Abstract. 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. 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 p eer-to-peer network. The network timestamps transactions by hashing them into an ongoing chain of hash-based proof-of-work, forming a record that cannot be changed without redoing the proof-of-work. 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, they’ll 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 proof-of-work chain as proof of what happened while they were gone.

[摘要]:本文提出了一种完全通过点对点技术实现的电子现金系统,它使得在线支付能够直接由一方发起并支付给另外一方,中间不需要通过任何的金融机构。虽然数字签名部分解决了这个问题,但是如果仍然需要第三方的支持才能防止双重支付的话,那么这种系统也就失去了存在的价值。我们在此提出一种解决方案,使现金系统在点对点的环境下运行,并防止双重支付问题。该网络通过随机散列对全部交易加上时间戳,将它们合并入一个不断延伸的基于随机散列的工作量证明的链条作为交易记录,除非重新完成全部的工作量证明,形成的交易记录将不可更改。最长的链条不仅将作为被观察到的事件序列的证明,而且被看做是来自 CPU 计算能力最大的池。只要大多数的 CPU 计算能力都没有打算合作起来对全网进行攻击,那么诚实的节点将会生成最长的、超过攻击者的链条。这个系统本身需要的基础设施非常少。信息尽最大努力在全网传播即可,节点可以随时离开和重新加入网络,并将最长的工作量证明链条作为在该节点离线期间发生的交易的证明。

1、简介 (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 non-reversible 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 non-reversible payments for non- reversible 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 double-spending problem using a peer-to-peer 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.



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.

我们定义,一枚电子货币是这样的一串数字签名:每一位所有者通过对前一次交易和下一位拥有者的公钥签署一个随机散列的数字签名,并将这个签名附加在这枚电子货币的末尾,电子货币就发送给了下一位所有者。而收款人通过对签名进行检验,就能够验证该链条的所有者。 alt text

The problem of course is the payee can’t verify that one of the owners did not double-spend 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 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. For our purposes, the earliest transaction is the one that counts, so we don’t care about later attempts to double-spend. 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.

我们需要收款人有某种方法,能够确保之前的所有者没有对更早发生的交易实施签名。从逻辑上看,为了达到目的,实际上我们需要关注的只是于本交易之前发生的交易,而不需要关注这笔交易发生之后是否会有双重支付的尝试。为了确保某一次交易是不存在的,那么唯一的方法就是获悉之前发生过的所有交易。在造币厂模型里面,造币厂获悉所有的交易,并且决定了交易完成的先后顺序。如果想要在电子系统中排除第三方中介机构,那么交易信息就应当被公开宣布[1] ,我们需要整个系统内的所有参与者,都有唯一公认的历史交易序列。收款人需要确保在交易期间绝大多数的节点都认同该交易是首次出现。

3、时间戳服务器(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 [2-5]. 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.

本解决方案首先提出一个“时间戳服务器”。时间戳服务器通过对以区块(block)形式存在的一组数据实施随机散列而加上时间戳,并将该随机散列进行广播,就像在新闻或世界性新闻组网络的发帖一样[2-5] 。显然,该时间戳能够证实特定数据必然于某特定时间是的确存在的,因为只有在该时刻存在了才能获取相应的随机散列值。每个时间戳应当将前一个时间戳纳入其随机散列值中,每一个随后的时间戳都对之前的一个时间戳进行增强,这样就形成了一个链条。

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To implement a distributed timestamp server on a peer-to-peer basis, we will need to use a proof- of-work system similar to Adam Back’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. The average work required is exponential in the number of zero bits required and can be verified by executing a single hash.

为了在点对点的基础上构建一组分散化的时间戳服务器,仅仅像报纸或世界性新闻网络组一样工作是不够的,我们还需要一个类似于亚当•柏克提出的哈希现金[6]。在进行随机散列运算时,工作量证明机制引入了对某一个特定值的扫描工作,比方说 SHA-256 下,随机散列值以一个或多个 0 开始。那么随着 0 的数目的上升, 找到这个解所需要的工作量将呈指数增长,而对结果进行检验则仅需要一次随机散列运算。

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.

我们在区块中补增一个随机数 (Nonce),这个随机数要使得该给定区块的随机散列值出现了所需的那么多个 0。我们通过反复尝试来找到这个随机数,直到找到为止,这样我们就构建了一个工作量证明机制。只要该 CPU 耗费的工作量能够满足该工作量证明机制,那么除非重新完成相当的工作量,该区块的信息就不可更改。由于之后的区块是链接在该区块之后的,所以想要更改该区块中的信息,就还需要重新完成之后所有区块的全部工作量。

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The proof-of-work also solves the problem of determining representation in majority decision making. If the majority were based on one-IP-address-one-vote, 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 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. We will show later that the probability of a slower attacker catching up diminishes exponentially as subsequent blocks are added.

同时,该工作量证明机制还解决了在集体投票表决时,谁是大多数的问题。如果决定大多数的方式是基于 IP 地址的,一 IP 地址一票,那么如果有人拥有分配大量 IP 地址的权力,则该机制就被破坏了。而工作量证明机制的本质则是一 CPU 一票。“大多数”的决定表达为最长的链,因为最长的链包含了最大的工作量。如果大多数的 CPU 为诚实的节点控制,那么诚实的链条将以最快的速度延长,并超越其他的竞争链条。如果想要对业已出现的区块进行修改,攻击者必须重新完成该区块的工作量外加该区块之后所有区块的工作量,并最终赶上和超越诚实节点的工作量。我们将在后文证明,设想一个较慢的攻击者试图赶上随后的区块,那么其成功概率将呈指数化递减。

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 they’re generated too fast, the difficulty increases.



