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Bitcoin A PeertoPeer Electronic Cash System Satoshi Nakamoto satoshingmxcom wwwbitcoinorg Abstract A purely peertopeer version of electronic cash would allow online payments to be sent directly from one party to another without going through a financial institution Digital signatures provide part of the solution but the main benefits are lost if a trusted third party is still required to prevent doublespending We propose a solution to the doublespending problem using a peertopeer network The network timestamps transactions by hashing them into an ongoing chain of hashbased proofofwork forming a record that cannot be changed without redoing the proofofwork 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 As long as a majority of CPU power is controlled by nodes that are not cooperating to attack the network theyll generate the longest chain and outpace attackers The network itself requires minimal structure Messages are broadcast on a best effort basis and nodes can leave and rejoin the network at will accepting the longest proofofwork chain as proof of what happened while they were gone 1 Introduction Commerce on the Internet has come to rely almost exclusively on financial institutions serving as trusted third parties to process electronic payments While the system works well enough for most transactions it still suffers from the inherent weaknesses of the trust based model Completely nonreversible transactions are not really possible since financial institutions cannot avoid mediating disputes The cost of mediation increases transaction costs limiting 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 nonreversible payments for nonreversible services With the possibility of reversal the need for trust spreads Merchants must be wary of their customers hassling them for more information than they would otherwise need A certain percentage of fraud is accepted as unavoidable 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 Transactions that are computationally impractical to reverse would protect sellers from fraud and routine escrow mechanisms could easily be implemented to protect buyers In this paper we propose a solution to the doublespending problem using a peertopeer distributed timestamp server to generate computational proof of the chronological order of transactions The system is secure as long as honest nodes collectively control more CPU power than any cooperating group of attacker nodes 1 2 Transactions We define an electronic coin as a chain of digital signatures 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 A payee can verify the signatures to verify the chain of ownership Transaction Transaction Owner 1s Public Key Transaction Owner 2s Public Key Hash Owner 3s Public Key Hash Ver if Hash Ver ify y Owner 0s Signature Owner 1s Signature gn Si Owner 1s Private Key Owner 2s Signature Si gn Owner 2s Private Key Owner 3s Private Key The problem of course is the payee cant verify that one of the owners did not doublespend the coin A common solution is to introduce a trusted central authority or mint that checks every transaction for double spending 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 doublespent 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 For our purposes the earliest transaction is the one that counts so we dont care about later attempts to doublespend The only way to confirm the absence of a transaction is to be aware of all transactions In the mint based model the mint was aware of all transactions and decided which arrived first 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 The payee needs proof that at the time of each transaction the majority of nodes agreed it was the first received 3 Timestamp Server The solution we propose begins with a timestamp server A timestamp server works by taking a hash of a block of items to be timestamped and widely publishing the hash such as in a newspaper or Usenet post 25 The timestamp proves that the data must have existed at the time obviously in order to get into the hash Each timestamp includes the previous timestamp in its hash forming a chain with each additional timestamp reinforcing the ones before it Hash Hash Block Item Block Item Item 2 Item 4 ProofofWork To implement a distributed timestamp server on a peertopeer basis we will need to use a proofofwork system similar to Adam Backs Hashcash 6 rather than newspaper or Usenet posts The proofofwork involves scanning for a value that when hashed such as with SHA256 the hash begins with a number of zero bits The average work required is exponential in the number of zero bits required and can be verified by executing a single hash For our timestamp network we implement the proofofwork by incrementing a nonce in the block until a value is found that gives the blocks hash the required zero bits Once the CPU effort has been expended to make it satisfy the proofofwork the block cannot be changed without redoing the work As later blocks are chained after it the work to change the block would include redoing all the blocks after it Block Block Prev Hash Tx Nonce Tx Prev Hash Tx Tx Nonce The proofofwork also solves the problem of determining representation in majority decision making If the majority were based on oneIPaddressonevote it could be subverted by anyone able to allocate many IPs Proofofwork is essentially oneCPUonevote The majority decision is represented by the longest chain which has the greatest proofofwork effort invested in it If a majority of CPU power is controlled by honest nodes the honest chain will grow the fastest and outpace any competing chains To modify a past block an attacker would have to redo the proofofwork of the block and all blocks after it and then catch up with and surpass the work of the honest nodes 