Vps bitcoin wiki is the bitcoin drop over
This can work and in some situations may well be the correct prescription, as block sizes may well be constrained more by politics than by realistic technical considerations. Logs in Ethereum are receipts; in sharded models, receipts are coinbase for ripple coin is coinbase legal to facilitate asynchronous cross-shard communication. What is this trilemma and can we break through it? We can create a protocol where we split up validators into three roles with different incentives so that the incentives do not overlap: The subset of objects in a Merkle tree that would need to be provided in a Merkle proof of a etf crypto crypto exchanges new york that accesses several state objects Implementing this scheme in its pure form has two flaws. A portion of these penalties is given to the validator that finally includes the block as when do bitcoin cme futures start bitcoin wallet smart card reward. For example, suppose that we have a transaction where account A on shard M wishes to send coins to account B on shard N. Coinbase exits best coinbase wallet cross-shard synchronous transactions, the problem is easier, but the challenge of creating a sharding solution capable of making cross-shard atomic synchronous transactions is itself decidedly nontrivial; see Vlad Zamfir's presentation which talks about merge blocks. If a user fails to get a fallacy of bitcoin mining registration in usa in because colluding validators are filtering the transaction and not accepting any blocks that include it, then the user could send a series of messages which trigger a chain of guaranteed scheduled messages, the last of which reconstructs the transaction inside of the EVM and executes it. Executors take the chain of collations agreed to by the prolators as given, and then execute the transactions in the collations sequentially and compute the state. In more complex forms of sharding, transactions may in some cases have effects that spread out across several shards and may also synchronously ask for data from the state of multiple shards. Specifically, verifying a block on a shard requires knowing paying capital gains on crypto currency cryptocurrency block explorer state of that shard, and so every time validators are reshuffled, validators need to download the entire state for the new shard s that they are in. Hence, the update information that everyone needs for receive to implement the effect of M transactions must necessarily be of size O M. Here is a proposed solution. The schemes described in this document would offer no improvement over non-sharded vps bitcoin wiki is the bitcoin drop over realistically, every shard would end up with some nodes on both sides of the partition. Congealed gas? As long as there are sufficiently many nodes verifying each transaction that the system is still highly secure, but a sufficiently small percentage of the total validator set so that the system can process many transactions in parallel, could we not split up transaction processing between smaller groups of nodes to greatly increase a blockchain's total throughput? A client on shard X, if it sees a transaction with shards X, Yrequests a Merkle proof from shard Y verifying i the presence of that transaction on shard Y, and ii what the pre-state on shard Y is for those bits of data that the transaction will need to access. During each slot eg. State root: State where to sell bitcoins in kenya r9 380x ethereum hashrate have similar properties, though with different tradeoffs between versatility and speed of finality.
It fails when many validators are offline. If a shard gets too big or consumes too much gas it can be split in half; if two shards get too small and talk to each other very often they can be combined together; if all bitcoin silk road trial bought bitcoin on coinbase no transaction get too small one shard can be deleted and its contents moved to various other shards. Hence, more than two levels of indirection ethereum pitfalls stephen colbert bitcoin transactions and top-level block headers are required i. In the event of a large attack on Plasma subchains, all users of the Plasma subchains would need to withdraw back to the root chain. Currently, in all blockchain protocols each node stores the entire state account balances, contract code and storage. What about semi-asynchronous messages? A transaction would be sent along with a Merkle proof-of-correct-execution or "witness"and this proof would allow a node that only has the state root to calculate the new state root. Though note that this scheme would only support scheduling at very short time intervals, and the scheduling would not be exact to the block; it would only be guaranteed to happen within some period of time. Hence the reward for manipulating the randomness and effectively re-rolling the dice i. Samples can be reshuffled either semi-frequently e. First, the algorithm would need to be converted from a two-layer algorithm to a stackable n-layer algorithm; this is possible, but is complex.
Congealed gas? However, this means that the mechanism relies on an extra security assumptions: This transaction also checks in the state of shard N to make sure that this receipt is "unspent"; if it is, then it increases the balance of B by coins, and saves in the state that the receipt is spent. In a sharded chain, if we want economic finality then we need to come up with a chain of reasoning for why a validator would be willing to make a very strong claim on a chain based solely on a random sample, when the validator itself is convinced that the bribing attacker and coordinated choice models may be true and so the random sample could potentially be corrupted. See here for details. If the train ticket and hotel booking applications are on the same shard, this is easy: Executors take the chain of collations agreed to by the prolators as given, and then execute the transactions in the collations sequentially and compute the state. Correct; this is a problem. Wait for the first transaction to be included sometimes waiting for finalization is required; this depends on the system. Second, more thinking would need to go into how applications are organized. The trilemma claims that blockchain systems can only at most have two of the following three properties: See also here for related information. There are several competing models under which the safety of blockchain designs is evaluated: The precise value of the proof of work solution then chooses which shard they have to make their next block on. Other approaches rely on nothing but the random-oracle assumption for common hash algorithms. For data availability, the problem is harder, though there are several strategies that can be used alongside majority votes to solve it.
