Blockchain orhpend blocks decrease mining profit
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Try out PMC Labs and tell us what you think. Learn More. Two double-spend attack strategies on a proof-of-stake consensus are considered. For each strategy, the probability of its success is obtained, which depends on the network parameters and the number of confirmation blocks.
These results can be used to define how many confirmation blocks a vendor should wait after a correspondent transaction before sending goods or services. Since Bitcoin launched in , blockchain systems and distributed ledger technologies have become popular, received widespread adoption, and attracted significant research effort [ 1 ].
They provide a great use case and have big advantages in environments that require no trust. That includes various financial applications DeFi , cryptocurrencies, different types of distributed registries, etc. The decentralized blockchain-based systems provide the common view on the history of transaction ledger, censorship resistance, and no single point of failure. Although, comparing to the centralized approach, a decentralized environment has much longer latencies on transaction confirmations.
As there is no central server s , the majority of network nodes in a trustless environment should receive a new transaction, validate it, and share that with other nodes, working in conditions with delayed message delivery over the network. Moreover, some part of network participants may be well coordinated by an adversary who attacks the system.
At the same time, honest nodes have no ability to discern the malicious behavior until an attack is finished with any result. Within such conditions, a distributed system user must decide whether she accepts the transaction and provides corresponding services or goods for the accepted value or she should wait for higher confirmation assurance or just reject the transaction. For many practical applications, such as on-line exchanges or retail, it is critical to minimize the confirmation time latency.
So, on given input parameters such as the adversarial ratio among all nodes reaching consensus , it is important to define concrete criterion regarding when a transaction may be secure and accepted with low risk and when it should be removed from the final history of the blockchain. Thus, the special case of persistence, as one of two major ledger properties [ 2 ], needs to be analyzed: the resistance to the double-spend attack. The essence of this attack does not depend on the type of consensus protocol.
Technically, it happens as follows. An adversary carries out some transaction in the block with number i , transferring coins to a supplier of goods for some purchase. The supplier receives those coins and accordingly supplies the goods to the buyer. The adversary also starts mining forging a different block with the same height i —that is, a block following the block with number i —1 , but one that either does not contain this transaction—or he transfers coins to another one of his own accounts.
If he succeeds in making the alternative chain longer, then exactly this chain, according to the consensus protocol, will be the one that is considered correct. Obviously, the larger the share kept by the adversary it is not essential whether is it computing power in the case of PoW or a share of a stake in the case of PoS , the higher chance his attack has of being successful.
A double-spend attack may seem to be very similar to a selfish mining attack, but they have two main differences. The second difference yields from the first one: in the double-spend attack, an adversary should keep his alternative branch in secret until the necessary number of confirmation blocks are created; therefore, he builds this chain only by himself, while in selfish mining, honest miners see the alternative chain and occasionally may maintain its creation.
In this work, we investigate only the security of the general model of PoS protocol against a double-spend attack under only one assumption, which is quite standard: the probability that the next block is generated by some stakeholder is proportional to its stake.
Our innovative contribution is that we for the first time obtain formulas for exact values of probability of a double-spend attack, unlike lots of previous papers, which give only asymptotic estimations of such probabilities or their upper bounds, which for some sets of parameters are trivial i.
However, nobody wants to wait an infinitely long time; the vendor wants to know exactly how many confirmation blocks he should wait to be sure with some predefined probability that transaction is irreversible. Our results are just for such case—for an arbitrary ratio of adversaries and numbers of confirmation blocks, the vendor can achieve the following:.
For a given number of confirmation blocks, calculate the probability that his transaction is irreversible; or. Set some desirable level of probability say, 0. A more detailed comparative analysis between our results and previous works will be given in the next section.
We also give a lot of examples of numerical results, which were obtained according our formulas, and corresponding graphs. They also confirm the correctness and practical benefits of the statements and formulas obtained in this work.
The first mention of a double-spend attack and its detailed description was made by Nakamoto in his historical paper [ 3 ]. To ensure protection against this attack in Bitcoin, Nakamoto proposed not to supply the goods as soon as the transaction occurred, but to wait for some time, more precisely for a number of confirmation blocks, and only then, if the transaction has not disappeared from the blockchain, to supply the goods.
In this case, the adversary cannot open his alternative chain immediately after the payment, as then the provider will see that the transaction disappears and then appears in the blockchain and thus reject the transaction. During this waiting period, he can try to seamlessly generate a fork that starts before the block with the transaction; that is, in our notations, he may generate an alternative i th block with the blocks to follow, but in no case does he share this alternative chain during the confirmation period, so that the supplier will not suspect anything bad.
