Peter l bitcoin calculator
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- 8 problems with Plan B's stock-to-flow bitcoin models
- Cryptocurrency Footprint Calculator
- What is Bitcoin?
- Bitcoin resources
- CoinDesk Podcast Network
- Peter Brandt Says Tether Is a 'Gigantic Mind Fart'
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MathOverflow is a question and answer site for professional mathematicians. It only takes a minute to sign up. What computational mathematics problems that could be used as proof-of-work problems for cryptocurrencies? To make this question easier to answer, I want proof-of-work systems that work in cryptocurrencies that contain many different kinds of proof-of-work problems the use of many different kinds of proof-of-work problems is more secure than the use of only one type of proof-of-work problem instead of proof-of-work systems that work in cryptocurrencies with only one kind of proof-of-work problem.
To make things simple, cryptocurrency mining requires one to solve computational problems as a proof-of-work.
For example, in Bitcoin, the miners must find data whose SHA hash begins with many zeroes. Unfortunately, solutions to the proof-of-work problem for most cryptocurrencies have no intrinsic value in themselves, and these problems use up great amounts of resources and people have even made malware to solve these proof-of-work problems.
Mathematicians have a limited amount of computational resources and cryptocurrency mining could potentially supply mathematicians with a nearly unlimited amount of computational power. For example, cryptocurrency miners receive an equivalent of millions of dollars in revenue per day and they spend much computational power solving the problems required to mine these cryptocurrencies. Most computational mathematics problems are unsuitable as proof-of-work problems for cryptocurrencies.
Here are some requirements and things we would like in such a problem. Many NP-complete problems will satisfy this requirement.
Optimization problems can easily be made to satisfy this requirement since with an optimization problem one can simply choose the best solution every 5 minutes or so optimization problems may not be the best for cryptocurrencies though. These solutions and not just the process of obtaining the solutions should be of a scientific, mathematical or practical interest.
This way someone cannot steal someone else's solution. The following traits are necessary only if there is one or a couple kinds of proof-of-work problem per cryptocurrency or there is no process to automatically remove broken proof-of-work problems.
The security of cryptocurrencies depends on the fact that no party should have a secret algorithm that quickly solves the problems and that no body is likely to develop such a secret algorithm in the future. If Alice works on the problem from noon and Alice has not found a solution by , then at Alice will have no advantage over another participant who begins working on the problem at In other words, the amount of time it takes to solve the given problem follows an exponential distribution.
One way to obtain this desired property is to make the proof-of-work problem dependent on random data such as current transactions. One could also make future problems depend on previous solutions.
I am slightly more interested in mathematical problems which have or may have future practical applications instead of problems which are only of a purely mathematical interest. In a best case scenario, I would like to see problems which may have cryptographic applications. This question differs from this previous question since the previous question did not ask for problems which are specifically suitable as proof-of-work problems for cryptocurrency mining and the answers given are not suitable as proof-of-work problems for cryptocurrency mining either.
The problem would be finding a sequence of Reidemeister moves for a random link graph that reduces it to the unknot. Unknotting itself is in NP, as discussed here: Is there a polynomial-time algorithm for untangling the unknot? Unknotting has many real-life applications.
Furthermore, given a potential sequence of Reidemeister moves that might unknot the knot, it is quite easy to verify that it produces the unknot. There may be some problems with this maybe a secret fast algorithm in the works?
Calculating the permanent of a small matrix is a computationally challenging problem, as discussed here , here , and here. See also the Wikipedia article. A cryptocurrency already has a large number of coins that are agreed to be random — namely, the merkle root of previous blocks. As a proof-of-work based on calculating the permanent, the following protocol may be a starting point:. Calculating permanents of random matrices may have some intrinsic value in block-designs, matchings in bipartite graphs, symmetric tensors, etc.
Work since the late '90's has significantly reduced the burden on the prover, and I sense that there's a feeling that a true succinct non-interactive argument of knowledge may be just around the corner.
Lund, L. Fortnow, H. Karloff, and N. Algebraic methods for interactive proofs. A note on efficient zero-knowledge proofs and arguments. Finding cycles in graphs is a standard graph theory problem that lends itself well to proof-of-work. Of course, the specific pseudo-random graphs generated in Cuckoo Cycle have no practical use whatsoever I find this to be an excellent suggestion, though not sure all requirements can be satisfied.
More specifically, 3 and 5 - if we randomly generate instances, then why would they have any intrinsic value? Would factoring large integers have any intrinsic value? One example that I can think of is chess endgames. The problem is that the proof might be hard to verify, though probably not impossible to have a proof format that can be checked quite fast. Also, if the bitcoin budget is in the millions, I think it would be nice to have a central board that would select every once in a while an important computational problem for whose solution there is a bounty of many bitcoins.
At least I don't see anything wrong with this version of the proposal. Here is a recent paper , which has been received positively in the cryptocurrency community. I will expand on this paper here. While conventional hash functions do not allow one to construct very useful proof-of-work problems, if one replaces the hash function for the proof-of-work with a randomizing function specifically designed to be computed by reversible circuits, then the proof-of-work problem has practical use besides simply securing the blockchain.
