The Original Bitcoin White Paper by Satoshi Nakamoto

Bitcoin: A Peer-to-Peer Electronic Cash System
by Satoshi Nakamoto 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 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. 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, 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. 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, 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. 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,
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. 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 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: And here there’s some mathematics which you
can look at at p=probability an honest node finds the next
block q1=probability the attacker finds the next
block qz=probability the attacker will ever catch
up from z blocks behind 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: And here you can check the document, and realize
with the equations and c code you will find that the probability becomes enormously tiny. 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. This is Stefan Molyneux from Freedomain Radio
and I hope this has been very helpful, and I encourage you to explore this very exciting
world, of shared database information.

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