This is the first stage of the attack. Suppose that while six confirmation blocks are being generated, the adversary was able to generate four blocks of the alternative chain. Now, he lags behind by at least two blocks. In particular, if he managed to generate seven or more blocks at the first stage of the attack while he waited for the confirmation blocks, then the attack was already successful: there is nothing to catch up.
Having received the goods, he simply presents his own longer chain, in which the money remains with him. Now, the next question is: how many confirmation blocks should the supplier wait? The answer to this question, given in [ 3 ] by Nakamoto and in [ 4 ] by Saleh, requires correction.
The assumptions made in [ 3 ] do not quite correspond to the real deployment model. The first assumption is that the time of generation of the block and the time of its appearance in the network coincide, so the block propagation delay is zero.
The second assumption states that the random variable, which is equal to the number of attempts that honest miners do to generate z confirmation blocks, where p is the probability of success, is replaced by its expectation z p. Due to these assumptions, the number of confirmation blocks in [ 3 ] is underestimated. After [ 3 ], the probability of a double-spending attack was analyzed in papers [ 6 , 7 ], which also have some lacks, including unproved statements.
For the first time, the problem gets a fully correct solution in [ 8 ], which is really wonderful from the mathematical point of view.
It was first proved in this paper, using special functions, that the fork probability decreases exponentially with the growth of the number of confirmation blocks. However, the authors of [ 8 ] could not and even did not try to get rid of the same assumption on the instantaneous propagation of the block in the network. The work [ 9 ] generalized the results obtained in [ 8 ]. In this work, for the first time in model with continuous time, without simplified assumptions about discrete timeslots , the author obtained and strictly proved the expression that gives the value of double-spend attack probability in dependence on network parameters, including network synchronization time.
Note that all these works [ 3 , 4 , 6 , 7 , 8 , 9 ] investigate proof-of-work consensus protocol, but there are still no analogical results for proof-of-stake [ 10 , 11 , 12 ]. However, consensus protocol proof-of-stake is much more preferable than proof-of-work from a lot of points of view.
The main problems that occur on block generation with PoW consensus are the following:. To solve these problems, as well as several other ones, a proof-of-stake-based approach was proposed.
The first provable secure PoS was presented in [ 13 ] as well as its next generations [ 14 , 15 , 16 , 17 ]. The main idea of PoS consensus is randomized slot leader selection; i. The probability to become a slot leader is proportional to the stake owned by the participant. A detailed description of PoS approaches is given in [ 13 , 14 , 15 , 16 , 17 , 18 , 19 ], as well as definitions, a model with strict formalizations, and security proofs.
For the first time, the rationale for the robustness of PoS protocol was given in [ 13 ] under the standard assumption that slot leaders are chosen among stakeholders with probabilities that are proportional to their stakes. To assure such an assumption, an Ouroboros protocol was proposed, which was modified and improved in the next papers [ 13 , 14 , 15 , 16 ]:.
Ouroboros Classic [ 13 ]—the first provable secure PoS consensus protocol;. Ouroboros Praos [ 14 ]—security against fully-adaptive corruption in the semi-synchronous model;.
Ouroboros Genesis [ 15 ]—security with a dynamic participation model;. Ouroboros Chronos [ 16 ]—a provable secure PoS consensus protocol that is independent of global time. Informally speaking, the deeper the block, the higher the probability that it is stable.
Most of the statements about block stabilization given in [ 13 ] are upper estimations of probabilities which sometimes turn out to be trivial for certain values of parameters or descriptions of their asymptotic behavior. Such results persuade us that the probability of block stabilization increases fast when the depth of the block increases, but it cannot be used to calculate the minimal number of confirmation blocks after which we are sure that the block is stable.
A lot of papers published every year analyze different additional properties and applications of PoS protocols. Among others, we can note [ 20 ], where the authors combine PoS protocol with secure BTC blockchain to obtain a consistent subchain; [ 21 ] analyzes the liveness of sidechains, built on PoS, using a special multisignature; [ 22 ] discusses PoS with a digital signature scheme that prevents the validators from creating multiple blocks at the same height; [ 23 ] considers two cases of smart-contracts of blockchain with PoS; [ 24 ] is also devoted to the use of smart-contracts on a private Ethereum blockchain.
These works analyze some special aspects of PoS security, but none of them give the answer on such a simple, practical, and specific question: how many confirmation blocks is enough to guaranty block stability with a given probability?
In our paper, we provide analytical estimations of a double-spend attack in the covert adversary model for an arbitrary version of Ouroboros protocol. Our estimations are strict not asymptotic , which allows using them to define a necessary number of transaction confirmation blocks that is sufficient to make the transaction irreversible with any given probability e. It is interesting that the estimations obtained in this work for PoS protocol are very close to the corresponding results for PoW protocols, which were firstly obtained with a full mathematical background in [ 8 ].
