TOP TEN (10) QUESTIONS REGARDING BITCOIN

Bitcoin is a relatively new form of currency that is really beginning to hit the mainstream, but many people still don’t understand its significant value, and why they should make the effort to use it, both for their own benefit and that of humanity in general. In this post, Dream Foundation founder Philip Agyei Asare will identify some top 10 questions about Bitcoin to give you a clearer understanding of what it is, what it does, and how you can use it to buy products or services online.

1. What Is Bitcoin? Any discussion of Bitcoin must be preceded by an explanation of what the Blockchain is, since Bitcoin is the currency of the Blockchain, in much the same way that the dollar is the currency of the United States, or email is a communications mode of the internet. The Blockchain is the public ledger that documents all confirmed Bitcoin transactions, and therefore offers a platform of virtually limitless algorithms that support all of the transactions on the blockchain. Since it consists of mathematics, it is incorruptible, unlike the existing centralized currency systems of the world, that rely on human transaction “verification”. Mathematics can be trusted to be true, but as we have found out, banking cannot be trusted to be true, or supportive of its users’ best interests. Bitcoin (BTC) is a form of currency that is digital; that is, it does not consist of physical notes and coins and instead exists as a solved logarithm on the Blockchain. In this era of Internet and digitization, we’ve moved from phone to VoIP calls, face-to-face meeting to video conferencing, fax to email, cable television to IP TV, and now Bitcoin joins this growing list of advancements.

2. Who Developed The Idea Of Bitcoin? The concept of the Blockchain and Bitcoin was developed by Satoshi Nakamoto, who resides in mysterious anonymity. Investigations as to his real identity have been extensive and intense, and there are only scattered clues. For example, he is said to be from Japan, but Bitcoin software was not originally available in Japan, and his mail ID was from Germany. He developed the system and the Bitcoin software (that is used to run the system) in 2009, but disappeared into seemingly thin air in 2010, apparently after he saw that Bitcoin was well on its way to development and adoption. The other developers of the system stopped hearing from him in 2010, and since then, plenty of entertaining speculation about his real identity has occurred. For example, it was suggested that his name was just a mashup of popular Japanese companies — SAmsung TOSHIba NAKAmichi MOTOrola. But what he created was definitely the joyful fantasy of every tech guy in the world, and clearly Bitcoin was his gift to the world.

3. What Is So Special About the Bitcoin System? Bitcoin is a system which enables anonymous currency transactions: the identification of the persons making such transactions will remain anonymous, and cannot be traced back At the same time, each transaction is verified and recorded publicly on the Blockchain (as explained above, basically, the hosting platform upon which Bitcoin functions) and once confirmed cannot be reversed or tampered with. The fact that the Blockchain is a public ledger makes transactions witnessed and verified by all users. Satoshi purposely designed his system to be de-centralized and a peer-to-peer network. Thus, it is not controlled by any central authority – unlike the current centrally controlled banking system in which the people are at the mercy of its policies and practices. Instead, because it is comprised of the growing millions of users, increasing daily, each of whose computers is a node of the whole system, this giant de-centralized network of computers is in the hands of the People. Likewise, it is run by a worldwide network of brilliantly innovative programmers and developers, contributors, and freedom enthusiasts who contribute their time, talent and energy to the Blockchain and Bitcoin. Essentially, Satoshi Nakamoto gave to the people of the world a system of currency, communication and exchange which makes possible independence from the corrupt and destructive central banking system, by simply replacing it with the Blockchain and Bitcoin. While attempts at crypto currencies were unsuccessfully tried for years prior to Satoshi Nakamoto, he not only created a successful replacement for central banking, he was so talented that he even solved the previously long-standing problem of double spending of digital currency which had plagued those early attempts.

4. What is Double Spending? We can make many copies of digital data, and abuse that ability; e.g. people copy software and sell it as counterfeit or pirated copies. In the same way, because BTC is digital currency, any merchant or transactor could run the risk that the payer (the holder of that digital token BTC) could copy the BTC, send one copy as payment and retain the other still in his possession, thus enabling double spending of the same BTC. However, because of Satoshi Nakamoto’s brilliant design, every BTC transaction must be verified and publicly posted on the Blockchain to be spent, thus solving the double spending dilemma, as follows. The Blockchain retains a list of all BTC created, using the complex unique identification number which is automatically generated for each newly created BTC. Whenever a new transaction is made, its validity is checked by confirming from that list that the BTC was not used before. Thus, no one can copy the currency and use it for more than one time. It’s a brilliantly simple and effective idea to stop even the possibility of double spending Bitcoin.

