Yes, this is strict identity verification. There are numerous authorities which do so and which are not central. Every identity verification system of a modern state is distributed and depends on trust relations between the various offices and employees. as mentioned, this is not Bitcoin-related work and it is much more vague than the thoughts on PoW.


I agree - although challenging every absolutely I find is part of my daily work as researcher and the way I feed myself 

A non-parallelizable PoW will not help me to distinguish 1 person running 100 computers from 100 persons running 1 computer each and this also is not what I intend to do with non-parallelizable PoWs.

So what do I want to do?

Right now, Bitcoin uses PoW to (1) randomly select a winner (2) ensure a waiting time between two blocks. Both, selection of winner and waiting time, may be described by a probability distribution. The currently employed PoW in Bitcoin produces two very particular probability distributions. Probability of selection is proportional to (pooled) performance and waiting time is Poisson / exponential with a mean which can be nearly arbitrarily lowered by an attacker.

1) I want to prevent an attacker from arbitrarily lowering the mean of the waiting time (this is a direct consequence of parallelizability)

2) I want to understand if the distributions we get from the current implementation really are the distributions we want (non-parallelizable PoWs give rise to completely different distributions)



 

Yes. I currently fail to explain.

The thread started out trying to understand why the current PoWs are completely parallelizable. Throughout the discussion I realized that different PoWs might be better. I do not yet have a completely convincing argument for or against a specific form of PoWs (although my guts are telling me, there could be some advantages for non-parallelizable PoWs). Since I did not see an argument why the PoWs must be the way they currently are, I spent some 20 hours researching other possibilities. I do not have a final answer yet but I am developing some systematic approach to settle this question. Currently I am convinced this can be done, but this still will need a bit of time (and I am not working fulltime on this issue as well).


A completely serial PoW clearly is not better but just does not work, as you point out in your posting.

I suppose that a non-parallelizable PoW may be better. Our current PoWs are parallelizable to an extreme degree. Maybe the optimal situation is something in between.


According to my current understanding: No and no.

Verification could use some kind of trapdoor mechanism and thus be faster. In the literature there are some non-parallelizable PoWs with faster trapdoor verification, however they have the issue that the trapdoor secret must be kept secret. One of the natural approaches to this is to share or split this secret (which could lead to a significantly more complex protocol). While I do not buy into Verification requires the proof-of-work to be repeated (there are counter examples) I do not have a working example either (at least by now...)

Also, I am not yet convinced that a verification, which takes a bit of time, really is a problem.


In Bitcoin, I think, the PoW serves additional purposes next to choosing a winner and making a majority consensus be a winner. For example, it also provides some kind of clocking in the block chain which slows down the transaction rate (which ensures that the probabilistic gossip does not go out of control). It may contain some kind of inbuilt DDoS protection as well.

Actually, Bitcoin realizes some kind of distributed central trusted store.

The ideas I mentioned on trust are far down the road and still need more time of thinking. My interest here is along the "proof-of-stake" idea mentioned by an earlier poster.

With regard to distributed central authorities: Most algorithms for distributed central authority of which I know have some other nasty problem. Either they scale badly (usually in number of communications). Or they make unrealistic assumptions (like having a common trusted random noise generator, or having a pre-shared common secret etc). Or they pose problems in ad-hoc networks with an unknown number of nodes joining and leaving the network. Or their description looks so awkward that I did not muster up time or courage to understand them. Bitcoin therefore fascinates me, since it seems to be a good mix here. However, Bitcoin does not seem to very well understood from a formalized approach and many design choices (to me) are not as obvious. Also it lacks strict complexity analysis. That's why I love to poke Bitcoin once in a while and understand what happens when a core part gets modified.

Yes. By your post I suppose that I finally managed to make myself understood. The idea actually also was reshaping due to the good discussion on the board here. Thanx to all, guys.


From what I see right now (have 2 leave train in some minutes and may need some more thoughts) this is identical to one of the non-parallelizable PoWs I found in the literature.