This proof-of-work problem will prompt the development of super-efficient reversible computers. Furthermore, these new proof-of-work problems will satisfy all of the requirements that one will want in a proof-of-work problem for cryptocurrencies that I have listed in the question. A bijective gate such as the NOT, Toffoli, and Fredkin gates is also called a reversible gate and by definition every bijective gate must have the same number of input bits as output bits. A circuit is said to be reversible if all of its logic gates are reversible.
As combinatorial circuits model ordinary computation, the reversible circuits model reversible computation. Any computation that can be efficiently carried out by an ordinary computer can also be reasonably efficiently computed using a reversible computer. While conventional computing always costs energy since with conventional computing, one always has to erase information, there is most likely no lower limit to the efficiency of reversible computation since reversible computing does not erase any information.
Since reversible computers will be more efficient than ordinary computers, reversible computers will not generate as much heat as ordinary computers, so reversible computers will be able to operate at much higher speeds than ordinary computers. While a reversible computer should in theory be much more efficient than an irreversible computer, there are currently no reversible computers out in the market today which are more efficient than their irreversible counterparts.
If the proof-of-work problems for cryptocurrencies require one to solve problems designed for super efficient reversible computers, then corporations will have a great incentive to produce reversible integrated circuits which can quickly solve these problems without using so much energy.
We shall now select a proof-of-work problem which should be carried out by a reversible computer just as easily as it is carried out by a classical computer. I therefore want the randomizing function to be computable on a reversible circuit without any ancilla.
Discussion of the prospect of a cryptocurrency based on cellular automata prompted me to start developing the Catagolue project in the summer of The proof-of-work system was deliberately chosen to enable a cryptocurrency to be built upon it:. One of the more interesting objects to appear spontaneously was this one. This proof-of-work satisfies points 1, 4, and 5.
Point 2 is also satisfiable: in order to set the difficulty of the problem, modify the criterion of 'interesting' to exclude a given proportion of randomly-chosen soups. Choosing that threshold is straightforward by examining the empirical object frequency tables on Catagolue itself. Arguably, it also satisfies point 3: whilst the problem is not of general mathematical interest, it is still sufficiently interesting to the or so people who have contributed CPU time to the distributed search without any extrinsic reward.
I don't see how you will have a problem which is progress free but still in NP requirement 7 ; or any kind of problem that is suitable for your purpose for that matter. To see why this seems unlikely lets consider the solution space for your problem as I start and when I have progressed in an arbitrary algorithm that searches the solution space.
This reduces the solution space. If I don't do this I run the risk of repeating solutions to no avail. Therefore I suspect there is no problem for which a solution can be found for sure that has the desired property. This in combination with the requirement that the problem should be scalable so there is no guarantee that only large problems will be used makes it hard to have any real solutions to this problem.
If your drop this requirement, travelling salesman problems for random regions might be interesting since This could help transport companies alot while offering a huge potential number of problems that are highly customizable.
However use would be somewhat limited since it would be quite random what TSPs would be solved. However It would be quite nice to have a database in which you enter some cities and a maximum distance and get a route between them that is shorter than that distance.
Another possibility is approximations of the Navier stokes equations for typical requirements. But this is somewhat outside my field. Not being able to coordinate which problems are solved when is a major problem for the usefullness, so all problems that have these kind of properties should be problems which are in general very useful. I think TSP problems with a pool of the largest cities in the world would have this property, but still alot of computations would be useless.
A useful problem for cryptography could be SAT since boolean statisfiability can be easily re-written into most cryptography problems.
However, the problem is still that there is no central authority to generate the problem and so finding a relevant SAT problem is much harder than it appears. One idea maybe is to not have one authority but instead some huge database of useful SAT instances where one is randomly pulled from. If the randomizer is apt precomputation is impossible. Let me have another go, because I really love this question. Essentially it's like a SETI home project - without going into details, let's just consider the theoretical model that some signals arrive from a source that is sufficiently random and then we have to do some computation on it to get some data.
If you prefer groundhogs to E. Then whoever computes the data first, will get a coin. The main issue I see with similar models is that they don't satisfy property 1 verifiability. I thought this could be solved through some court, but as pointed out by Joseph in the comments to the first version of this answer, this would lead to problems.
So instead, we should pick a problem that can be verified. Unfortunately, I don't know much about what SETI was doing with the data, but probably there was something that they were looking for and now I don't mean aliens, but some signals. So we could say that every 10 minutes there's a data that comes from space, the first person to find a signal wins a coin, but the data might contain no signal, in which case nobody is rewarded - I don't see an issue with this happening sometimes.
A cousin to this idea involves finding proofs in Peano Arithmetic of small statements of number theory. Choice of problems: Because programs must be newly found to halt, i.
Convert Bitcoin to Papua New Guinea Kina Today
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8 problems with Plan B's stock-to-flow bitcoin models
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Get best and latest bitcoin news today with coinsurges. While some panicked, other industry experts pointed out that the Bitcoin network has become verifiably stronger than ever before. The growth of the Bitcoin network has become apparent, as hash rate figures for BTC continue to set new highs this month. For example, on Jan. Samir Tabar, chief strategy officer at Bit Digital — a publicly listed Bitcoin miner — told Cointelegraph that the BTC hash rate refers to the amount of computing power being contributed to the network at any given time. Tabar explained that when it comes to Bitcoin mining, a higher hash rate equates to a good hash rate.
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Peter Brandt Says Tether Is a 'Gigantic Mind Fart'
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