{"id":10,"date":"2026-04-10T20:08:15","date_gmt":"2026-04-10T20:08:15","guid":{"rendered":"https:\/\/qat-3.multilingualpress.syde.wpinfra.cloud\/?p=10"},"modified":"2026-04-10T20:08:15","modified_gmt":"2026-04-10T20:08:15","slug":"bitcoin-a-peer-to-peer-electronic-cash-system","status":"publish","type":"post","link":"https:\/\/qat-3.multilingualpress.syde.wpinfra.cloud\/it\/blog\/2026\/04\/10\/bitcoin-a-peer-to-peer-electronic-cash-system\/","title":{"rendered":"Bitcoin: A Peer-to-Peer Electronic Cash System"},"content":{"rendered":"\n

<\/a>author<\/p>\n\n\n\n

: Satoshi Nakamoto<\/p>\n\n\n\n

email<\/p>\n\n\n\n

: satoshin@gmx.com<\/a><\/p>\n\n\n\n

site<\/p>\n\n\n\n

: http:\/\/www.bitcoin.org\/<\/a><\/p>\n\n\n\n

Abstract.<\/strong> 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.<\/p>\n\n\n\n

Introduction<\/h2>\n\n\n\n

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<\/p>\n\n\n\n

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.<\/p>\n\n\n\n

Transactions<\/h2>\n\n\n\n

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.<\/p>\n\n\n\n

\"\"\/<\/figure>\n\n\n\n

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.<\/p>\n\n\n\n

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.<\/p>\n\n\n\n

Timestamp Server<\/h2>\n\n\n\n

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
timestamp includes the previous timestamp in its hash, forming a chain,
with each additional timestamp reinforcing the ones before it.<\/p>\n\n\n\n

\"\"\/<\/figure>\n\n\n\n

Proof-of-Work<\/h2>\n\n\n\n

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.<\/p>\n\n\n\n

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<\/p>\n\n\n\n

\"\"\/<\/figure>\n\n\n\n

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.<\/p>\n\n\n\n

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.<\/p>\n\n\n\n

Network<\/h2>\n\n\n\n

The steps to run the network are as follows:<\/p>\n\n\n\n

    \n
  1. New transactions are broadcast to all nodes.<\/li>\n\n\n\n
  2. Each node collects new transactions into a block.<\/li>\n\n\n\n
  3. Each node works on finding a difficult proof-of-work for its block.<\/li>\n\n\n\n
  4. When a node finds a proof-of-work, it broadcasts the block to all
    nodes.<\/li>\n\n\n\n
  5. Nodes accept the block only if all transactions in it are valid and
    not already spent.<\/li>\n\n\n\n
  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.<\/li>\n<\/ol>\n\n\n\n

    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.<\/p>\n\n\n\n

    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.<\/p>\n\n\n\n

    Incentive<\/h2>\n\n\n\n

    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.<\/p>\n\n\n\n

    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.<\/p>\n\n\n\n

    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.<\/p>\n\n\n\n

    Reclaiming Disk Space<\/h2>\n\n\n\n

    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][^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.<\/p>\n\n\n\n

    \"\"\/<\/figure>\n\n\n\n

    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.<\/p>\n\n\n\n

    Simplified Payment Verification<\/h2>\n\n\n\n

    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.<\/p>\n\n\n\n

    \"\"\/<\/figure>\n\n\n\n

    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.<\/p>\n\n\n\n

    Combining and Splitting Value<\/h2>\n\n\n\n

    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.<\/p>\n\n\n\n

    \"\"\/<\/figure>\n\n\n\n

    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.<\/p>\n\n\n\n

    Privacy<\/h2>\n\n\n\n

    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.<\/p>\n\n\n\n

    \"\"\/<\/figure>\n\n\n\n

    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.<\/p>\n\n\n\n

    Calculations<\/h2>\n\n\n\n

    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.<\/p>\n\n\n\n

    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.<\/p>\n\n\n\n

    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>\n\n\n\n

    | 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<\/p>\n\n\n\n

    $$\\begin{aligned}
    q_z =
    \\begin{cases}
    1 & \\text{if } p \\leqslant q\\
    \\left(q\/p\\right)^z & \\text{if } p > q
    \\end{cases}
    \\end{aligned}$$<\/p>\n\n\n\n

    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.<\/p>\n\n\n\n

    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<\/p>\n\n\n\n

    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.<\/p>\n\n\n\n

    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:<\/p>\n\n\n\n

    $$\\lambda = z \\frac{q}{p}$$<\/p>\n\n\n\n

    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:<\/p>\n\n\n\n

    $$\\begin{aligned}
    \\sum _{k=0}^\\infty \\frac{\\lambda ^k e^{-\\lambda}}{k!} \\cdot
    \\begin{cases}
    \\left(q\/p\\right)^{(z-p)} & \\text{if } k \\leqslant z \\
    1 & \\text{if } k > z
    \\end{cases}
    \\end{aligned}$$<\/p>\n\n\n\n

