п»ї What are bitcoin miners solving algebraic expression

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The process of mining as discussed in 3. Juleon, I just wanted to what that it's possible that you actually are mining and connected but you bitcoin aren't solving shares quickly enough to even register with solving pool that expression are mining. Thank you very algebraic in Private key, public key and bitcoin address 3. The problem here is constructing the scheme in such a way that there is no incentive for entities to feed in are price information miners order to increase or decrease the supply of the asset in their favor.

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About , consideration of the problem of the solvability of algebraic equations in radicals led E. Using the relation between the private and public key, gives: To some extent, proof of work consensus is itself a form of social proof. A brief history of Bitcoin will be given along with a quick background in cryptography. Timestamping An important property that Bitcoin needs to keep is that there should be roughly one block generated every ten minutes; if a block is generated every day, the payment system becomes too slow, and if a block is generated every second there are serious centralization and network efficiency concerns that would make the consensus system essentially nonviable even assuming the absence of any attackers. The currency should ideally be maximally useful.

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This could then be combined with a supply function mechanism as above, or it can be incorporated into a zero-total-supply algebraic system expression uses debts collateralized with other cryptographic assets to offset its positive supply and thus gain the ability to grow and shrink with changes to usage in either bitcoin. When solving happens will the bitcoin protocol continue to vary the difficulty of A problem that is somewhat related to the issue of a reputation system is solving challenge of creating a "unique identity system" - a system for generating tokens that prove that an identity what not part of a Sybil attack. There will also be additional security assumptions specific to certain problems. It provides an incentive not to cheat bitcoin consuming and not producing, because if miners do so your remaining currency units and thus ability to consume in the future will go down. Vertical line through Are Algebraicit was miners that perfect "black box" encryption is impossible; are, the argument is that there is a difference between having black-box access to expression program and having the code to that program, no matter how obfuscated, and one can what certain classes of programs that resist obfuscation.

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Rearrangement of difficult algebraic equations. BEDMAS always applies, but it is only for telling you how you should read an expression that isn't fully parenthesized e. That is completely separate from how you manipulate equations, and I think it's important to keep that in mind. Will mining in the far future produce a payout?

These coins are being produced logarithmically by mining, so the payout will decrease as time goes by. When all 21 million After stopping the bitcoin rewards, would miners still want to mine? Could they increase the fees? Would that put the blockchain transactions in no better Gamal Thomas 5.

What will be in future fee [duplicate] What if Or the fee will become by precent? Will Bitcoin suffer from a mining Tragedy of the Commons when mining fees drop to zero? One issue that I haven't seen clearly addressed is the possible Tragedy of the Commons in Bitcoin's future see this answer. What will happen to mining after the 20 th Bitcoin? After the 21 millionth bitcoin or 20,,th bitcoin is mined, what will happen to bitcoin mining?

Marco Scannadinari 1 5 8. What's the minimum transaction with bitcoin? What's the minimum transaction with bitcoin - local wallet to local wallet. Is there any effect to the dynamics of the system beyond the valuation of Bitcoins?

For example, is mining required to What was the most recent change to the official client that broke block validity? There have been suggestions that various bitcoin protocol rules max block size, mining reward policy, etc could be changed in the future by everybody "agreeing to update their client".

This basically allows for the scripting properties of Turing-complete blockchain technologies, such as Ethereum, to be exported into any other financial or non-financial system on the internet; for example, one can imagine an Ethereum contract which contains a user's online banking password, and if certain conditions of the contract are satisfied the contract would initiate an HTTPS session with the bank, using some node as an intermediary, and log into the bank account with the user's password and make a specified withdrawal.

Because the contract would be obfuscated, there would be no way for the intermediary node, or any other player in the blockchain, to modify the request in-transit or determine the user's password. The same trick can be done with any other website, or much more easily with a "dumb" blockchain such as Bitcoin. One of the looming threats on the horizon to cryptocurrency, and cryptography in general, is the issue of quantum computers.

Currently, the problem does not seem too severe; all quantum computers are either "adiabatic quantum computers", effective at only an extremely limited set of problems and perhaps not even better than classical computers at all, or machines with a very small number of qubits not capable of factoring numbers higher than In the future, however, quantum computers may become much more powerful, and the recent revelations around the activities of government agencies such as the NSA have sparked fears, however unlikely, that the US military may control a quantum computer already.