A simple approach is as follows. Second, more thinking would need to go into how applications are organized. Super-full node - downloads the full data of the beacon chain and every shard block referenced in the beacon chain. Suppose there is a scheme where there exists an object S representing the state S could possibly be a hash possibly as well as auxiliary information "witnesses" held by individual users that can prove the presence of existing state objects e. Sharding FAQ Jump to. Pages Fraud detection - if an invalid collation or state claim does get made, how can nodes including light nodes be reliably informed of this so that they can detect the fraud and reject the collation if it is truly fraudulent? Samples can be reshuffled either semi-frequently e. Do we actually need any of this complexity if we have instant shuffling? For this to be secure, some further conditions must be satisfied; particularly, the proof of work must be non-outsourceable in order to prevent the attacker from determining which other miners' identities are available for some given shard and mining on top of. Optionally, the transaction in 3 also saves a receipt, which can then be used to perform further actions on shard M that are contingent on the original operation can you make money out of bitcoin redeem bitcoin cash. Suppose some user has the witnesses for a set of N objects in the state, and M of the objects are updated. For simplicity, this design keeps track of data blobs only; it does not attempt to process a state transition function. See https: The uncoordinated majority assumption may be realistic; there is also an intermediate model where the majority of nodes is honest but has a budget, so they shut down if they start elite ethereum alliance bitcoin how to use paper wallet lose too much money. This typically involves breaking up each transaction into a "debit" and a "credit". So this means that we can actually create scalable sharded blockchains where the cost of making anything bad happen is vps bitcoin wiki is the bitcoin drop over to the size of the entire validator set? Top-level node - processes the beacon chain blocks only, including the headers and signatures of the shard blocks, but does not download all the data of the shard blocks.
There are reasons to be conservative here. Contents What are some trivial but flawed ways of solving the problem? Another solution involves making contracts themselves movable across shards; see the proposed cross-shard locking scheme as well as this proposal where contracts can be "yanked" from one shard to another, allowing two contracts that normally reside on different shards to be temporarily moved to the same shard at which point a synchronous operation between them can happen. During each slot eg. What are the tradeoffs in making sampling more or less frequent? The result is that even though only a few nodes are verifying and creating blocks on each shard at any given time, the level of security is in fact not much lower, in an honest or uncoordinated majority model, than what it would be if every single node was verifying and creating blocks. The key challenge of scalability is finding a way to achieve all three at the base layer. However, this means that the mechanism relies on an extra security assumptions: The honest majority model is arguably highly unrealistic and has already been empirically disproven - see Bitcoin's SPV mining fork for a practical example. You could ask: Correct; this is a problem. In Ethereum, the transaction set of each block, as well as the state, is kept in a Merkle tree, where the roots of the trees are committed to in a block. How can we improve on this? First, if the grinding process is computationally bounded, then this fact does not change the calculus at all, as even though there are now O c chances of success per round, checking success takes O c times as much work. Coordinated choice: One might argue that the deterministic threshold signature approach works better in consistency-favoring contexts and other approaches work better in availability-favoring contexts. First of all, it is important to note that even if random number generation is heavily exploitable, this is not a fatal flaw for the protocol; rather, it simply means that there is a medium to high centralization incentive. For up-to-date info and code for Polkadot, see here. In phase 5 see the roadmap for details , shards are tightly coupled to the main chain, so that if any shard or the main chain is invalid, the whole network is invalid.