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 proofofwork difficulty is determined by a moving average targeting an average number of blocks per hour If theyre generated too fast the difficulty increases 5 Network The steps to run the network are as follows 1 2 3 4 5 6 New transactions are broadcast to all nodes Each node collects new transactions into a block Each node works on finding a difficult proofofwork for its block When a node finds a proofofwork it broadcasts the block to all nodes Nodes accept the block only if all transactions in it are valid and not already spent 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 If two nodes broadcast different versions of the next block simultaneously some nodes may receive one or the other first In that case they work on the first one they received but save the other branch in case it becomes longer The tie will be broken when the next proofofwork is found and one branch becomes longer the nodes that were working on the other branch will then switch to the longer one 3 New transaction broadcasts do not necessarily need to reach all nodes As long as they reach many nodes they will get into a block before long Block broadcasts are also tolerant of dropped messages If a node does not receive a block it will request it when it receives the next block and realizes it missed one 6 Incentive By convention the first transaction in a block is a special transaction that starts a new coin owned by the creator of the block 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 In our case it is CPU time and electricity that is expended The incentive can also be funded with transaction fees If the output value of a transaction is less than its input value the difference is a transaction fee that is added to the incentive value of the block containing the transaction Once a predetermined number of coins have entered circulation the incentive can transition entirely to transaction fees and be completely inflation free The incentive may help encourage nodes to stay honest 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 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 Space Once the latest transaction in a coin is buried under enough blocks the spent transactions before it can be discarded to save disk space To facilitate this without breaking the blocks hash transactions are hashed in a Merkle Tree 725 with only the root included in the blocks hash Old blocks can then be compacted by stubbing off branches of the tree The interior hashes do not need to be stored Block Block Block Header Block Hash Prev Hash Nonce Block Header Block Hash Prev Hash Root Hash Hash01 Nonce Root Hash Hash23 Hash0 Hash1 Hash2 Hash3 Tx0 Tx1 Tx2 Tx3 Hash01 Hash23 Hash2 Hash3 Tx3 Transactions Hashed in a Merkle Tree After Pruning Tx02 from the Block A block header with no transactions would be about 80 bytes If we suppose blocks are generated every 10 minutes 80 bytes 6 24 365 42MB per year With computer systems typically selling with 2GB of RAM as of 2008 and Moores Law predicting current growth of 12GB per year storage should not be a problem even if the block headers must be kept in memory 4 8 Simplified Payment Verification It is possible to verify payments without running a full network node A user only needs to keep a copy of the block headers of the longest proofofwork chain which he can get by querying network nodes until hes convinced he has the longest chain and obtain the Merkle branch linking the transaction to the block its timestamped in He cant 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 Longest ProofofWork Chain Block Header Prev Hash Block Header Nonce Block Header Prev Hash Merkle Root Nonce Prev Hash Merkle Root Hash01 Nonce Merkle Root Hash23 Merkle Branch for Tx3 Hash2 Hash3 Tx3 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 While network nodes can verify transactions for themselves the simplified method can be fooled by an attackers fabricated transactions for as long as the attacker can continue to overpower the network One strategy to protect against this would be to accept alerts from network nodes when they detect an invalid block prompting the users software to download the full block and alerted transactions to confirm the inconsistency 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 Value Although it would be possible to handle coins individually it would be unwieldy to make a separate transaction for every cent in a transfer To allow value to be split and combined transactions contain multiple inputs and outputs Normally there will be either a single input from a larger previous transaction or multiple inputs combining smaller amounts and at most two outputs one for the payment and one returning the change if any back to the sender Transaction In Out In It should be noted that fanout where a transaction depends on several transactions and those transactions depend on many more is not a problem here There is never the need to extract a complete standalone copy of a transactions history 5 10 Privacy The traditional banking model achieves a level of privacy by limiting access to information to the parties involved and the trusted third party The necessity to announce all transactions publicly precludes this method but privacy can still be maintained by breaking the flow of information in another place by keeping public keys anonymous The public can see that someone is sending an amount to someone else but without information linking the transaction to anyone This is similar to the level of information released by stock exchanges where the time and size of individual trades the tape is made public but without telling who the parties were Traditional Privacy Model Identities Transactions Trusted Third Party Counterparty Public New Privacy Model Identities Transactions Public