pBitcoin A Peer-to-Peer Electronic Cash SystemSatoshi Nwww.bitcoin.orgAbstract. nbsp;A purely peer-to-peer version of electronic cash would allow online payments to be sent directly from one party to another without going through a financial institution. nbsp;Digital signatures provide part of the solution, but the main benefits are lost if a trusted third party is still required to prevent double-spending. We propose a solution to the double-spending problem using a peer-to-peer network. The network timestamps transactions by hashing them into an ongoing chain of hash-based proof-of-work, ing a record that cannot be changed without redoing the proof-of-work. nbsp;The longest chain not only serves as proof of the sequence of events witnessed, but proof that it came from the largest pool of CPU power. nbsp;As long as a majority of CPU power is controlled by nodes that are not cooperating to attack the network, they39;ll generate the longest chain and outpace attackers. nbsp;The network itself requires minimal structure. nbsp;Messages are broadcast on a best effort basis, and nodes can leave and rejoin the network at will, accepting the longest proof-of-work chain as proof of what happened while they were gone.1. IntroductionCommerce on the Internet has come to rely almost exclusively on financial institutions serving as trusted third parties to process electronic payments. nbsp;While the system works well enough for most nbsp;transactions, nbsp;it nbsp;still nbsp;suffers nbsp;from nbsp;the nbsp;inherent nbsp;weaknesses nbsp;of nbsp;the nbsp;trust nbsp;based nbsp;model. Completely non-reversible transactions are not really possible, since financial institutions cannot avoid nbsp;mediating nbsp;disputes. nbsp; The nbsp;cost nbsp;of nbsp;mediation nbsp;increases nbsp;transaction nbsp;costs, nbsp;limiting nbsp;the minimum practical transaction size and cutting off the possibility for small casual transactions, and there is a broader cost in the loss of ability to make non-reversible payments for non-reversible services. nbsp;With the possibility of reversal, the need for trust spreads. nbsp;Merchants must be wary of their customers, hassling them for more ination than they would otherwise need. A certain percentage of fraud is accepted as unavoidable. nbsp;These costs and payment uncertainties can be avoided in person by using physical currency, but no mechanism exists to make payments over a communications channel without a trusted party.What is needed is an electronic payment system based on cryptographic proof instead of trust, allowing any two willing parties to transact directly with each other without the need for a trusted third party. nbsp;Transactions that are computationally impractical to reverse would protect sellers from fraud, and routine escrow mechanisms could easily be implemented to protect buyers. nbsp;In this paper, we propose a solution to the double-spending problem using a peer-to-peer distributed timestamp server to generate computational proof of the chronological order of transactions. nbsp;The system nbsp;is nbsp;secure nbsp;as nbsp;long nbsp;as nbsp;honest nbsp;nodes nbsp;collectively nbsp;control nbsp;more nbsp;CPU nbsp;power nbsp;than nbsp;any cooperating group of attacker nodes.12. TransactionsWe define an electronic coin as a chain of digital signatures. nbsp;Each owner transfers the coin to the next by digitally signing a hash of the previous transaction and the public key of the next owner and adding these to the end of the coin. nbsp;A payee can verify the signatures to verify the chain of ownership.The problem of course is the payee can39;t verify that one of the owners did not double-spend the coin. nbsp;A common solution is to introduce a trusted central authority, or mint, that checks every transaction for double spending. nbsp;After each transaction, the coin must be returned to the mint to issue a new coin, and only coins issued directly from the mint are trusted not to be double-spent. The problem with this solution is that the fate of the entire money system depends on the company running the mint, with every transaction having to go through them, just like a bank.We need a way for the payee to know that the previous owners did not sign any earlier transactions. nbsp;For our purposes, the earliest transaction is the one that counts, so we don39;t care about later attempts to double-spend. nbsp;The only way to confirm the absence of a transaction is to be aware of all transactions. nbsp;In the mint based model, the mint was aware of all transactions and decided which arrived first. nbsp;To accomplish this without a trusted party, transactions must be publicly announced [1], and we need a system for participants to agree on a single history of the order in which they were received. nbsp;The payee needs proof that at the time of each transaction, the majority of nodes agreed it was the first received. 