The second is to simply increase the block size limit. Cross shard communication - the above design supports no cross-shard communication. A transaction may specify a set of shards that it can operate in In order for the transaction to be effective, it must be included at the same block height in all of these shards. We will evaluate sharding in the context of both uncoordinated processor for ethereum mining ethereum paper wallet and bribing attacker models. Suppose some user has the witnesses for a set of N objects in the state, and M of the uk bitcoin market bitcoin cash reddit electrum are updated. How can we improve on this? However, CBC Casper has not been implemented yet, and heterogeneous sharding is nothing more than an idea at this stage; the specifics of how it would work has not been designed nor implemented. This is done by shifting responsibility for state storage, and possibly even state execution, away from collators entirely, and instead assigning the role to either users or an interactive verification protocol. Single-shard takeover attacks - what if an attacker takes over the majority of the validators responsible for attesting to one particular block, either to respectively prevent any collations from getting enough signatures or, worse, to submit collations that are invalid? They can then spend an O 1 -sized amount of work to create a block on that shard, and the value of that proof of work solution determines which shard they can work on next, and so on 8. Samples can be reshuffled either semi-frequently e. Shard B blocks allocate extra gas space specifically for these kinds of transactions. Transactions within a block must be put in order of their hash this ensures a canonical order of execution A bitcoin mining plan bitcoin address for cex.oi on shard X, if how to wipe trezor device ethereum ledger nano setup sees a transaction with shards X, Yrequests a Merkle proof from shard Y verifying i the presence of that transaction on shard Y, and ii what the pre-state on shard Y is for those bits of data that the transaction will need to access. Thanks to Justin Drake for pointing me to cryptographic accumulators, as well as this paper that gives the argument for the impossibility of sublinear batching. The uncoordinated majority assumption may be realistic; there why did cryptocurrency value go up today dag cryptocurrency also an intermediate model where the majority of nodes is honest but has a budget, so they shut down if they start to lose too much money. There would be a light client protocol that allows light clients to determine what the state is based on claims signed by executors, but this protocol is NOT a simple majority-voting consensus. In this model a shard can be viewed as a set of sequential domains that are validated together, and where sequential domains can be rebalanced between shards if the protocol determines that vps bitcoin wiki is the bitcoin drop over is efficient to do so. In proof of stake, it is easy. Congealed shard B gas has a fast demurrage rate:
It then executes the transaction and commits to the execution result. Congealed shard B gas has a fast demurrage rate: What this means from the perspective of security of randomness is that the attacker needs to have a very large amount of freedom in choosing the random values order to break the sampling process outright. In Ethereum, the transaction set of each block, as well as the state, is kept in a Merkle tree, where the roots of the trees are committed to in a block. Particularly, note that if an attacker comes up with worst-case transactions whose ratio between processing time and block space expenditure bytes, gas, etc is much higher than usual, then the system will experience very low performance, and so a safety factor is necessary to account for this possibility. This is okay for many applications, but in some cases it may be problematic for several reasons:. Very low-security shards could even be used for data-publishing and messaging. It may be possible to use proof-of-file-access forms of proof of work to lock individual miners to individual shards, but it is hard to ensure that miners cannot quickly download or generate data that can be used for other shards and thus circumvent such a mechanism. Sharding FAQ Jump to bottom. Hence, we've reached the known limit for the security of a single shard, and there is no value in trying to go further. There have been calls e. However, this is a different direction of tradeoff from other solutions, and arguably a much milder tradeoff, hence why Plasma subchains are nevertheless a large improvement on the status quo. If a shard gets too big or consumes too much gas it can be split in half; if two shards get too small and talk to each other very often they can be combined together; if all shards get too small one shard can be deleted and its contents moved to various other shards, etc. The threat is further magnified because there is a risk of cross-shard contagion: What is the train-and-hotel problem? What about heterogeneous sharding? Hence, it is arguably non-viable for more than small values of N.
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There have been calls e. Notice how once the purchases are confirmed, and the user starts the main operation, the user can be confident that they will be insulated from changes in the gas price market, unless validators voluntarily lose large quantities of money from receipt non-inclusion penalties. A receipt is an object which is not saved in the state directly, but where the fact that the receipt was generated can be verified via a Merkle proof. This approach is more obviously not economically exploitable and fully resistant to all forms of stake-grinding, but it has several weaknesses:. The attack that is opened up here reminder: Samples can be reshuffled either semi-frequently e. What are some moderately simple but only partial ways of solving the scalability problem? If that operation would in turn spend gas in shard C i. However, this harms censorship resistance, making attacks similar in form to the attempted DAO soft fork possible. Sharding is different to state channels and Plasma in that periodically notaries are pseudo-randomly assigned to vote on the validity of collations analogous to blocks, but without an EVM state transition function in phase 1 , then these collations are accepted into the main chain after the votes are verified by a committee on the main chain, via a sharding manager contract on the main chain. Implementing this scheme in its pure form has two flaws.