I am not so sure how big the problem of a long verification really is (could we overlap checking the last block with producing the next one ?). We are using PoWs in a bit different manner in Bitcoin than in, for example, spam and dos protection (where it is essential that the server can do a quick verification and the client does a complicated puzzle). In Bitcoin, we are more symmetric and would probably just slow down block production speed by a factor of 2.

Moreover, I just found some nice recent papers on non-par PoWs and I hope one of them contains a suggestion.

Sybil is on my mind.

I plan a register of persons to prevent fake multiple identities. Assuming a core number of trusted users, every user would show up in person at a certain number of users in his area (partially to be selected by random choice, to prevent systematic collusion). The user would present some official documents and then get a uid based on a standardized id scheme, eg a hash on "Firstname Middleinitial Lastname-When-Born Birthplace Birthdate". To be able to act anonymously, the user would first logon using this id and then use this to generate secondary anonymous credentials for login. These will be produced in a manner that there will only be one credential for every user per time unit. Thus, the user is anonymous AND the risc of a large number of fake users is small. It is kind-of a decentral implementation of a PKI, similar to the web-of-trust in PGP (but preventing collusion attacks).

Having prevented a Sybil attack by that mechanism, a trust based system is now possible as next level or user management.

The disadvantage, of course, is the requirement to establish identity first, which is rather tedious.

I can handle this disadvantage, since users who did not establish identity may use the system but will not have additional access rights and will not have rights in the trust layer. Of course, this is a not feasible for Bitcoin, because there is essentially just a single functionality (no different access right levels and no trust) and users would be very frustrated, if they had to do all kinds of registration before receiving or making payments.

This line specifically shows a complete lack of understanding about how human motivation works. 

That said, from a crypto point of view, I am also highly sceptical that the approach taken by the OP will work out. Hash functions are constructions whose many task is to make the suggested approach fail. To the contrary: I am happy to bet quite some BTC that this attempt will fail.

However, we are here (on this forum) to learn and to improve and generally move ahead with Bitcoin. So I am happy about every attack on Bitcoin, every suggestion on improval and every step to move ahead with our common interest. Phrases like "shows a complete lack of" or "is nonsense" isn't exactly what motivates people. And: So long as there are still so many ecosystem elements missing in Bitcoin, so long as there are still so many problems with the client, so long as we have no formal specification, an RFC, and and ... and so long as my favorite online shop does not accept Bitcoin - we still need more people in the field. Not everyone is a Satoshi and even he had a time of learning, trial and error.

Thank you for listening.

You got email. 

Where could that information have been obtained earlier ?   

I would have been in touch earlier if I had had a chance to know more details about this organizational process in advance. Moreover, there would have been more contributions and more participants. Sad that this chance now remains unused. Maybe we should discuss how in the next event an approach can be used which is also adapted to the boundary conditions under which academic and research people have to function. 

Ah. That's a concept which might fit nicely into my application. Actually, by reading the other thread, I realize that it is much easier to express what I want, and probably also easy to implement: As part of the proof-of-work and branch selection concept !

I favor a technique of "those who have more documents, key-value pairs stored and have been active in the system for a longer time and are trusted/interconnected to more users have a stronger say on branch selection" over the "those who have more $$$ for GPUs have a stronger say".

I am not completely aware of the process / workflow you are using for this. and how suggestions get selected . From my personal point of view I would be ready to offer some topics myself.

Bitcoin - How I understand it: My high-level conceptual understanding of the Bitcoin mechanism after having read and documented the entire reference client code for myself. 45 minutes, tutorial style.

An Analysis of Bitcoin Anonymity: To which degree is Bitcoin really anonymous? How do Bitcoin usage patterns affect anonymity? What can be done to improve Bitcoin anonymity? How can Bitcoin payment flows can be traced? 30 minutes, talk, describes work-in-progress (and will contain first results when applying our analysis algorithm to the current block chain).

