Bitcoin: A Peer-to-Peer Electronic Cash
System
摘要
電子現金便用數字簽名允許支付一方不經過金融機構，利用網絡直接發送給另一方。但它仍然需要第三方來防止雙重支出。
本文提出了一個使用點對點網絡來解決雙重支出的方案。它是為毎次交易打上時間戳，再將其列成一個證明鏈。最長的鏈成了最可信的方案，因為它來自最大的CPU功率池。只要大多數CPU功率由誠實的節點控制，它們將防止攻擊者。建議中的方案簡單。節點可以自由加入或離開網絡，它將接受最長的工作證明鏈作交易保證。
引言
互聯網上經濟普及，但當中的問題是過份依賴金融機構作為第三方處理電子支付。
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 peer-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.
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 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
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 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.
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. 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.
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 [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
4. Proof-of-Work
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. 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. 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. 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..
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.
1）向所有節點知會新的交易。
2）每個節點將新的交易紀錄到一個區塊中。
3）每個節點分別為其區塊尋找一個複雜的「驗證機制」。
4）當一個節點滿足於其「驗證」時，它將這「驗證機制」廣播到所有節點。
5）只區塊中的所有交易都有效並且沒有重複支付時，其他節點才接受該區塊。
6）當節點接受一個區塊後，它們會在它之上建立另一個區塊，連成一條鍵，並將之前的區塊的“指纹”紀錄在新區塊內。
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.
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.
獎勵
按慣例，區塊中的第一個交易是一個特殊的交易，創造者可以得到一個新的硬幣。由於沒有央行，這作法增加了節點加入網絡的動機，並提供一種讓硬幣進入流通的方法。
新的硬幣數量的不斷增加與淘金者不斷增添黃金進入流通相似。在我們這種情況下，黃金就這是CPU時間和耗電量。交易費的支付也可以用來作獎勵。如果交易的輸出值小於輸入值，其交易費用差額當作獎勵加入該區塊。當一定數量的硬幣進入流通後，獎勵可以完全轉移到交易費用，做成沒有通貨膨脹現象。
獎勵有助於鼓勵節點誠實。如果一個貪婪的攻擊者能夠組裝比所有誠實節點更多的CPU電源，他可以選擇用它來產生新的硬幣，這會比來用它來竊取別人的硬幣更佳。這樣的規則有利於他獲得更多的新硬幣，而不是破壞系統和自己的財富。
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. 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 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. 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 smaller amounts, and at most two outputs: one for the
payment, and one returning the change, if any, back to the sender. 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.
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. 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.
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. 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 qz = probability the attacker
will ever catch up from z blocks behind qz={ 1 if p≤q q/ pz if pq} 6 Identities Transactions
Trusted Third Party Counterparty Public Identities Transactions Public New
Privacy Model Traditional Privacy Model 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. 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: =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: Σk =0 ∞ k e− k! ⋅{q/ p z−k if k≤z 1 if kz} Rearranging to avoid summing
the infinite tail of the distribution... 1−Σ k =0 z k e− k! 1−q/ p z−k Converting to C code... #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;
} 7 Running some results, we can see the probability drop off exponentially
with z. q=0.1 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 q=0.3 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 Solving for
P less than 0.1%... 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
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 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
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