However, for obtaining such estimations, rather different probabilistic methods were used e. Our analytical estimations allowed obtaining concrete values of the confirmation of block numbers depending on system parameters including adversarial stake participating in consensus and building dependence diagrams for them.
In this section, we describe two possible strategies for the implementation of a double-spend attack. The first one is more universal; it is suitable for almost any consensus protocol. It was first proposed by Nakamoto in his historical work [ 3 ] for PoW consensus protocol. The second one is specific for the PoS and, may be, for some limited class of other protocol. If the adversary needs unreachable computational efforts to implement the attack with significant probability during some appropriate period of time, or if the probability of attack is negligible, we say that this object model, system process, etc.
In the model of a double-spend attack discussed in our work, we make some assumptions in favor of the adversary: we assume that he has unlimited time to implement the attack. It means that the vendor can reduce the probability of a double-spend attack to an arbitrarily small and negligible value, waiting for some certain number of confirmation blocks. In other words, in such a manner, we can achieve an arbitrarily large level of security of PoS protocol against a double-spend attack, even in the model when the adversary has unlimited time but a minority of stake.
In what follows, we will use the next designations. Then, the vendor waits until z blocks have been linked after this block to be sufficiently certain the sender cannot prune it. At the same time, the adversary sender wants to prune the block B i with his transaction and take money back. We will consider two different strategies of the adversary. The adversary does not form his blocks in his timeslots in the chain that honest miners build.
In this case, the adversary can form the alternative chain:. To find the probability for successful attack, we will use the random excursions model REM [ 12 ]. The event A k is just the event that after k confirmation blocks were built, at some moment, the adversary managed to build the longer chain using his timeslots.
We formulate this result as the next lemma. In designations 1 — 3 , let us define.
Mastering Bitcoin by
However, the creation of ad-hoc scripts to lock and unlock transactions allows for also generating non-standard transactions, which can be nevertheless broadcast and mined as well. In this work, we explore the Bitcoin block-chain with the purpose to analyze and classify standard and non-standard transactions, understanding how much the standard behavior is respected. Money transactions do not require a third-party intermediary, with no traditional financial-institution involved in transactions. Therefore, the Bitcoin network is completely decentralized, with all the transaction components performed by the users of the system.
Sometimes the reward for the found block can be lower than usual or there may be no reward at all. Are you interested in finding out why that happens? Then keep on reading, but make sure to read this article first. Every new block contains information about the previous block. No gaps are allowed. Number 1 is always followed by number 2 which is followed by 3 and then 4, and so on. This means that at that moment all miners worldwide are trying to solve the same block —
An Analysis of Non-standard Transactions
Since everyone would experience the orphaning, the difficulty will stabilize at a lower level and profitability should be the same. RustyRussell on Aug 1, [—]. No, you don't have an orphaning problem on your own blocks, so it drives centralization. This is exactly what happened when blocksize jumped from k to k: every small miner jumped to the largest pool ghash.
Optimal Selfish Mining Strategies in Bitcoin
Tron mining calculator. Look no further! To get started, just type in the amount of TRX in the left window; you will immediately see an estimate of its current value in USD. Default values are adapted for three cards. The Markets Insider currency calculator offers a currency conversion from Tron to DomRaider within seconds.
Bitcoins are still only accepted by a very small group of online merchants. This makes it unfeasible to completely rely on Bitcoins as a currency. There is nothing that can done to recover it. These coins will be forever orphaned in the system. This can bankrupt a wealthy Bitcoin investor within seconds with no way form of recovery.
Ethereum just activated a major change called the 'London hard fork' — here's why it's a big deal
There's also live online events, interactive content, certification prep materials, and more. Mining is the process by which new bitcoin is added to the money supply. Mining also serves to secure the bitcoin system against fraudulent transactions or transactions spending the same amount of bitcoin more than once, known as a double-spend.
Orphan BlockRELATED VIDEO: Crypto mining profit decrease explained
Ethereum 's much-hyped and somewhat controversial "London" hard fork has just activated. So far, news of the successful upgrade has coincided with a runup in the price of ether, the native token of ethereum's blockchain. A big part of the enthusiasm has to do with the fact that the software upgrade means a few big — and necessary — changes are coming to the code underpinning the world's second-biggest cryptocurrency. It has always been a tough go for ethereum users.
Blockchain Technologies: Probability of Double-Spend Attack on a Proof-of-Stake Consensus
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Orphan, Stale & Uncle Blocks in Bitcoin and Ethereum
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