2009 Bitcoin A Peer-to-Peer Electronic Cash System

文件名称: 2009 Bitcoin A Peer-to-Peer Electronic Cash System.pdf

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详细说明：Bitcoin: A Peer-to-Peer Electronic Cash System（Satoshi Nakamoto）4. Proof-of-Work To implement a distributed timestamp server on a pccr-to-pccr basis, we will nccd to use a proof- of-work system Similar to Adam Backs 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. 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 proof-of-work by incrementing a nonce in the block until a value is found that gives the block's hash the required zero bits. Once the CPu effort has been expended to make it satisfy the proof-of-work, 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 Prev Hash Nonce Prey Hash Nonce X T The proof-of-work also solves the problem of determining representation in majority decision making. If the majority were based on onc-IP-address-onc-votc, it could be subverted by anyone able to allocate many IPs. Proof-of-work is essentially one-CPU-one-vote. The majority decision is represented by the longest chain, which has the greatest proof-of-work 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 edo 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. 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. If theyre generated too fast, the difficulty increases 5. Network The steps to run the network are as follows 1)New transactions are broadcast to all nodes 2) Each node collects new transactions into a block 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. 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 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 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 block's hash transactions are hashed in a Merkle Tree [7[2][5], with only the root included in the block's 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) Block Header( Block Hash) Prey Hash Prey Hash Nonce Root ha Root hash Hash01 Hash23 Hash01 Hash23 Hash0; Hash1: Hash2: i Hash 3 Hash2 Hash Tx3 Transactions hashed in a merkle Tree After Pruning Tx0-2 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=4.2MB per year. With computer systems typically selling with 2GB of raM as of 2008, and Moore'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 8. Simplified Payment Verification It is possiblc to verify payments without running a full nctwork nodc. A uscr only nccds to keep a copy of the block headers of the longest proof-of-work chain, which he can get by queryin network nodes until he's convinced he has the longest chain, and obtain the merkle branch linking the transaction to the block it's timestamped in. He can'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 Longest Proof-of-Work Chain Block Header Block Header Block Header Prey hash Nonce Prey hash Nonce Prey hash Nonce Merkle Root Merkle root Merkle root Hash01 Hash 23 Merkle Branch for Tx3 Hash2iHash3 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 attacker's 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 user's 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 smallcr amounts, and at most two outputs: one for the payment, and one returning the change, if any, back to the sender Transaction Ou 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. There is never the need to extract a complete standalone copy of a transactions histor 10. Privacy The traditional banking modcl 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 Traditiona Privacy Model dentist。s Transactions Third Party Counterparty Public New Privacy model Identities Transaction! Public As an additional firewall, a new key pair should be used for cach transaction to kcep them from being linked to a common owner. Some linking is still unavoidable with multi-input 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 belc the same owner 11. Calculations We consider the scenario of an attacker trying to generate an alternate chain faster than the honest hain. 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 pay des will ccept a block containing them. an attacker can only try to change onc 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 lcad by +1, and the failure event is the attacker's chain bcing extended by onc block, reducing the gap by -1 The probability of an attacker catching up from a given deficit is analogous to a Gambler's 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 q2=probability the attacker will ever catch up from z blocks behind 1ifp≤q (iqlp) if p>q Given our assumption that p the probability drops exponentially as the number of blocks the attacker has to catch up with increases. With the odds against him. if he doesn't 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 can't 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 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 attacker's potential progress will be a poisson distribution with expected value q 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 /p)=k≤zl k! ifk> Rearranging to avoid summing the infinite tail of the distribution ∑^e(1-(q/p k! Converting to c code include double attacker SuccessProbability(double g, int z) doubl double lambda =z *(g, p) double sum =1.0: t i, ki for (k=0; k doub_e poisson =exp(-lambda)i poisson *= lambda /i Sun 1- pow(q/p,z-k)) et Running some results, we can see the probability drop off exponentially with z q P=1.00000C0 z=1P=0.2045873 P=0.0509779 P=0.0131722 P=0.0034552 P=0.0009137 P=0.0002428 P=0.0000647 P=0.0000173 9P=0.0000046 P=1.0000000 P=0.17 10P=0.041660 z=25P=0.0006132 30P=0.0001522 5P=0.0000379 40P=0.0000095 Z=45P=0.0000024 z=50P=0.0000006 Solving for P less than 0. 1% P<0.001 q=C.10 g-C. =C.20 C.25z=15 C.30 q=C.35z=4- 12. Conclusion We have proposed a system for electronic transactions without relving 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 double-spending. To solve this, we proposed a peer-to-peer network using proof-of-work 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 proof-of-work 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 References [iW.Dai,"b-money,"http://www.weidai.com/bmoney.txt,1998 [2] IL. Massias, X.S. Avila, and J -J. 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, w.S. Stornetta, "How to time-stamp a digital document, In Journal of cryptology, vol 3, no 2, pages99-111,1991 [4]D. Bayer, S. Haber, W.S. Stornetta, "Improving the efficiency and reliability of digital time-stamping, In Sequences / Methods in Communication, Security and Computer Science, pages 329-334, 1993 [5]S Haber, W.S. Stornetta, "Secure names for bit-strings, In Proceedings of the 4th ACM Conference on Computer and Communications Security, pages 28-35, April 1997 [6 A Back,"Hashcash-a denial of service counter-measure, http://www.hashcash.org/papers/hashcash.pdf2002 [7 R C Merkle, "Protocols for public key cryptosystems, "In Proc: 1980 Symposium un Securily anu Privacy, IEEE Computer Society, pages 122-133, April 1980 [8]w. Feller, "An introduction to probability theory and its applications, "1957

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