did ABSOLUTELY nothing.  One miner solved the entire problem ALL BY HIMSELF.

However there is huge volatility in mining yourself (due to the high reward and low chance of "winning").   A pool normalizes the results (smaller reward, higher chance of winning) but the expected value is the same.


The protocols of the pool (i.e. checking low difficulty shares, rpc, etc) merely exist to keep people honest.  The simplest pool requires no protocols just trust.

Me and 4 friends (all with exactly the same hardware) all hash independently.  If one of us "wins" we split the prize 5 ways.  Expected value is exactly the same but volatility has decreased.   Now as pool gets larger the risk of cheating gets higher so pools implement protocols and procedures to ensure "fairness".

So back to the OP point.  Please provide an example where the reward can't be shared by a pool.   You can't.  Even if the work is completely non-parallizable the reward certainly can be via INDEPENDENT actors sharing the reward via mutual agreement.

So what exactly would a non-parallelizable solution solve?  Of course the fastest miner would always win the non-parallelizable solution.

And bitcoin gets taken over by a single botnet.

How would you prevent the fastest miner from winning every block?

That is all that a pool currently does.

It is possible to design a proof-of-work scheme where being part of a pool doesn't provide any (or negligible) advantage, aside from the benefit of having a more predictable revenue stream.  Perhaps that's what the OP is wondering about.