File: blk03391.txt
c/Foundry USA Pool #dropgold/
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Mined by AntPool900J
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Hspamming bitcoin is the highest form of avant garde artistic expression
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<title>Bitcoin Face</title>
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<title>Bitcoin Face</title>
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Copyright (c) 1998 Hewlett-Packard Company
IEC http://www.iec.ch
IEC http://www.iec.ch
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Bitcoin: A Peer-to-Peer Electronic Cash System
==============================================
: Satoshi Nakamoto
: <satoshin@gmx.com>
: <http://www.bitcoin.org/>
**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-spM
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
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.
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
tions, 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 needM
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
ly 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 cM
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 M
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
We need a way for the payee to know that the previous owners did nM
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 whichM
they were received. The payee
needs proof that at the time of each transaction, the majority of nodes
agreed it was the first received.
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][^3][^4][^5]. The timestamp proves that the data must have
existed at the time, obviously, in order to get into the hash. Each
ncludes the previous timestamp in its hash, forming a chain,
with each additional timestamp reinforcing the ones before it.
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 reqM
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
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
ny 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 blocksM
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
5. Nodes accept the block only if all transactions in it are valid and
not already spent.
6. Nodes express their acceptance oM
f 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 fM
ound and one branch becomes longer; the
nodes that were working on the other branch will then switch to the
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 M
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
The incentive can also be funded with transaction fees. If the output
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 stealiM
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.
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
in a Merkle Tree[^7][^8][^9], 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
rage should not be a problem even if the block headers must
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 forM
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 continuM
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.
Combining and Splitting Value
-----------------------------
Although it would be possible to handle coins individuM
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
sactions, 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 aM
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 M
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.
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 belongedM
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,
educing 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[^10]:
| p = probability an honest node finds the next block
| q = probability the attacker finds the next block
robability the attacker will ever catch up from z blocks behind
1 & \text{if } p \leqslant q\\
\left(q/p\right)^z & \text{if } p > q
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 M
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 prM
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
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 bloM
average expected time per block, the attacker\'s potential progress will
be a Poisson distribution with expected value:
$$\lambda = z \frac{q}{p}$$
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:
\sum _{k=0}^\infty \frac{\lambda ^k e^{-\lambda}}{k!} \cdot
\left(q/p\right)^{(z-p)} & \text{if } k \leqslant z \\
& \text{if } k > z
Rearranging to avoid summing the infinite tail of the distribution\...
$$1 - \sum _{k=0}^z \frac{\lambda ^k e^{-\lambda}}{k!} \left(1 - \left(q/p\right)^{(z-k)}\right)$$
Converting to C code\...
double AttackerSuccessProbability(double q, int z)
double p = 1.0 - q;
double lambda = z * (q / p);
double sum = 1.0;
for (k = 0; k <= z; k++)
double poisson = exp(-lambda);
poisson *= lambda / i;
sum -= poisson * (1 - pow(q / p, z - k));
Running some results, we can see the probability drop off exponentially
z=10 P=0.0000012
z=10 P=0.0416605
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%\...
We have proposed a system for electronic transactions without relying on
trust. We started with the usual framework of coins made from digital
ch 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 particuM
lar 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.
[^1]: W. Dai, \"b-money,\" <http://www.weidai.com/bmoney.txM
[^2]: H. 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,
[^3]: S. Haber, W.S. Stornetta, \"How to time-stamp a digital
document,\" In Journal of Cryptology, vol 3, no 2, pages
99-111, 1991.
[^4]: D. Bayer, S. Haber, W.S. Stornetta, \"Improving the efficiency
and reliability of digital time-stamping,\" In Sequences IIM
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.pdf>, 2002.
[^7]: R.C. Merkle, \"Protocols for public key cryptosystems,\" In Proc.
1980 Symposium on SecurityM
and Privacy, IEEE Computer Society, pages
122-133, April 1980.
[^8]: H. 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,
[^9]: 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.
[^10]: W. Feller, \"An introduction to: probability theory and its
applications,\" 1957.
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Android RP1A.200720.012.F926BXXS1AUJB
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<title>Bitcoin Face</title>
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<title>Bitcoin Face</title>
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