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.


1) 新的交易向全网进行广播;

2) 每一个节点都将收到的交易信息纳入一个区块中;

3) 每个节点都尝试在自己的区块中找到一个具有足够难度的工作量证明;

4) 当一个节点找到了一个工作量证明,它就向全网进行广播;

5) 当且仅当包含在该区块中的所有交易都是有效的且之前未存在过的,其他节点才认同该区块的有效性;

6) 其他节点表示他们接受该区块,而表示接受的方法,则是在跟随该区块的末尾,制造新的区块以延长该链条,而将被接受区块的随机散列值视为先于新区快的随机散列值。

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.



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.

激励系统也有助于鼓励节点保持诚实。如果有一个贪婪的攻击者能够调集比所有诚实节点加起来还要多的 CPU 计算力,那么他就面临一个选择:要么将其用于诚实工作产生新的电子货币,或者将其用于进行二次支付攻击。那么他就会发现,按照规则行事、诚实工作是更有利可图的。因为该等规则使得他能够拥有更多的电子货币,而不是破坏这个系统使得其自身财富的有效性受损。

7、回收硬盘空间(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.

如果最近的交易已经被纳入了足够多的区块之中,那么就可以丢弃该交易之前的数据,以回收硬盘空间。为了同时确保不损害区块的随机散列值,交易信息被随机散列时,被构建成一种Merkle树 [7] 的形态,使得只有根(root)被纳入了区块的随机散列值。通过将该树(tree)的分支拔除(stubbing)的方法,老区块就能被压缩。而内部的随机散列值是不必保存的。

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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.

不含交易信息的区块头(Block header)大小仅有80字节。如果我们设定区块生成的速率为每10分钟一个,那么每一年产生的数据位4.2MB。(80 bytes * 6 * 24 * 365 = 4.2MB)。2008年,PC系统通常的内存容量为2GB,按照摩尔定律的预言,即使将全部的区块头存储于内存之中都不是问题。

8、简化的支付确认(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 proof-of-work chain, which he can get by querying 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.

在不运行完整网络节点的情况下,也能够对支付进行检验。一个用户需要保留最长的工作量证明链条的区块头的拷贝,它可以不断向网络发起询问,直到它确信自己拥有最长的链条,并能够通过 merkle 的分支通向它被加上时间戳并纳入区块的那次交易。节点想要自行检验该交易的有效性原本是不可能的,但通过追溯到链条的某个位置,它就能看到某个节点曾经接受过它,并且于其后追加的区块也进一步证明全网曾经接受了它。

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、价值的组合与分割(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.


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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 transaction’s history.



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.


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 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 belonged to the same owner.


计算 (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 attacker’s chain being extended by one block, reducing the gap by -1.

诚实链条和攻击者链条之间的竞赛,可以用二叉树随机漫步来描述。成功事件定义为诚实链条延长了一个区块,使其领先性 + 1,而失败事件则是攻击者的链条被延长了一个区块,使得差距 - 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]:

攻击者成功填补某一既定差距的可能性,可以近似地看做赌徒破产问题。假定一个赌徒拥有无限的透支信用,然后开始进行潜在次数为无穷的赌博,试图填补上自己的亏空。那么我们可以计算他填补上亏空的概率,也就是该攻击者赶上诚实链条,如下所示[8] :

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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 doesn’t make a lucky lunge forward early on, his chances become vanishingly small as he falls further behind.

假定 p > q,那么攻击成功的概率就因为区块数的增长而呈现指数化下降。由于概率是攻击者的敌人,如果他不能幸运且快速地获得成功,那么他获得成功的机会随着时间的流逝就变得愈发渺茫。

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 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 doesn’t 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:


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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:


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Rearranging to avoid summing the infinite tail of the distribution…


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   #include <math.h>
   double AttackerSuccessProbability(double q, int z)
       double p = 1.0 - q;
       double lambda = z * (q / p);
       double sum = 1.0;
       int i, k;
       for (k = 0; k <= z; k++)
           double poisson = exp(-lambda);
           for (i = 1; i <= k; i++)
               poisson *= lambda / i;
           sum -= poisson * (1 - pow(q / p, z - k));
		return sum;


   z=0    P=1.0000000
   z=1    P=0.2045873
   z=2    P=0.0509779
   z=3    P=0.0131722
   z=4    P=0.0034552
   z=5    P=0.0009137
   z=6    P=0.0002428
   z=7    P=0.0000647
   z=8    P=0.0000173
   z=9    P=0.0000046
   z=10   P=0.0000012

   z=0    P=1.0000000
   z=5    P=0.1773523
   z=10   P=0.0416605
   z=15   P=0.0101008
   z=20   P=0.0024804
   z=25   P=0.0006132
   z=30   P=0.0001522
   z=35   P=0.0000379
   z=40   P=0.0000095
   z=45   P=0.0000024
   z=50   P=0.0000006

求解令 P<0.1% 的 z 值:

   P < 0.001
   q=0.10   z=5
   q=0.15   z=8
   q=0.20   z=11
   q=0.25   z=15
   q=0.30   z=24
   q=0.35   z=41
   q=0.40   z=89
   q=0.45   z=340


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 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.