5. How Does A Public Listing Make Things Anonymous? The public listing only shows the transaction ID and the amount of currency transferred. The user is anonymous in the system because you don’t provide any of your personal details like your name, address, email, phone number, etc. that is required identifying information in the existing central banking system, like when using payment gateways like Paypal, credit cards, etc. When using Bitcoin, your personal information is sacrosanct, by intention and design.

6. How do you use Bitcoins? Bitcoin are kept in a digital wallet which you create easily online, and can keep on your computer, or on a website online, which will manage and secure your wallet for you. If you follow Bitcoin news and activities, you will have heard that sometimes Bitcoin are stolen from wallets by hackers. While this is infrequent and very difficult to do, (like bank robberies or hacking of the central banking system by criminals) unlike the current central banking system, you can totally safeguard against this possibility by simply storing your wallet(s) on a computer which is not connected to the internet. This will therefore exclude the possibility of having it accessed and hacked. You can then transfer BTC from your stored wallet to a computer with internet access only for the short period of time needed to transact any purchases, and then restore the balance in your wallet to your offline computer for safe storage until your next purchase. And you can also have as many wallets and Bitcoin addresses (where you receive money from others) as you like. What’s more, you can use Bitcoin software on top of Tor to prevent anyone from tracking your IP address – total anonymity guaranteed!

7. How many people are using this new Bitcoin system? At this very moment, more than 10 million Bitcoin are in existence, which currently converts to 207.929 million USD worth! In one day, more than 45,000 transactions of a total of 2.5 million BTC (48.5 million worth of USD) is handled by the Bitcoin network. To get an idea of the considerable and fast-growing acceptance of Bitcoin use around the world, you can review the information on the report issued at the end of July 2014 entitled The State of Bitcoin, here: http://www.slideshare.net/CoinDesk/state-of-bitcoin-q2-report

8. How Do I Acquire Bitcoin? Getting and using Bitcoin is easy. There are various ways to get Bitcoin: · ‘Mining’ · Currency exchange (bitcoin in return for Dollars or Euros) via Bitcoin provider services like Coinbase, etc. · Providing services to others in return for Bitcoin

9. What’s Mining? Mining is the process of extracting Bitcoin currency from the Blockchain by using hardware specifically designed to solve the necessary logarithms, which then generate BTC. Whenever a new logarithmic block is thus “found” by such mining equipment, its owner is gifted with 50 Bitcoins. The capability of mining equipment to so solve the necessary logarithms on the Blockchain is referred to as hashing power, and the necessary hashing power required to solve each subsequent logarithm on the Blockchain likewise increases with each successful mining of BTC. Bitcoin mining itself is a business, since most people involved in BTC mining do so to gain profit by generating BTC which can then be sold, traded or used for purchases.

10. How Do You Spend A Bitcoin? Bitcoin is used in all the same ways that traditional “currency” is used: BTC can be sent to a person, to a merchant to buy goods or services, or to make donations to non-profit foundations who accept BTC (a growing list), such as Wikileaks, Wikipedia, WantToKnow.info, Dream Foundation Ghana, etc. To send to a private party, you only need their Bitcoin address. To pay for merchandise, you simply use the payment platform set up by Hey, Nana merchants that accept Bitcoin, like merchants who accept PayPal payments do now. This is one of the implementations that Dream Foundation is planning to put in place in Ghana and beyond. I will be putting out other articles explaining the new people’s world of Bitcoin and the Blockchain further, and in the interim, I welcome any questions you may have, which can be sent to the following email address: drimin99@gmail.com or ceo@paksmsgh.com or philip@dreambitcoinfoundation.org

AFRICA – LAND OF DREAMS AND POTENTIALS

37COINS (THE BEST BITCOIN WALLET FOR AFRICANS)
Africa is often demeaned as the “Lost” or “Hopeless” continent due to 1st World Afro-pessimism that gorges itself on a generous media diet of AIDS, genocide, raping armies, Biafra, Darfur, Somalia, matchstick children crawling with insects, tyrants chopping off limbs, etc. The majority of Westerners believe Africa is a trapped nightmare; they expect no transcendence from the natal land of Homo sapiens. Attention, world, wake up! Africa is rising with entrepreneurship, powered by Bitcoin and other crypto currencies and the expansive Blockchain on which they exist.