As an additional firewall a new key pair should be used for each transaction to keep them from being linked to a common owner Some linking is still unavoidable with multiinput transactions which necessarily reveal that their inputs were owned by the same owner The risk is that if the owner of a key is revealed linking could reveal other transactions that belonged to the same owner 11 Calculations We consider the scenario of an attacker trying to generate an alternate chain faster than the honest chain 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 Nodes are not going to accept an invalid transaction as payment and honest nodes will never accept a block containing them An attacker can only try to change one of his own transactions to take back money he recently spent The race between the honest chain and an attacker chain can be characterized as a Binomial Random Walk The success event is the honest chain being extended by one block increasing its lead by 1 and the failure event is the attackers chain being extended by one block reducing the gap by 1 The probability of an attacker catching up from a given deficit is analogous to a Gamblers Ruin problem Suppose a gambler with unlimited credit starts at a deficit and plays potentially an infinite number of trials to try to reach breakeven We can calculate the probability he ever reaches breakeven or that an attacker ever catches up with the honest chain as follows 8 p probability an honest node finds the next block q probability the attacker finds the next block qz probability the attacker will ever catch up from z blocks behind q z 1 if pq z q p if pq 6 Given our assumption that p q the probability drops exponentially as the number of blocks the attacker has to catch up with increases With the odds against him if he doesnt make a lucky lunge forward early on his chances become vanishingly small as he falls further behind We now consider how long the recipient of a new transaction needs to wait before being sufficiently certain the sender cant change the transaction We assume the sender is an attacker who wants to make the recipient believe he paid him for a while then switch it to pay back to himself after some time has passed The receiver will be alerted when that happens but the sender hopes it will be too late The receiver generates a new key pair and gives the public key to the sender shortly before signing This prevents the sender from preparing a chain of blocks ahead of time by working on it continuously until he is lucky enough to get far enough ahead then executing the transaction at that moment Once the transaction is sent the dishonest sender starts working in secret on a parallel chain containing an alternate version of his transaction The recipient waits until the transaction has been added to a block and z blocks have been linked after it He doesnt know the exact amount of progress the attacker has made but assuming the honest blocks took the average expected time per block the attackers potential progress will be a Poisson distribution with expected value z q p To get the probability the attacker could still catch up now we multiply the Poisson density for each amount of progress he could have made by the probability he could catch up from that point k zk if k z ke q p1 if k z k 0 Rearranging to avoid summing the infinite tail of the distribution z 1 k 0 k e 1q p z k k Converting to C code include mathh double AttackerSuccessProbabilitydouble q int z double p 10 q double lambda z q p double sum 10 int i k for k 0 k z k double poisson explambda for i 1 i k i poisson lambda i sum poisson 1 powq p z k return sum 7 Running some results we can see the probability drop off exponentially with z q01 z0 z1 z2 z3 z4 z5 z6 z7 z8 z9 z10 P10000000 P02045873 P00509779 P00131722 P00034552 P00009137 P00002428 P00000647 P00000173 P00000046 P00000012 q03 z0 z5 z10 z15 z20 z25 z30 z35 z40 z45 z50 P10000000 P01773523 P00416605 P00101008 P00024804 P00006132 P00001522 P00000379 P00000095 P00000024 P00000006 Solving for P less than 01 P 0001 q010 z5 q015 z8 q020 z11 q025 z15 q030 z24 q035 z41 q040 z89 q045 z340 12 Conclusion We have proposed a system for electronic transactions without relying on trust We started with the usual framework of coins made from digital signatures which provides strong control of ownership but is incomplete without a way to prevent doublespending To solve this we proposed a peertopeer network using proofofwork to record a public history of transactions that quickly becomes computationally impractical for an attacker to change if honest nodes control a majority of CPU power The network is robust in its unstructured simplicity Nodes work all at once with little coordination They do not need to be identified since messages are not routed to any particular place and only need to be delivered on a best effort basis Nodes can leave and rejoin the network at will accepting the proofofwork chain as proof of what happened while they were gone They vote with their CPU power expressing their acceptance of valid blocks by working on extending them and rejecting invalid blocks by refusing to work on them Any needed rules and incentives can be enforced with this consensus mechanism 8 References 1 W Dai bmoney httpwwwweidaicombmoneytxt 1998 2 H Massias XS Avila and JJ Quisquater Design of a secure timestamping service with minimal trust requirements In 20th Symposium on Information Theory in the Benelux May 1999 3 S Haber WS Stornetta How to timestamp a digital document In Journal of Cryptology vol 3 no 2 pages 99111 1991 4 D Bayer S Haber WS Stornetta Improving the efficiency and reliability of digital timestamping In Sequences II Methods in Communication Security and Computer Science pages 329334 1993 5 S Haber WS Stornetta Secure 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