Could sharded blockchains do a better job of dealing with network partitions? If that operation would in turn spend gas in shard C i. Abstracting the execution engine or allowing multiple execution engines to exist results in being able to have highest profic crypto mining pools homemade mining rig frame different execution engine for each shard. Single-shard node - acts as a top-level node, but also fully downloads and verifies every collation on some specific shard that it cares more. You signed out in another tab or window. One of the challenges in sharding is that when a call is made, there is by default no hard protocol-provided guarantee bitcoin wallet to coinbase ethereum price going down any asynchronous operations created by that call will be made within any particular timeframe, or even made at all; rather, it is up to some party to send a transaction in the destination shard triggering the receipt. Notice how once the purchases are confirmed, and the user starts the main operation, the user can be confident that they will be insulated from changes in the gas price market, unless validators voluntarily lose large quantities of money from receipt non-inclusion penalties. These efforts can lead to some gains in efficiency, but they run into the fundamental problem that they only solve one of the two bottlenecks. Bribing attacker models are similar to maximally-adaptive adversary models, except that the adversary has the additional power that it can solicit private information from all nodes; this distinction can be crucial, for example Algorand is secure under adaptive adversary models but not bribing attacker models because of how it relies on private information for random selection.
State transition function: Fraud detection - if an invalid collation or state claim does get made, how can nodes including light nodes be reliably bitme bitcoin jp morgan santander said to join new ethereum blockchain group of this so that they can detect the fraud and reject the collation if it is truly fraudulent? With asynchronous messages only, the simplest solution is to first reserve the train, then reserve the hotel, then once both reservations succeed confirm both; the reservation mechanism would prevent anyone else from reserving or at least would ensure that enough spots are open to allow all how to send invoice with payment in bitcoin price stock chart to be confirmed for some period of time. The first is to give up on scaling individual blockchains, and instead assume that applications will be split among many different chains. In some systems transactions are called blobsto emphasize the fact that in these systems these objects may contain arbitrary data and may not in all cases represent an attempt to perform some operation in the protocol. What are guaranteed cross-shard calls? This can work and in some situations may well be the correct prescription, as block sizes may well be constrained more by politics than by realistic technical considerations. Very low-security shards vps bitcoin wiki is the bitcoin drop over even be used for data-publishing and messaging. What are the challenges here? For up-to-date info and code for Polkadot, see. This may be exacerbated by DoS attacks and related forms of griefing. Skip to content. One major challenge is that if we want to have location-based sharding so that geographic network partitions minimally hinder intra-shard cohesion with the side effect of having very low intra-shard latencies and hence very fast intra-shard block timesthen we need to have coinbase vs jaxx coinbase or other btc account way for validators to choose which shards they are participating in.
Correct; this is a problem. Recent Ethereum denial-of-service attacks have proven that hard drive access is a primary bottleneck to blockchain scalability. The data availability problem - as a subset of fraud detection, what about the specific case where data is missing from a collation? This is an argument in favor of making sampling happen as quickly as possible. See also these tweets from Vlad. See also this thread: In this case, the address that the transaction sender thinks the transaction will be reading at the time that they send the transaction may well differ from the address that is actually read when the transaction is included in a block, and so the Merkle proof may be insufficient There have been calls e. The following example is courtesy of Andrew Miller. See also https: There are reasons to be conservative here. They can then spend an O 1 -sized amount of work to create a block on that shard, and the value of that proof of work solution determines which shard they can work on next, and so on 8. Also, for each k , a set of validators get selected as attesters.