Improving Bitcoin Wallet Security: How can we split the authorization phase in the Bitcoin mechanisms to two machines in such a manner that compromising ONE machine does not result in money being stolen? Which crypto possibilities are there? Which solution are we in the process of implementing? 30 minutes, talk, describes work-in-progress (currently at the stage of starting to work on the selected embedded hardware)

Bitcoin Todo List: Critical remarks on the state of development in Bitcoin. What must be done (and at which level or priority) if Bitcoin shall become a success any time soon. 20 - 30 minutes, could be part of a brainstorming session or panel discussion.

I am not sure what fits the conference mode best and how things get organized there - as I am more used to the traditional ol' style of "over"organized conferences with submission deadlines and schedules and stuff. Just post what suits you best.

To give you an idea on myself: I have been regularly lecturing in class and giving industry talks for the last twenty years or so. Currently I am hacking on a forked version of the reference client to which I added some 1.000 lines of code and I am supervising two students working on Bitcoin related topics.

I am dependent on the precise schedule of the program, because I have to match some time & travelling constraints. "Just come and see" will not work for myself (besides being detrimental to the possibility of preparing something).

I can provide more details on my suggestions above.

And in different applications it depends on the motivation of the attacker. In a monetary application (Bitcoin) the attackers may be botnets which want to make some $$$ (or, rather, BBB); unless you are the FED or Visa, of course. If you look at directory applications, an attacker is not interested in double spending but might be interested in preventing a certain result or document from being stored in the system or to disrupt the operation of the system. Here, the motivation of an attacker is different, as well as the means he can use for an attack.


@Meni Care to give a hint about what you are thinking of? Working on a new application type, a "fundamental change" in how branches are selected is a real option. Therefore I would be very interested in learning about this, even if it is "just" a "raw" idea and not a source code patch.

Let me see if I understood correctly, where I lost you.


Your ability to parallelize depends on the number of computers you have and on the type of problem you want to solve.

If the problem you want to solve is finding the correct nonce for a bitcoin block to meet its target, you can parallelize very nicely. Generally speaking, every problem which consists of brute-force attacks is nicely parallelizable. Also, multi-dimensional problems can be parallelized very nicely, for example matrix mulitplication. Let us assume we multiply a 10x10 matrix with another 10x10 matrix. When I have 10 computers instead of 1 I will be (nearly) 10 times as fast. Even having 100 computers may help (one for every element of the result matrix). What about 200 computers? Still good, since I now could split the calculation of each sum into two halfs. What about 1 billion computers? Well, probably there is a limit to the degree to which matrix multiplication is parallelizable.

This observation may motivate a search for problems, which cannot be parallelized very well.

For example, assume you have a number x and want to calculate sha(x). Fine, we have an algorithm for that. But now let us calculate sha(sha(x)). How would we parallelize this? Actually we FIRST have to calculate sha(x) and THEN we have to evaluate the hash function again. It does not help me to have an additional computer. We know of no shortcut for parallelization. (There are functions, where we know shortcuts, like in addition: Many invocations of an addition can be expressed as multiplication, but with, for example sha, there is an issue).

So the idea was to replace the proof-of-work problem in Bitcoin (which currently is highly parallelizable) by a problem which is not parallelizable at all. (As outlined, this is only part of the concept, because a completely serialized proof-of-work would not lead to the probabilistic behaviour we want).

Hope I got the point where I lost you.
 

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.

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. 

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.

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.

Grundsätzlich finde ich eine Vereinsgründung eine gute Idee.

Das mit der Gemeinnützuigkeit bekommt man schon hin (ich habe das mit einem anderen Verein schon einmal geschafft).

Ich frage mich, ob die Community die Substanz für nachhaltige PR Arbeit nach außen schon aufbringen kann. Das macht viel Arbeit, die nicht unbedingt der technischen Seite von BTC zu gute kommt. Wichtig wäre es aber.