Why did a nine-page paper on electronic cash, sent to a cryptography mailing list in 2008, spark a global financial revolution? The Bitcoin Whitepaper by Satoshi Nakamoto challenged traditional finance by proposing a purely peer-to-peer (P2P) currency model that operates without intermediaries. This “trustless” digital money model was groundbreaking, offering a decentralized alternative to banks and centralized institutions. Today, Bitcoin’s whitepaper is regarded as a pioneering document that laid the foundation for cryptocurrencies and decentralized finance (DeFi). In this lesson, we’ll analyze the mechanics and principles of Bitcoin as presented in the whitepaper, while exploring how these ideas have redefined finance and prompted the rise of an entire crypto ecosystem. This critical exploration aligns with our CFIRE program’s mission to equip learners with a deep understanding of the concepts reshaping modern finance.
Bitcoin is more than just “digital money”; it’s a response to the inefficiencies and risks of traditional banking. The whitepaper opens with Satoshi’s assertion that Bitcoin can solve what he calls the “double-spending problem” without needing a trusted intermediary. He then explains Bitcoin’s P2P network, the importance of cryptographic proof, and how miners—individuals or entities validating transactions—play a role in Bitcoin’s decentralized security model. Through this design, transactions can be verified without relying on banks, and users maintain control over their funds via private keys. Nakamoto’s arguments provide a blueprint for a self-sustaining currency model, powered by incentives and consensus among network participants rather than centralized oversight. Each section of the whitepaper addresses a core component of this model, from transaction mechanics to mining incentives, bringing together technical rigor and an ideological stance on decentralization.
Decentralization as a Foundational Principle
Nakamoto’s decentralized approach challenged a core assumption in finance: the need for centralized intermediaries. By removing banks from the process, Bitcoin creates a more accessible, censorship-resistant system. This shift has empowered people globally who lack access to traditional banking and finance, and it’s particularly impactful in regions with unstable banking systems or high inflation.
Proof of Work (PoW) as a Security Mechanism
PoW is an elegant solution to network security, requiring miners to solve complex mathematical problems that validate transactions. This process is energy-intensive, but it deters malicious actors from attempting to manipulate the network. Bitcoin’s PoW model also ensures transparency, as each transaction is public and immutable, a stark contrast to the often opaque traditional financial system.
The Solution to Double-Spending
Satoshi’s insight into the double-spending problem was revolutionary. By recording every transaction on a public blockchain, Bitcoin ensures each digital coin can only be spent once, something that earlier digital currencies failed to address adequately. This approach has led to the development of countless secure digital assets that use blockchain as a reliable source of record.
Scalability Challenges
While PoW offers security, it also slows transaction processing, which raises concerns about scalability. As Bitcoin adoption grows, the network may struggle to handle increased transaction volumes, affecting its viability as a mainstream payment solution. Solutions like the Lightning Network attempt to address this but introduce a level of complexity and centralization that some argue undermines Bitcoin’s original ethos.
Energy Consumption of Mining
Bitcoin’s mining process is energy-intensive, leading to environmental concerns. PoW requires vast amounts of electricity, sparking debates about Bitcoin’s environmental impact and prompting some to argue for alternative consensus mechanisms, like Proof of Stake (PoS). Bitcoin’s energy consumption presents a potential barrier to adoption in a world increasingly concerned about sustainability.
Privacy Considerations
Although Bitcoin transactions are pseudonymous, they are also publicly accessible on the blockchain. This transparency can compromise user privacy, as transactions can be traced back to individuals through exchanges and other regulatory checkpoints. While privacy-centric coins like Monero offer more anonymity, Bitcoin’s open ledger makes it less private than cash or other privacy-focused cryptocurrencies.
Bitcoin’s success has inspired countless cryptocurrencies and sparked an era of decentralized finance (DeFi), which brings traditional financial services—like lending, borrowing, and trading—onto blockchain networks without intermediaries. For example, Ethereum expanded on Bitcoin’s decentralized principles by introducing smart contracts, enabling programmable agreements that execute automatically when conditions are met. This functionality supports DeFi applications like Compound and Uniswap, which allow users to earn interest, trade assets, and more without needing a bank.
Moreover, the concept of “hard money” introduced by Bitcoin’s 21 million coin supply limit has also influenced DeFi and crypto ecosystems. For instance, Ethereum has adopted a partial burn mechanism, where a fraction of transaction fees are destroyed, creating a deflationary effect. Additionally, DeFi projects like MakerDAO’s DAI cryptocurrency use collateralized debt to stabilize value, echoing Bitcoin’s principles of decentralization while aiming for a more stable, spendable asset.
The Decentralized Advantage
Bitcoin’s decentralized design offers distinct advantages, such as censorship resistance and the potential for global, borderless transactions. These attributes are powerful in nations with unstable currencies or authoritarian governments, where Bitcoin provides an alternative to potentially unreliable local banking systems.
Challenges in the Decentralized Ecosystem
However, decentralization also introduces regulatory challenges. As cryptocurrencies grow, governments face pressure to implement regulations to protect investors and prevent illicit activity. Bitcoin’s transparency could become a double-edged sword in this scenario, as regulators push for more transparency that could compromise the privacy of users.