3. Timestamp ServerThe solution we propose begins with a timestamp server. nbsp;A timestamp server works by taking a hash nbsp;of a block of items nbsp;to nbsp;be timestamped nbsp;and nbsp;widely publishing nbsp;the hash, nbsp;such as nbsp;in nbsp;a newspaper or Usenet post [2-5]. nbsp;The timestamp proves that the data must have existed at the time, obviously, in order to get into the hash. nbsp;Each timestamp includes the previous timestamp in its hash, ing a chain, with each additional timestamp reinforcing the ones before it.2BlockItem Item ...HashBlockItem Item ...HashTransactionOwner 139;sPublic KeyOwner 039;sSignatureHashTransactionOwner 239;sPublic KeyOwner 139;sSignatureHashVerifyTransactionOwner 339;sPublic KeyOwner 239;sSignatureHashVerifyOwner 239;sPrivate KeyOwner 139;sPrivate KeySignSignOwner 339;sPrivate Key4. Proof-of-WorkTo implement a distributed timestamp server on a peer-to-peer basis, we will need to use a proof-of-work system similar to Adam Back39;s Hashcash [6], rather than newspaper or Usenet posts. The proof-of-work involves scanning for a value that when hashed, such as with SHA-256, the hash begins with a number of zero bits. nbsp;The average work required is exponential in the number of zero bits required and can be verified by cuting a single hash.For our timestamp network, we implement the proof-of-work by incrementing a nonce in the block until a value is found that gives the block39;s hash the required zero bits. nbsp;Once the CPU effort has been expended to make it satisfy the proof-of-work, the block cannot be changed without redoing the work. nbsp;As later blocks are chained after it, the work to change the block would include redoing all the blocks after it.The proof-of-work also solves the problem of determining representation in majority decision making. nbsp;If the majority were based on one-IP-address-one-vote, it could be subverted by anyone able nbsp;to nbsp;allocate nbsp;many nbsp;IPs. nbsp; Proof-of-work nbsp;is nbsp;essentially nbsp;one-CPU-one-vote. nbsp; The nbsp;majority decision is represented by the longest chain, which has the greatest proof-of-work effort invested in it. nbsp;If a majority of CPU power is controlled by honest nodes, the honest chain will grow the fastest and outpace any competing chains. nbsp;To modify a past block, an attacker would have to redo the proof-of-work of the block and all blocks after it and then catch up with and surpass the work of the honest nodes. nbsp;We will show later that the probability of a slower attacker catching up diminishes exponentially as subsequent blocks are added.To compensate for increasing hardware speed and varying interest in running nodes over time, the proof-of-work difficulty is determined by a moving average targeting an average number of blocks per hour. nbsp;If they39;re generated too fast, the difficulty increases.5. NetworkThe steps to run the network are as follows1 New transactions are broadcast to all nodes.2 Each node collects new transactions into a block. nbsp;3 Each node works on finding a difficult proof-of-work for its block.4 When a node finds a proof-of-work, it broadcasts the block to all nodes.5 Nodes accept the block only if all transactions in it are valid and not already spent.6 Nodes express their acceptance of the block by working on creating the next block in the chain, using the hash of the accepted block as the previous hash.Nodes always consider the longest chain to be the correct one and will keep working on extending it. nbsp;If two nodes broadcast different versions of the next block simultaneously, some nodes may receive one or the other first. nbsp;In that case, they work on the first one they received, but save the other branch in case it becomes longer. nbsp;The tie will be broken when the next proof-of-work is found and one branch becomes longer; the nodes that were working on the other branch will then switch to the longer one.3BlockPrev Hash NonceTx Tx ...BlockPrev Hash NonceTx Tx ...New transaction broadcasts do not necessarily need to reach all nodes. nbsp;As long as they reach many nodes, they will get into a block before long. nbsp;Block broadcasts are also tolerant of dropped messages. nbsp;If a node does not receive a block, it will request it when it receives the next block and realizes it missed one.6. IncentiveBy convention, the first transaction in a block is a special transaction that starts a new coin owned by the creator of the block. nbsp;This adds an incentive for nodes to support the network, and provides a way to initially distribute coins into circulation, since there is no central authority to issue them. The steady addition of a constant of amount of new coins is analogous to gold miners expending resources to add gold to circulation. nbsp;In our case, it is CPU time and electricity that is expended.The incentive can also be funded with transaction fees. nbsp;If the output value of a transaction is less than its value, the difference is a transaction fee that is added to the incentive value of the block nbsp;containing nbsp;the transaction. nbsp; Once nbsp;a nbsp;predetermined number of coins nbsp;have nbsp;entered circulation, the incentive can transition entirely to transaction fees and be completely inflation free.The incentive may help encourage nodes to stay honest. nbsp;If a greedy attacker is able