According to the World Bank, Sub-Saharan Africa is now home to approximately 650 million mobile phone subscribers, a number that surpasses the United States and the European Union, and represents an explosion of new communication technologies that are being tailored to the developing world. Mobile phones, to me, are the fastest growing technology on the continent. “More people have access to mobile phones today in Africa than they do to clean water or even sanitation.” So we can say this has been the most significant revolution in terms of changing the African landscape and how people live their daily life. And what surprised me greatly was the latest World Bank report, which states that mobile phones were directly associated with the creation of more than five million jobs in Africa last year and contributed seven percent to Africa’s Gross Domestic Product — higher than the global average. That’s a great statistic for young African entrepreneurs(Cheetahs) who have dreams and ambitions of introducing their products and services throughout the world, as the world is now a global village due to technological advancements. The benefits of mobile phones in developing countries could be even greater if more people understood how to use and take advantage of mobile phone technology, especially SMS.

WHAT 37COINS HAS FOR AFRICA

To me, 37coins is the best bitcoin wallet for Africans as I have already done the analysis researched by the world bank on the speed of mobile phone penetration in Africa and how it has started to help the continent. We are in a world whereby everyone wants his or her privacy guaranteed, no more centralized system of banking as its being monitor by the governments and even have the audacity to lay charges on you for money laundering when you are moving money more than what the government has, your own hard earned money, that’s why BITCOIN and other CRYPTOCURRENCIES has come to overpower the governments control over the centralized FIAT MONEY. Bitcoin is alternative to African mobile money and its also more potentials and advantageous than the mobile money in Africa as it is works without boarders and barriers.
37coins.com was founded by social entrepreneur Songyi Lee, developer Johann Barbie and designer Jonathan Zobro and its based in USA.Its bitcoin wallet that can be used on any mobile phone, by using the lowest technological common denominator – SMS.
SMS is an attractive way of handling cryptocurrencies as it opens up a whole new tier of users around the world. However, it would be worth the risk to cater for the billions of “unbanked” individuals by making cryptocurrencies more accessible. The so-called “unbanked” are those people who live in poorer parts of the world, and to whom bank accounts are just not available or too expensive. For these same people, knowledge from the Internet has been made accessible through various SMS services and We Africans can benefit the most from cryptocurrencies, which provides fast and secure payment transactions with no centralized authority over it. Sending bitcoin is flexible as the SEND command will accept a phone number or bitcoin wallet address. If funds are sent to someone who does not use the service, a wallet is created and the coins are stored for the recipient to transfer the funds.
As more bitcoin recipients send payments on to other phone numbers, more and more people will have wallets available to them via 37Coins.
Signing up for a wallet is easy, one just needs to sign up at the website with their phone number, or just text to the local gateway number. For example, the “Addr” command returns your bitcoin wallet address on 37Coins. If a new user sends this to their local 37Coins gateway number, their phone number will be added to the system and a wallet generated for them. 37Coins could be an important step for cryptocurrencies, as it takes out the complication of creating and looking after a wallet, Furthermore, the spread of mobile phones outstrips those who are currently on the Internet. Interaction with the service is done by sending text commands by SMS to one’s local 37Coins gateway number like the table below

“It’s simple and is even usable on the Nokia 100, this basic SMS phone. While mobile money works within the country of operation, 37coins can work anywhere in the world.
CONCLUSION
I therefore put it to my fellow freedom fighters in Africa, let all come together to embrace this new technological advancement as it has come to liberate young Africans from the poverty ridden by the FIAT MONEY that has dominated the continent and has given those in Authority more power over its own citizens. FIAT MONEY will be a thing of the past soon, if you don’t believe it, just come for a BET and let see the future of fiat money as CODING, PROGRAMMING and CRYTOGRAPHY has start to eliminate the Government Schools that only teaches how to get a government work and accept FIAT MONEY as the mode of payment for salary and other stuffs thereby making the government powerful all the time. Its time for the Cheetahs to reclaim what belong them.