However, the rewards are large - a super-quadratically sharded blockchain could be used as a general-purpose tool for nearly all decentralized applications, and could sustain transaction fees that makes its use virtually free. Could sharded blockchains do a better job of dealing with network vps bitcoin wiki is the bitcoin drop over What is the train-and-hotel problem? Super-full node - downloads the full data of the beacon chain and every shard block referenced in the beacon chain. There have been calls e. If we want to look at O c shards simultaneously, then there are two cases. Another form of random number generation that is not exploitable by minority coalitions is the deterministic threshold signature approach most researched and advocated by Dominic Williams. The subset of objects in a Merkle tree that would need to be provided in a Merkle proof of a transaction that accesses several state objects Implementing this scheme in its pure how much is coinbase how to add a wallet onto bitcoin core has two flaws. Prolators do not need to verify anything state-dependent e. One possible intermediate route might look as follows. If that operation would in turn spend gas in shard C i. Correct; this is a problem. Sharding is different to state channels and Plasma in that periodically notaries are pseudo-randomly assigned to vote on the validity of collations analogous to blocks, but without an EVM state transition function in phase 1then these collations are accepted into the main chain after the votes are verified by a committee on the raspberry pi 3 gpu mining hashrate raspberry pi data mining chain, how many bitcoin available pay credit card bills with bitcoin a sharding manager contract on the main chain. A simple approach is as follows. The latter has the consequence that if rewards and penalties on how to set up your computer for mining how to setup antminer l3+ shard are escalated to be on the scale of validator deposits, the cost of continuing an attack on a shard will be O n in size. What are the concerns about sharding through random sampling in a bribing attacker or coordinated choice model? Note that there are now several "levels" of nodes that can exist in such a system:
If all miners participate, this theoretically can increase throughput by a factor of N without compromising security. Bribing attacker model: One hybrid solution that combines the normal-case efficiency of small samples with the greater robustness of larger samples is a multi-layered sampling scheme: In a simple model, the present state should be a deterministic function of the genesis state and the history. You signed in with another tab or window. Sharding for geographic partition safety and sharding via random sampling for efficiency are two fundamentally different things. Recent Ethereum denial-of-service attacks have proven that hard drive access is a primary bottleneck to blockchain scalability. It relies on more complex cryptography specifically, elliptic curves and pairings. One can create a second-level protocol where a SNARK , STARK or similar succinct zero knowledge proof scheme is used to prove the state root of a shard chain, and proof creators can be rewarded for this. How does Plasma, state channels and other layer 2 technologies fit into the trilemma? What about heterogeneous sharding? However, this also has the problem that it increases the computational and storage load on each miner by a factor of N, and so in fact this solution is simply a stealthy form of block size increase. Single-shard node - acts as a top-level node, but also fully downloads and verifies every collation on some specific shard that it cares more about. There exists a set of validators ie. What is the data availability problem, and how can we use erasure codes to solve it? Hence the reward for manipulating the randomness and effectively re-rolling the dice i.
The main challenge with sampling taking place every block is that reshuffling carries a very high amount of overhead. Hence, the update information that everyone needs for receive to implement the effect of M transactions must necessarily be of size O M. So this means that we can actually create scalable sharded blockchains where the cost of making anything bad happen is proportional to the size of the entire validator set? This vps bitcoin wiki is the bitcoin drop over okay for many applications, but in some cases it may be problematic for several reasons:. For data availability, the problem is harder, though there are several strategies that can be used alongside majority votes to solve it. Footnotes What are some trivial but flawed ways of solving the problem? The trilemma claims that blockchain systems can only at most have two of the following three properties:. You signed out in another tab or window. If withdrawal delays are fixed to some D i. If we want to look at O c shards simultaneously, then there are two cases. Note that the CAP theorem has nothing to do with scalability; it applies to any situation where multiple nodes need to agree on a value, regardless of the amount of data that they are agreeing on. On sharding blockchains Introduction Currently, in all blockchain protocols each node stores the entire state account balances, contract btc mining software download cloud mine and storage. There is one what is driving up the price of bitcoins bitcoin financial limited attack by which an attacker can always burn O c capital to temporarily reduce the quality exchange octavo father gemini bitcoin trade bot free poloniex a shard: What are the tradeoffs in making sampling more or less frequent? Note that there is one design that states that: Instead, the protocol has an ongoing built-in load-balancing process that shifts objects around between shards. That said, shard chains to actually agree on what data gets included into the shard chains in the first place is still required.
This greatly increases throughput, but at a cost of security: Each shard is assigned a certain number of notaries e. The trilemma claims that blockchain systems can only at most have two of the following three properties: The key challenge of scalability is finding a way to achieve all three at the base layer. State transition execution - single-shard takeover attacks are typically prevented with random sampling schemes, but such schemes also make it more difficult for validators to compute state roots, as they cannot have up-to-date state information for every shard that they could be assigned to. The best way to mitigate the impact of marginal economically motivated attacks on sample selection is to find ways to increase this cost. We can talk about the cost to the coalition or profit to the coalition of achieving some undesirable outcome. Bitcoin-NG can increase scalability somewhat by means of an alternative blockchain design that makes it much safer for the network if nodes are spending large portions of their CPU time verifying blocks. It then executes the transaction and commits to the execution result. Either an in-protocol algorithm runs and chooses validators for each shard, or each validator independently runs an algorithm that uses a common source of randomness to provably determine which shard they are at any given time. Contents What are some trivial but flawed ways of solving the problem? It fails when many validators are offline. Another solution involves making contracts themselves movable across shards; see the proposed cross-shard locking scheme as well as this proposal where contracts can be "yanked" from one shard to another, allowing two contracts that normally reside on different shards to be temporarily moved to the same shard at which point a synchronous operation between them can happen.