to assemble more CPU power than all the honest nodes, he would have to choose between using it to defraud people by stealing back his payments, or using it to generate new coins. nbsp;He ought to find it more profitable to play by the rules, such rules that favour him with more new coins than everyone else combined, than to undermine the system and the validity of his own wealth.7. Reclaiming Disk SpaceOnce the latest transaction in a coin is buried under enough blocks, the spent transactions before it can be discarded to save disk space. nbsp;To facilitate this without breaking the block39;s hash, transactions are hashed in a Merkle Tree [7][2][5], with only the root included in the block39;s hash. Old blocks can then be compacted by stubbing off branches of the tree. nbsp;The interior hashes do not need to be stored.A block header with no transactions would be about 80 bytes. nbsp;If we suppose blocks are generated every 10 minutes, 80 bytes * 6 * 24 * 365 4.2MB per year. nbsp;With computer systems typically selling with 2GB of RAM as of 2008, and Moore39;s Law predicting current growth of 1.2GB per year, storage should not be a problem even if the block headers must be kept in memory.4BlockBlock Block Header Block HashPrev Hash NonceHash01Hash0 Hash1 Hash2 Hash3Hash23Root HashHash01Hash2Tx3Hash23Block Header Block HashRoot HashTransactions Hashed in a Merkle Tree After Pruning Tx0-2 from the BlockPrev Hash NonceHash3Tx0 Tx1 Tx2 Tx38. Simplified Payment VerificationIt is possible to verify payments without running a full network node. nbsp;A user only needs to keep a copy of the block headers of the longest proof-of-work chain, which he can get by querying network nodes until he39;s convinced he has the longest chain, and obtain the Merkle branch linking the transaction to the block it39;s timestamped in. nbsp;He can39;t check the transaction for himself, but by linking it to a place in the chain, he can see that a network node has accepted it, and blocks added after it further confirm the network has accepted it.As such, the verification is reliable as long as honest nodes control the network, but is more vulnerable if the network is overpowered by an attacker. nbsp;While network nodes can verify transactions for themselves, the simplified can be fooled by an attacker39;s fabricated transactions for as long as the attacker can continue to overpower the network. nbsp;One strategy to protect against this would be to accept alerts from network nodes when they detect an invalid block, prompting the user39;s nbsp;software to download the full nbsp;block and alerted transactions to confirm the inconsistency. nbsp;Businesses that receive frequent payments will probably still want to run their own nodes for more independent security and quicker verification.9. Combining and Splitting ValueAlthough it would be possible to handle coins individually, it would be unwieldy to make a separate transaction for every cent in a transfer. nbsp;To allow value to be split and combined, transactions contain multiple s and outputs. nbsp;Normally there will be either a single from a larger previous transaction or multiple s combining smaller amounts, and at most two outputs one for the payment, and one returning the change, if any, back to the sender. nbsp;It should be noted that fan-out, where a transaction depends on several transactions, and those transactions depend on many more, is not a problem here. nbsp;There is never the need to extract a complete standalone copy of a transaction39;s history.5TransactionIn...In Out...Hash01Hash2 Hash3Hash23Block HeaderMerkle RootPrev Hash NonceBlock HeaderMerkle RootPrev Hash NonceBlock HeaderMerkle RootPrev Hash NonceMerkle Branch for Tx3Longest Proof-of-Work ChainTx310. PrivacyThe traditional banking model achieves a level of privacy by limiting access to ination to the parties involved and the trusted third party. nbsp;The necessity to announce all transactions publicly precludes this , but privacy can still be maintained by breaking the flow of ination in another place by keeping public keys anonymous. nbsp;The public can see that someone is sending an amount to someone else, but without ination linking the transaction to anyone. nbsp;This is similar to the level of ination released by stock exchanges, where the time and size of individual trades, the quot;tapequot;, is made public, but without telling who the parties were.As an additional firewall, a new key pair should be used for each transaction to keep them from being linked to a common owner. nbsp;Some linking is still unavoidable with multi- transactions, which necessarily reveal that their s were owned by the same owner. nbsp;The risk is that if the owner of a key is revealed, linking could reveal other transactions that belonged to the same owner.11. CalculationsWe consider the scenario of an attacker trying to generate an alternate chain faster than the honest chain. nbsp;Even if this is accomplished, it does not throw the system open to arbitrary changes, such as creating value out of thin air or taking money that never belonged to the attacker. nbsp;Nodes are n/p