Bitcoin’s introduction has forever changed the financial landscape, and its principles are gradually permeating other areas of finance and technology. Concepts like decentralized autonomous organizations (DAOs) have emerged, where groups can govern themselves using blockchain protocols, enabling a community-driven approach to management and decision-making. While DAOs are still in their infancy, they hold the potential to decentralize everything from charities to corporate governance.
In finance, Bitcoin’s deflationary model is sparking renewed debate about inflation and monetary policy. Bitcoin’s fixed supply stands in stark contrast to fiat currencies, where central banks can print money as they see fit, potentially leading to inflation. As economic uncertainty continues, Bitcoin’s limited supply may make it more attractive as a hedge against inflation, much like gold. Additionally, central banks worldwide are experimenting with digital currencies (CBDCs), but unlike Bitcoin, CBDCs are typically centralized, raising concerns about surveillance and control.
Looking ahead, Bitcoin’s foundational principles could influence emerging fields like artificial intelligence and the Internet of Things (IoT). As devices become more autonomous, decentralized networks like Bitcoin may provide the infrastructure for secure, peer-to-peer data sharing and micropayments. Such developments underscore Bitcoin’s relevance as more than just digital money but as a technology that could underpin future advancements across multiple sectors.
Reflecting on Bitcoin’s inception, it’s remarkable how a seemingly niche technological experiment has evolved into a global phenomenon. As someone deeply engaged in the intersection of finance and technology, I see Bitcoin as both a technical marvel and a cultural movement. It challenges the traditional financial power structures by empowering individuals to take control of their wealth, an idea that resonates with people across socioeconomic boundaries.
However, I also recognize the limitations that Bitcoin faces. While it offers freedom, it’s not yet accessible to everyone due to technical and economic barriers. The future of Bitcoin will depend on its ability to scale while maintaining its core principles. Additionally, as the crypto ecosystem matures, Bitcoin’s role may evolve from a transactional currency to more of a “digital gold,” a stable, secure store of value that complements other blockchain innovations.
Bitcoin’s whitepaper set in motion a financial revolution, proposing a secure, decentralized way to transfer value across borders without intermediaries. Its principles have inspired a movement, leading to thousands of new cryptocurrencies and reshaping how we think about money, privacy, and ownership. As we continue to witness rapid technological advancements, Bitcoin’s foundational ideas remain as relevant as ever, providing a blueprint for decentralization that extends far beyond finance.
With each lesson in the CFIRE training program, we’re delving deeper into these pioneering concepts, bridging traditional finance and the transformative potential of blockchain. As we look to the future, we see Bitcoin not just as digital cash but as the catalyst for a decentralized world. Let’s keep moving forward with this powerful foundation as we explore the next stages in the CFIRE journey.
This lesson offers a critical perspective on the Bitcoin whitepaper, providing context and connections to the broader crypto ecosystem. It aims to encourage CFIRE learners to think about Bitcoin not just as a technology, but as a transformative idea that challenges financial norms and fuels the decentralization movement. Let’s prepare to dive even deeper into this journey!
In this lesson, we’ll explore the foundational ideas of Bitcoin as outlined by Satoshi Nakamoto in the original whitepaper. This whitepaper doesn’t just define Bitcoin but lays out the bedrock of modern decentralized finance (DeFi) and blockchain technology. Its creation resolved long-standing issues in digital payments, such as the double-spending problem, without relying on intermediaries. Understanding Bitcoin’s framework and its revolutionary decentralized model is essential for grasping the cryptocurrency ecosystem and the potential of blockchain to transform financial systems.
Peer-to-Peer Network
Double-Spending Problem
Blockchain
Proof of Work (PoW)
Private and Public Keys
Introduction: The Digital Cash Revolution
Transactions: Defining Bitcoin as Digital Cash
Timestamp Server: The Foundation of the Blockchain
Proof of Work: Securing the Network
Incentives and Sustainability
Bitcoin has directly influenced the development of decentralized finance (DeFi), a rapidly growing sector where financial services operate on blockchain networks, eliminating intermediaries. Concepts such as “smart contracts” on platforms like Ethereum extend Bitcoin’s ideas by enabling programmable transactions.
Congratulations on mastering this essential lesson in CFIRE! Bitcoin’s foundations form the backbone of the crypto landscape, and now you’re ready to dive deeper into the world of decentralized finance and blockchain. Let’s gear up for the next exciting stage of your journey in the CFIRE training program!
author
: Satoshi Nakamoto
site
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.
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.
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.
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.
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.
The steps to run the network are as follows:
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.
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.
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.
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.
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.
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.
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.
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[^10]:
| 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
$$\begin{aligned} q_z = \begin{cases} 1 & \text{if } p \leqslant q\ \left(q/p\right)^z & \text{if } p > q \end{cases} \end{aligned}$$
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:
$$\lambda = z \frac{q}{p}$$
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:
$$\begin{aligned} \sum _{k=0}^\infty \frac{\lambda ^k e^{-\lambda}}{k!} \cdot \begin{cases} \left(q/p\right)^{(z-p)} & \text{if } k \leqslant z \ 1 & \text{if } k > z \end{cases} \end{aligned}$$
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…
#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;
}
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
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.
[^1]: W. Dai, \”b-money,\” http://www.weidai.com/bmoney.txt, 1998.
[^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.
[^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 II: 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 Security 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, May 1999.
[^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.