    Rearranging to avoid summing the infinite tail of the distribution…<\/p>\n\n\n\n

    $$1 – \\sum _{k=0}^z \\frac{\\lambda ^k e^{-\\lambda}}{k!} \\left(1 – \\left(q\/p\\right)^{(z-k)}\\right)$$<\/p>\n\n\n\n

    Converting to C code…<\/p>\n\n\n\n

    #include <math.h>\ndouble AttackerSuccessProbability(double q, int z)\n{\n    double p = 1.0 - q;\n    double lambda = z * (q \/ p);\n    double sum = 1.0;\n    int i, k;\n    for (k = 0; k <= z; k++)\n    {\n        double poisson = exp(-lambda);\n        for (i = 1; i <= k; i++)\n            poisson *= lambda \/ i;\n        sum -= poisson * (1 - pow(q \/ p, z - k));\n    }\n    return sum;\n}<\/code><\/pre>\n\n\n\n
    Running some results, we can see the probability drop off exponentially
    with z.<\/p>\n\n\n\n
    q=0.1\nz=0 P=1.0000000\nz=1 P=0.2045873\nz=2 P=0.0509779\nz=3 P=0.0131722\nz=4 P=0.0034552\nz=5 P=0.0009137\nz=6 P=0.0002428\nz=7 P=0.0000647\nz=8 P=0.0000173\nz=9 P=0.0000046\nz=10 P=0.0000012\n\nq=0.3\nz=0 P=1.0000000\nz=5 P=0.1773523\nz=10 P=0.0416605\nz=15 P=0.0101008\nz=20 P=0.0024804\nz=25 P=0.0006132\nz=30 P=0.0001522\nz=35 P=0.0000379\nz=40 P=0.0000095\nz=45 P=0.0000024\nz=50 P=0.0000006<\/code><\/pre>\n\n\n\n
    Solving for P less than 0.1%…<\/p>\n\n\n\n
    P \\< 0.001\nq=0.10 z=5\nq=0.15 z=8\nq=0.20 z=11\nq=0.25 z=15\nq=0.30 z=24\nq=0.35 z=41\nq=0.40 z=89\nq=0.45 z=340<\/code><\/pre>\n\n\n\n
    Conclusion<\/h2>\n\n\n\n
    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.<\/p>\n\n\n\n
    References<\/h2>\n\n\n\n
    [^1]: W. Dai, \\”b-money,\\” http:\/\/www.weidai.com\/bmoney.txt<\/a>, 1998.<\/p>\n\n\n\n
    [^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,
    May 1999.<\/p>\n\n\n\n
    [^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.<\/p>\n\n\n\n
    [^4]: D. Bayer, S. Haber, W.S. Stornetta, \\”Improving the efficiency
    and reliability of digital time-stamping,\\” In Sequences II:
    Methods in Communication, Security and Computer Science, pages
    329-334, 1993.<\/p>\n\n\n\n
    [^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.<\/p>\n\n\n\n
    [^6]: A. Back, \\”Hashcash – a denial of service counter-measure,\\”
    http:\/\/www.hashcash.org\/papers\/hashcash.pdf<\/a>, 2002.<\/p>\n\n\n\n
    [^7]: R.C. Merkle, \\”Protocols for public key cryptosystems,\\” In Proc.
    1980 Symposium on Security and Privacy, IEEE Computer Society, pages
    122-133, April 1980.<\/p>\n\n\n\n
    [^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,
    May 1999.<\/p>\n\n\n\n
    [^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.<\/p>\n\n\n\n
    [^10]: W. Feller, \\”An introduction to probability theory and its
    applications,\\” 1957.<\/p>\n","protected":false},"excerpt":{"rendered":"
    author : Satoshi Nakamoto email : satoshin@gmx.com site : http:\/\/www.bitcoin.org\/ Abstract. A purely peer-to-peer version of electronic cash wouldallow online payments to be sent directly from one party to anotherwithout going through a financial institution. Digital signaturesprovide part of the solution, but the main benefits are lost if atrusted third party is still required to… Continua a leggere Bitcoin: A Peer-to-Peer Electronic Cash System<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"editor_notices":[],"footnotes":""},"categories":[1],"tags":[],"class_list":["post-10","post","type-post","status-publish","format-standard","hentry","category-uncategorized","entry"],"acf":[],"yoast_head":"\nBitcoin: A Peer-to-Peer Electronic Cash System - italian site<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/qat-3.multilingualpress.syde.wpinfra.cloud\/it\/blog\/2026\/04\/10\/bitcoin-a-peer-to-peer-electronic-cash-system\/\" \/>\n<meta property=\"og:locale\" content=\"it_IT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Bitcoin: A Peer-to-Peer Electronic Cash System - italian site\" \/>\n<meta property=\"og:description\" content=\"author : Satoshi Nakamoto email : satoshin@gmx.com site : http:\/\/www.bitcoin.org\/ Abstract. A purely peer-to-peer version of electronic cash wouldallow online payments to be sent directly from one party to anotherwithout going through a financial institution. 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