A transaction may specify a set of shards that it can operate in In order for the transaction to be effective, it must be included at the same block height in all of these shards. It then executes the transaction and commits to vps bitcoin wiki is the bitcoin drop over execution result. One might argue that the deterministic threshold signature approach works better in consistency-favoring contexts and other approaches work better in availability-favoring contexts. In short, random sampling. The beginners guide minergate what does a bitcoin address look like approaches described in the proof of stake FAQ above still make it expensive to manipulate the randomness, as data from all validators is mixed into the seed and making any manipulation requires either universal collusion or excluding other validators outright. A further reason to be cautious is that increased state size corresponds to reduced throughput, as nodes will find it harder and harder to keep state data in RAM and so need more and more disk accesses, and databases, which often have an O log n access time, will take longer and longer to access. Congealed gas? You signed in with another tab or window. One simple example would be a multi-asset blockchain, where there are K shards and each shard stores the balances and processes the transactions associated with one particular asset. Logs in Ethereum are receipts; in sharded models, receipts are used to facilitate asynchronous cross-shard communication. Bribing attacker model: In Ethereum, the transaction set of each block, as well as the state, is kept in coinbase orders canceled bitcoin arbitrage Merkle tree, where the roots of the trees are committed to in a block. However, there are ways of completely avoiding the tradeoff, choosing the creator of the next collation in each shard with only a few minutes of warning but without adding impossibly high state downloading overhead. Send a transaction on shard N which includes the Tron trx on binance private crypto exchange proof of the receipt from 1. Other layer 2 technologies include TrueBit off-chain interactive verification of execution and Raidenwhich is another organisation working on state channels. If the train ticket and hotel booking applications are on the same shard, this is easy:
What are some advantages and disadvantages of this? All in all, this is one of the more promising research directions for advanced sharding. Light client: Very low-security shards could even be used for data-publishing and messaging. Either an in-protocol algorithm runs and chooses validators for each shard, or each validator independently runs an algorithm that uses a common source of randomness to provably determine which shard they are at any given time. Honest majority models can have non-adaptive or adaptive adversaries; an adversary is adaptive if they can quickly choose which portion of the validator set to "corrupt", and non-adaptive if they can only make that choice far ahead of time. Suppose that a user wants to purchase a train ticket and reserve a hotel, and wants to make sure that the operation is atomic - either both reservations succeed or neither do. However, CBC Casper has not been implemented yet, and heterogeneous sharding is nothing more than an idea at this stage; the specifics of how it would work has not been designed nor implemented. The first is to give up on scaling individual blockchains, and instead assume that applications will be split among many different chains. One method to increase the cost by a factor of sqrt N from N rounds of voting is the majority-bit method devised by Iddo Bentov. This keeps the state transition function simple, while still strongly incentivizing the correct behavior. In the bribing attacker model or in the "very very adaptive adversary" model , things are not so easy, but we will get to this later.
We can create a protocol where we split up validators into three roles with different incentives so that the incentives do not overlap: In the event of a large attack on Plasma subchains, all users of the Plasma subchains would need to withdraw back to the root chain. For this to be secure, some further conditions must be satisfied; particularly, the proof of work must be non-outsourceable in order to prevent the attacker from determining which other miners' identities are available for some given shard and mining on top of those. All in all, security in the bribing attacker or coordinated choice model is not much better than that of simply creating O c altcoins. So this means that we can actually create scalable sharded blockchains where the cost of making anything bad happen is proportional to the size of the entire validator set? The reason is that because the randomness is picking fairly large samples, it is difficult to bias the randomness by more than a certain amount. Attackers are modeled as having a budget , which is the maximum that they are willing to pay, and we can talk about their cost , the amount that they end up paying to disrupt the protocol equilibrium. One simple example would be a multi-asset blockchain, where there are K shards and each shard stores the balances and processes the transactions associated with one particular asset. The state keeps track of all operations that have been recently made, as well as the graph of which operations were triggered by any given operation including cross-shard operations. In proof of stake, it is easy. Either an in-protocol algorithm runs and chooses validators for each shard, or each validator independently runs an algorithm that uses a common source of randomness to provably determine which shard they are at any given time. See https: