Bitcoin: A Peer-to-Peer Electronic Cash System

in #bitcoin6 years ago

Bitcoin: A Peer-to-Peer Electronic Cash System

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.
    1
  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.
    2
    Block
    Item Item ...
    Hash
    Block
    Item Item ...
    Hash
    Transaction
    Owner 1's
    Public Key
    Owner 0's
    Signature
    Hash
    Transaction
    Owner 2's
    Public Key
    Owner 1's
    Signature
    Hash
    Verify
    Transaction
    Owner 3's
    Public Key
    Owner 2's
    Signature
    Hash
    Verify
    Owner 2's
    Private Key
    Owner 1's
    Private Key
    Sign
    Sign
    Owner 3's
    Private Key
  4. Proof-of-Work
    To implement a distributed timestamp server on a peer-to-peer basis, we will need to use a proofof-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.
    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 proofof-work
    is found and one branch becomes longer; the nodes that were working on the other
    branch will then switch to the longer one.
    3
    Block
    Prev Hash Nonce
    Tx Tx ...
    Block
    Prev Hash Nonce
    Tx Tx ...
    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.
  1. 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.
  2. 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.
    4
    Block Block
    Block Header (Block Hash)
    Prev Hash Nonce
    Hash01
    Hash0 Hash1 Hash2 Hash3
    Hash23
    Root Hash
    Hash01
    Hash2
    Tx3
    Hash23
    Block Header (Block Hash)
    Root Hash
    Transactions Hashed in a Merkle Tree After Pruning Tx0-2 from the Block
    Prev Hash Nonce
    Hash3
    Tx0 Tx1 Tx2 Tx3
  3. 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.
  4. 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.
    5
    Transaction
    In
    ...
    In Out
    ...
    Hash01
    Hash2 Hash3
    Hash23
    Block Header
    Merkle Root
    Prev Hash Nonce
    Block Header
    Merkle Root
    Prev Hash Nonce
    Block Header
    Merkle Root
    Prev Hash Nonce
    Merkle Branch for Tx3
    Longest Proof-of-Work Chain
    Tx3
  5. 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.
  6. 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/ p
    z
    if pq}
    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:

    k=0


    k
    e
    −
    k!
    ⋅{
    q/ p
    z−k 
    if k≤z
    1 if kz}
    Rearranging to avoid summing the infinite tail of the distribution...
    1−∑
    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 z=89
    q=0.45 z=340
  7. 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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Bitcoin is a good service for payments exchange.

Good explanations, so thanks for this article.

You have shared valuable knowledge I also want to invest in bitcoin.This article will help me a lot.

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