DREAM FOUNDATION

Dream Foundation is a non-profit organization created to empower young entrepreneurs, who are the intellectual, social and cultural life’s blood of a country – in this case, Ghana. Dream Foundation will be raising Bitcoin funds for projects that will build a bright future for our country by bringing together all young, ambitious and self-determining entrepreneurs and enabling them to achieve their dreams, without the need for government assistance. The Foundation will enable them to establish their various businesses online to serve the international market, and their mode of payment will be through Bitcoin, which will be the means by which their dream businesses will become a reality and a viable and resourceful presence in the world. This will, in turn, enable Ghana to fulfill her dreams and potential in the global community.

How Bitcoin Came

Bitcoin:
A Peer-to-Peer Electronic Cash System
Satoshi Nakamoto
October 31, 2008
Abstract
A purely peer-to-peer version of electronic cash would allow online payments to be sent directly from one party to another without going through a financial institution. Digital signatures provide part of the solution, but the main benefits are lost if a trusted third party is still required to prevent double-spending. We propose a solution to the double-spending problem using a peer-to-peer network. The network timestamps transactions by hashing them into an ongoing chain of hash-based proof-of-work, forming a record that cannot be changed without redoing the proof-of-work. The longest chain not only serves as proof of the sequence of events witnessed, but proof that it came from the largest pool of CPU power. As long as a majority of CPU power is controlled by nodes that are not cooperating to attack the network, they’ll generate the longest chain and outpace attackers. The network itself requires minimal structure. Messages are broadcast on a best effort basis, and nodes can leave and rejoin the network at will, accepting the longest proof-of-work chain as proof of what happened while they were gone.
1. Introduction
Commerce on the Internet has come to rely almost exclusively on financial institutions serving as trusted third parties to process electronic payments. While the system works well enough for most transactions, it still suffers from the inherent weaknesses of the trust based model. Completely non-reversible transactions are not really possible, since financial institutions cannot avoid mediating disputes. The cost of mediation increases transaction costs, limiting the minimum practical transaction size and cutting off the possibility for small casual transactions, and there is a broader cost in the loss of ability to make non-reversible payments for non-reversible services. With the possibility of reversal, the need for trust spreads. Merchants must be wary of their customers, hassling them for more information than they would otherwise need. A certain percentage of fraud is accepted as unavoidable. These costs and payment uncertainties can be avoided in person by using physical currency, but no mechanism exists to make payments over a communications channel without a trusted party.
What is needed is an electronic payment system based on cryptographic proof instead of trust, allowing any two willing parties to transact directly with each other without the need for a trusted third party. Transactions that are computationally impractical to reverse would protect sellers from fraud, and routine escrow mechanisms could easily be implemented to protect buyers. In this paper, we propose a solution to the double-spending problem using a peer-to-peer distributed timestamp server to generate computational proof of the chronological order of transactions. The system is secure as long as honest nodes collectively control more CPU power than any cooperating group of attacker nodes.
2. Transactions
We define an electronic coin as a chain of digital signatures. Each owner transfers the coin to the next by digitally signing a hash of the previous transaction and the public key of the next owner and adding these to the end of the coin. A payee can verify the signatures to verify the chain of ownership.
The problem of course is the payee can’t verify that one of the owners did not double-spend the coin. A common solution is to introduce a trusted central authority, or mint, that checks every transaction for double spending. After each transaction, the coin must be returned to the mint to issue a new coin, and only coins issued directly from the mint are trusted not to be double-spent. The problem with this solution is that the fate of the entire money system depends on the company running the mint, with every transaction having to go through them, just like a bank. We need a way for the payee to know that the previous owners did not sign any earlier transactions. For our purposes, the earliest transaction is the one that counts, so we don’t care about later attempts to double-spend. The only way to confirm the absence of a transaction is to be aware of all transactions. In the mint based model, the mint was aware of all transactions and decided which arrived first. To accomplish this without a trusted party, transactions must be publicly announced[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.
4. Proof-of-Work
To implement a distributed timestamp server on a peer-to-peer basis, we will need to use a proof-of-work system similar to Adam Back’s Hashcash[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 proof-of-work is found and one branch becomes longer; the nodes that were working on the other branch will then switch to the longer one.
New transaction broadcasts do not necessarily need to reach all nodes. As long as they reach many nodes, they will get into a block before long. Block broadcasts are also tolerant of dropped messages. If a node does not receive a block, it will request it when it receives the next block and realizes it missed one.
6. Incentive
By convention, the first transaction in a block is a special transaction that starts a new coin owned by the creator of the block. This adds an incentive for nodes to support the network, and provides a way to initially distribute coins into circulation, since there is no central authority to issue them. The steady addition of a constant of amount of new coins is analogous to gold miners expending resources to add gold to circulation. In our case, it is CPU time and electricity that is expended.