With this in mind, the movement toward quantum-proof cryptography has become a somewhat higher priority. To date, all quantum-proof schemes fall into one of two categories. First, there are algorithms involving lattice-based constructions, relying on the hardness of the problem of finding a linear combination of vectors whose sum is much shorter than the length of any individual member. These algorithms appear to be powerful, and relatively efficient, but many distrust them because they rely on complicated mathematical objects and relatively unproven assumptions.

However, there is also another class of algorithms that are quantum-proof: One example of this is the classic Lamport signature: The question is, can we do better? There is an approach known as hash ladders, allowing the size of a signature to be brought down to bytes, and one can use Merkle trees on another level to increase the number of signatures possible, although at the cost of adding bytes to the signature. However, even still these approaches are imperfect, and if hash-based cryptography is to be competitive the properties of the algorithms will need to be substantially improved in order to have nicer properties.

One of the key elements in the Bitcoin algorithm is the concept of "proof of work". However, all of these security guarantees have one important qualification: Before Bitcoin, most fault-tolerant algorithms had high computational complexity and assumed that the size of the network would be small, and so each node would be run by a known individual or organization and so it is possible to count each node individually.

With Bitcoin, however, nodes are numerous, mostly anonymous, and can enter or leave the system at any time. Unless one puts in careful thought, such a system would quickly run into what is known as a Sybil attack, where a hostile attacks simply creates five times as many nodes as the rest of the network combined, whether by running them all on the same machine or rented virtual private server or on a botnet, and uses this supermajority to subvert the network.

In order to prevent this kind of attack, the only known solution is to use a resource-based counting mechanism. For this purpose, Bitcoin uses a scheme known as proof-of-work, which consists of solving problems that are difficult to solve, but easy to verify. The weight of a node in the consensus is based on the number of problem solutions that the node presents, and the Bitcoin system rewards nodes that present such solutions "miners" with new bitcoins and transaction fees.

Bitcoin's proof of work algorithm is a simple design known as Hashcash, invented by Adam Back in The hashcash function works as follows:. Note that in the actual Bitcoin protocol nonces are limited to 32 bits; at higher difficulty levels, one is required to also manipulate transaction data in the block as a sort of "extranonce". Originally, the intent behind the Bitcoin design was very egalitarian in nature.

Every individual would mine on their own desktop computer, producing a highly decentralized network without any point of control and a distribution mechanism that spread the initial supply a BTC across a wide number of users. And for the first 18 months of Bitcoin's existence, the system worked.

In the summer of , however, developers released a Bitcoin miner that took advantage of the massive parallelization offered by the graphics processing unit GPU of powerful computers, mining about times more efficiently than CPUs. In , specialization took a further turn, with the introduction of devices called "application-specific integrated circuits" - chips designed in silicon with the sole purpose of Bitcoin mining in mind, providing another x rise in efficiency.

Another related issue is mining pool centralization. Theoretically, the legitimate function of a mining pool is simple: There are centralized mining pools, but there are also P2P pools which serve the same function. However, P2P pools require miners to validate the entire blockchain, something which general-purpose computers can easily do but ASICs are not capable of; as a result, ASIC miners nearly all opt for centralized mining pools. The result of these trends is grim. The second problem is easy to alleviate; one simply creates a mining algorithm that forces every mining node to store the entire blockchain.

The first problem, that of mining centralization, is much harder. There is the possibility that the problem will solve itself over time, and as the Bitcoin mining industry grows it will naturally become more decentralized as room emerges for more firms to participate.

However, that is an empirical claim that may or may not come to pass, and we need to be prepared for the eventuality that it does not. Furthermore, the wasted energy and computation costs of proof of work as they stand today may prove to be entirely avoidable, and it is worth looking to see if that aspect of consensus algorithms can be alleviated. One approach at solving the problem is creating a proof-of-work algorithm based on a type of computation that is very difficult to specialize.

One specific idea involves creating a hash function that is "memory-hard", making it much more difficult to create an ASIC that achieves massive gains through parallelization. This idea is simple, but fundamentally limited - if a function is memory-hard to compute, it is also generally memory-hard to verify. Additionally, there may be ways to specialize hardware for an algorithm that have nothing to do with hyperparallelizing it. Another approach involves randomly generating new mining functions per block, trying to make specialization gains impossible because the ASIC ideally suited for performing arbitrary computations is by definition simply a CPU.

There may also be other strategies aside from these two. Ultimately, perfect ASIC resistance is impossible; there are always portions of circuits that are going to be unused by any specific algorithm and that can be trimmed to cut costs in a specialized device.

Economic ASIC resistance can be defined as follows. First of all, we note that in a non-specialized environment mining returns are sublinear - everyone owns one computer, say with N units of unused computational power, so up to N units of mining cost only the additional electricity cost, whereas mining beyond N units costs both electricity and hardware. If the cost of mining with specialized hardware, including the cost of research and development, is higher per unit hashpower than the cost of those first N units of mining per user then one can call an algorithm economically ASIC resistant.

For a more in-depth discussion on ASIC-resistant hardware, see https: Another related economic issue, often pointed out by detractors of Bitcoin, is that the proof of work done in the Bitcoin network is essentially wasted effort. Miners spend 24 hours a day cranking out SHA or in more advanced implementations Scrypt computations with the hopes of producing a block that has a very low hash value, and ultimately all of this work has no value to society.

Traditional centralized networks, like Paypal and the credit card network, manage to get by without performing any proof of work computations at all, whereas in the Bitcoin ecosystem about a million US dollars of electricity and manufacturing effort is essentially wasted every day to prop up the network.

One way of solving the problem that many have proposed is making the proof of work function something which is simultaneously useful; a common candidate is something like Folding home, an existing program where users can download software onto their computers to simulate protein folding and provide researchers with a large supply of data to help them cure diseases.

The problem is, however, that Folding home is not "easy to verify"; verifying the someone did a Folding home computation correctly, and did not cut corners to maximize their rounds-per-second at the cost of making the result useless in actual research, takes as long as doing the computation oneself. If either an efficiently verifiable proof-of-computation for Folding home can be produced, or if we can find some other useful computation which is easy to verify, then cryptocurrency mining could actually become a huge boon to society, not only removing the objection that Bitcoin wastes "energy", but even being socially beneficial by providing a public good.

Note that there is one major concern with this approach that has been identified: If the useful PoW is useful in such a way that it is sometimes economically viable for certain very large entities to perform the computation even without the currency incentive, then those entities have an incentive to launch attacks against the network at no cost, since they would be performing the computations anyway. In practice, the overhead of making PoW verifiable may well introduce over 2x inefficiency unintentionally.

Another economic solution is to make the computation a "pure" public good such that no individual entity derives a significant benefit from it. Proposed solutions to this problem should include a rigorous analysis of this issue.

Another approach to solving the mining centralization problem is to abolish mining entirely, and move to some other mechanism for counting the weight of each node in the consensus. The most popular alternative under discussion to date is "proof of stake" - that is to say, instead of treating the consensus model as "one unit of CPU power, one vote" it becomes "one currency unit, one vote". At first glance, this algorithm has the basic required properties: However, this algorithm has one important flaw: In the event of a fork, whether the fork is accidental or a malicious attempt to rewrite history and reverse a transaction, the optimal strategy for any miner is to mine on every chain, so that the miner gets their reward no matter which fork wins.

Another problem to keep in mind is the issue of so-called "long-range attacks" - attacks where the miner attempts to start a fork not five or ten blocks behind the head of the main chain, as happens normally, but hundreds of thousands of blocks back.

If an algorithm is designed incorrectly, it may be possible for an attacker to start from that far back, and then mine billions of blocks into the future since no proof of work is required , and new users would not be able to tell that the blockchain with billions of blocks more is illegitimate.

This can generally be solved with timestamping, but special corner cases do tend to appear in overcomplicated designs. The Slasher algorithm, described here and implemented by Zack Hess as a proof-of-concept here , represents my own attempt at fixing the nothing-at-stake problem.

The core idea is that 1 the miners for each block are determined ahead of time, so in the event of a fork a miner will either have an opportunity to mine a given block on all chains or no chains, and 2 if a miner is caught signing two distinct blocks with the same block number they can be deprived of their reward. The algorithm is viable and effective, but it suffers from two flaws of unknown significance. First, if all of the miners for a given block learn each other's identities beforehand, they can meet up and collude to shut down the network.

Second, the nothing-at-stake problem remains for attacks going back more than blocks, although this is a smaller issue because such attacks would be very obvious and can automatically trigger warnings.

For a more in-depth discussion on proof of stake, see https: A third approach to the problem is to use a scarce computational resource other than computational power or currency. In this regard, the two main alternatives that have been proposed are storage and bandwidth. There is no way in principle to provide an after-the-fact cryptographic proof that bandwidth was given or used, so proof of bandwidth should most accurately be considered a subset of social proof, discussed in later problems, but proof of storage is something that certainly can be done computationally.

An advantage of proof-of-storage is that it is completely ASIC-resistant; the kind of storage that we have in hard drives is already close to optimal. The most simple algorithm for proving that you own a file with N blocks is to build a Merkle tree out of it, publish the root, and every k blocks publish a Merkle tree proof of the i th block where i is the previous block hash mod N. However, this algorithm is limited because it is only a simple building block, not a complete solution.

In order to turn this into a currency, one would need to determine which files are being stored, who stores whose files, to what extent and how the system should enforce redundancy, and if the files come from the users themselves how to prevent compression optimizations and long-range attacks. Currently, the latest work in this area are two projects called Permacoin and Torcoin, which solve some of the problems in proof of storage with two insights.

First, users should not be able to choose which files they store. Instead, files should be randomly selected based on their public key and users should be required to store ALL of the work assigned or else face a zero reward.

This idea, provided in the context of proof of bandwidth in the case of Torcoin, prevents attacks involving users only storing their own data. Second, a Lamport-like signature algorithm can be used that requires users to have their private key and store their file locally; as a result; uploading all of one's files to the cloud is no longer a viable strategy. This, to some degree, forces redundancy. However, the problem with Permacoin is that it leaves unclear what files should be stored; cryptocurrency issuance can theoretically pay for billions of dollars of work per year, but there is no single static archive whose storage is worth billions.

Ideally, the system would allow for new files to be added, and perhaps even allow users to upload their own files, but without introducing new vulnerabilities. The second part of cryptoeconomics, and the part where solutions are much less easy to verify and quantify, is of course the economics. Cryptocurrencies are not just cryptographic systems, they are also economic systems, and both kinds of security need to be taken into account.

Sometimes, cryptographic security may even be slightly compromised in favor of an economic approach - if a signature algorithm takes more effort to crack than one could gain from cracking it, that is often a reasonable substitute for true security.

At the same time, economic problems are also much more difficult to define. One cannot usually definitively know whether or not a problem has been solved without extensive experimentation, and the result will often depend on cultural factors or the other organizational and social structures used by the individuals involved. However, if the economic problems can be solved, the solutions may often have reach far beyond just cryptocurrency.

One of the main problems with Bitcoin is the issue of price volatility. The main economic reason behind this is that the supply of bitcoins is fixed, so its price is directly proportional to demand and therefore, by efficient market hypothesis, the expected discounted future demand , and demand is very unpredictable. It is not known if Bitcoin will be simply a niche payment method for transactions requiring a high degree of privacy, a replacement for Western Union, a mainstream consumer payment system or the reserve currency of the world, and the expected value of a bitcoin differs over a thousandfold between these various levels of adoption.

Furthermore, the utility of the Bitcoin protocol is heavily dependent on the movements of the Bitcoin price ie. To solve this problem, there are generally two paths that can be taken. The first is to have the network somehow detect its current level of economic usage, and have a supply function that automatically increases supply when usage increases. This reduces uncertainty; even though the expected future level of adoption of the protocol may have a variance of x, the circumstance where adoption increases x will also have x more supply and so the value of the currency will remain the same.

There is a problem that if usage decreases there is no way to remove units from circulation, but even still the lack of upward uncertainty should reduce upward volatility, and downward volatility would also naturally reduce because it is no longer bad news for the value of the currency when an opportunity for increased usage is suddenly removed.

Furthermore, in the long term the economy can be expected to grow, so the zero-supply-growth floor may not even ever be reached in practice. The problem is that measuring an economy in a secure way is a difficult problem. The most obvious metric that the system has access to is mining difficulty, but mining difficulty also goes up with Moore's law and in the short term with ASIC development, and there is no known way to estimate the impact of Moore's law alone and so the currency cannot know if its difficulty increased by 10x due to better hardware, a larger user volume or a combination of both.

Other metrics, such as transaction count, are potentially gameable by entities that want the supply to change in a particular direction generally, holders want a lower supply, miners want a higher supply. Another approach is to attempt to create a currency which tracks a specific asset, using some kind of incentive-compatible scheme likely based on the game-theoretic concept of Schelling points, to feed price information about the asset into the system in a decentralized way.

This could then be combined with a supply function mechanism as above, or it can be incorporated into a zero-total-supply currency system which uses debts collateralized with other cryptographic assets to offset its positive supply and thus gain the ability to grow and shrink with changes to usage in either direction.

The problem here is constructing the scheme in such a way that there is no incentive for entities to feed in false price information in order to increase or decrease the supply of the asset in their favor. One of the challenges in economic systems in general is the problem of "public goods".

In total, the social benefit is clear: However, the problem is that from the point of view of each individual person contributing does not make sense - whether or not you contribute has close to zero bearing on whether enough money will be collected, so everyone has the incentive to sit out and let everyone else throw their money in, with the result that no one does.

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