The incentive can also be funded with transaction fees. If the output value of a transaction is less than its input value, the difference is a transaction fee that is added to the incentive value of the block containing the transaction. Once a predetermined number of coins have entered circulation, the incentive can transition entirely to transaction fees and be completely inflation free.
The incentive may help encourage nodes to stay honest. If a greedy attacker is able to assemble more CPU power than all the honest nodes, he would have to choose between using it to defraud people by stealing back his payments, or using it to generate new coins. He ought to find it more profitable to play by the rules, such rules that favour him with more new coins than everyone else combined, than to undermine the system and the validity of his own wealth.
7. Reclaiming Disk Space
Once the latest transaction in a coin is buried under enough blocks, the spent transactions before it can be discarded to save disk space. To facilitate this without breaking the block’s hash, transactions are hashed in a Merkle Tree [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.
8. Simplified Payment Verification
It is possible to verify payments without running a full network node. A user only needs to keep a copy of the block headers of the longest proof-of-work chain, which he can get by querying network nodes until he’s convinced he has the longest chain, and obtain the Merkle branch linking the transaction to the block it’s timestamped in. He can’t check the transaction for himself, but by linking it to a place in the chain, he can see that a network node has accepted it, and blocks added after it further confirm the network has accepted it.
As such, the verification is reliable as long as honest nodes control the network, but is more vulnerable if the network is overpowered by an attacker. While network nodes can verify transactions for themselves, the simplified method can be fooled by an attacker’s fabricated transactions for as long as the attacker can continue to overpower the network. One strategy to protect against this would be to accept alerts from network nodes when they detect an invalid block, prompting the user’s software to download the full block and alerted transactions to confirm the inconsistency. Businesses that receive frequent payments will probably still want to run their own nodes for more independent security and quicker verification.
9. Combining and Splitting Value
Although it would be possible to handle coins individually, it would be unwieldy to make a separate transaction for every cent in a transfer. To allow value to be split and combined, transactions contain multiple inputs and outputs. Normally there will be either a single input from a larger previous transaction or multiple inputs combining smaller amounts, and at most two outputs: one for the payment, and one returning the change, if any, back to the sender.
It should be noted that fan-out, where a transaction depends on several transactions, and those transactions depend on many more, is not a problem here. There is never the need to extract a complete standalone copy of a transaction’s history.
10. Privacy
The traditional banking model achieves a level of privacy by limiting access to information to the parties involved and the trusted third party. The necessity to announce all transactions publicly precludes this method, but privacy can still be maintained by breaking the flow of information in another place: by keeping public keys anonymous. The public can see that someone is sending an amount to someone else, but without information linking the transaction to anyone. This is similar to the level of information released by stock exchanges, where the time and size of individual trades, the “tape”, is made public, but without telling who the parties were. As an additional firewall, a new key pair should be used for each transaction to keep them from being linked to a common owner. Some linking is still unavoidable with multi-input transactions, which necessarily reveal that their inputs were owned by the same owner. The risk is that if the owner of a key is revealed, linking could reveal other transactions that belonged to the same owner.
11. Calculations
We consider the scenario of an attacker trying to generate an alternate chain faster than the honest chain. Even if this is accomplished, it does not throw the system open to arbitrary changes, such as creating value out of thin air or taking money that never belonged to the attacker. Nodes are not going to accept an invalid transaction as payment, and honest nodes will never accept a block containing them. An attacker can only try to change one of his own transactions to take back money he recently spent.
The race between the honest chain and an attacker chain can be characterized as a Binomial Random Walk. The success event is the honest chain being extended by one block, increasing its lead by +1, and the failure event is the attacker’s chain being extended by one block, reducing the gap by -1.
The probability of an attacker catching up from a given deficit is analogous to a Gambler’s Ruin problem. Suppose a gambler with unlimited credit starts at a deficit and plays potentially an infinite number of trials to try to reach breakeven. We can calculate the probability he ever reaches breakeven, or that an attacker ever catches up with the honest chain, as follows[8]:
pqqz=== probability an honest node finds the next block probability the attacker finds the next block probability the attacker will ever catch up from z blocks behind
qz={1(q/p)zifp≤qifp>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 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:
λ=zqp
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∞λke−λk!⋅{(q/p)(z−k)1ifk≤zifk>z}
Rearranging to avoid summing the infinite tail of the distribution…
1−∑k=0zλke−λk!(1−(q/p)(z−k))
Converting to C code…
#include
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

12. Conclusion
We have proposed a system for electronic transactions without relying on trust. We started with the usual framework of coins made from digital signatures, which provides strong control of ownership, but is incomplete without a way to prevent double-spending. To solve this, we proposed a peer-to-peer network using proof-of-work to record a public history of transactions that quickly becomes computationally impractical for an attacker to change if honest nodes control a majority of CPU power. The network is robust in its unstructured simplicity. Nodes work all at once with little coordination. They do not need to be identified, since messages are not routed to any particular place and only need to be delivered on a best effort basis. Nodes can leave and rejoin the network at will, accepting the proof-of-work chain as proof of what happened while they were gone. They vote with their CPU power, expressing their acceptance of valid blocks by working on extending them and rejecting invalid blocks by refusing to work on them. Any needed rules and incentives can be enforced with this consensus mechanism.

PATIENCE

IMPATIENCE has been around for a long time. There is nothing new about people losing their patience while stuck in traffic or waiting in line. But some experts believe that people are less patient today than in the past and for reasons that might surprise you.
Some analysts suggest that in recent years, many people are less patient because of technology. According to The Gazette of Montreal, Canada, some researchers suggest that “digital technology, from mobile phones to cameras to email to IPods, is changing our lives. The instant results we get from this technology have in turn increased our appetite for instant gratification in other aspects of our lives.”
A family psychologist by name Dr. Jennifer Hartstein makes some sobering observations. She explains that “we have become an immediate gratification culture, and we expect things to move quickly, efficiently and in the way we want. When that doesn’t happen, we tend to become increasingly frustrated and irritable, [a sign] of impatience.” She adds, “We’ve lost the art of just slowing down and enjoying the moment.”
Some believe that e-mail is losing popularity and could soon become obsolete. Why? Because many people who send messages do not have the patience to wait hours, or even minutes, for a response. Also, with e-mails, as with letter writing, introductory and concluding greetings are often expected. But many people consider such formalities to be boring and time consuming. They prefer instant messaging, which does not require the protocols of e-mail. It seems that people just do not have the patience to type polite greetings! Many people do not take the time to proof-read what they put in writing. As a result, letters and e-mails go out to the wrong recipients or contain numerous grammatical and typographical errors.
The thirst for immediate results is not limited to the realm of digital communication. People seem to be losing their ability to wait in other areas of life. For instance, do you ever find yourself talking too fast, eating too fast, driving too fast, or spending money too fast? The few moments it takes to wait for a traffic light to change or for a computer to boot up may seem like an eternity.
Experts have observed that many people do not have the patience to read through lengthy text in print. Why? Because they are accustomed to navigating speedily through web pages, jumping from blurb to blurb and from bullet to bullet, hoping to land on the main point as quickly as possible.
What happened to impatience, Experts do not have all the answers when it comes to the causes of impatience. Yet, there seems there to be compelling evidence that impatience can be harmful. In my next article, am going to discuss some of the risks of impatience and what you can do to be more patient.