Bitcoin & Bitcoin Mining

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  • The only way a reward system which divides a fixed reward per round among the participants in the round can be hopping-proof, if the entire reward is given to the successful share.
  • http://www.zerohedge.com/news/2013-05-27/mapping-bitcoins-global-adoptionBitcoin is only as strong as the network on which it is based, so the value of connected nodes cannot be overlooked in an analysis of global adoption. The chart below shows a snapshot of the geographical breakdown of connected nodes taken on May 18.This chart represents individual node connections, not total hashing/mining power. We’re working on an article to cover this topic in the depth it deserves, but for now we can see a story consistent with the rest of this analysis. The United States remains the power player, with significant interest from China. The Nordic countries, not represented on the graph due to their relatively low total connections, were represented at an impressive level within the data set relative to their size – as would be expected given the download data shown earlier.
  • http://www.zerohedge.com/news/2013-03-10/demographics-bitcoin?page=6With the growing popularity and perhaps relevance of a globally decentralized currency system in a world adrift in fiat devaluation death-matches, it is perhaps interesting to understand just who these Bitcoin'ers are? The ongoing survey of Bitcoin users (here) has some intriguing results already: The 'average Bitcoin user' is male (96%), 32.7 years old, libertarian / anarcho-capitalist (37%), non-religious (61%), with a full time job (43%), and is in a relationship (56%). The biggest motivation for new users are curiosity, profit, and politics; and 39% of users do not drink, smoke, gamble, or take drugs. Just over half of users have mined bitcoins and the greatest community fear for Bitcoin is “regulatory/legal intervention” followed by ”reputation problems”. Overall more people seem to find Bitcoin intellectually rewarding (70% have learned more about cryptography) than socially rewarding (22% have made friends).Via Space Druid,Wait: If you haven’t filled out this survey please do so HERE! I will continue to draw on this dataset for future posts, and it is open for others to use, so by responding you are contributing to a community resource.Some highlights…The average user is a 32.7 year old libertarian male.Top motivators for new users are curiosity, profit, and politics.Bitcointalk.org is the dominant community platform.Far more people have used Bitcoin to make donations than to buy narcotics.39% of users do not drink, smoke, gamble, or take drugs.The “average Bitcoin user” is male (96%), 32.7 years old, libertarian / anarcho-capitalist (37%), non-religious (61%), with a full time job (43%), and is in a relationship (56%).But of course there is no such thing as an average Bitcoin user, and flattening out the figures like that ignores the large numbers of users who are Christian (20%) or single (37%). Also by using the broadest possible terms (ie including liberals and environmentalists), you get a left-of-centre contingent with over 45% of users.The arrival of new users correlates with price and media coverage, with Q2 2011 the most popular quarter for the question “When did you first install the Bitcoin client”.The biggest motivation in exploring Bitcoin is curiosity (4.3/5), followed by profit (3.7/5) and politics (3.5/5). Trailing behind are practical concerns (3.1/5), challenge (2.9/5), and community (2.7/5).The age distribution around the mean average of 32.7 is fairly balanced, with people in their late twenties slightly overrepresented. The mode is 31 years and standard deviation is 10.5 years.Just over half of users have mined bitcoins, most of them as part of a mining pool. The average hash rate (using geometric mean) is 318 MH/s. The average miner has spent $3,188 on a rig, but the spread is huge. The median spend is $500, 35% of miners have spent nothing, while 8% have spent $10,000 or more.How does a miner spend nothing? Well almost 10% of respondents have mined bitcoins on someone else’s hardware, so that’s one way to do it.CommunityAs expected Bitcointalk.org is the dominant platform of discussion, used by 76% of users. Reddit (39%) also had a strong showing, while the classic IRC got a mere 24%. Google+ had a strong showing among early respondents which is now somewhat dwindled, at 18%.The greatest community fear for Bitcoin is “regulatory/legal intervention” (29%) followed by ”reputation problems” (19%). A large number of people answered “Other” and in the free-form field wrote to the effect that Bitcoin was too technically demanding for mainstream use.The most common use of bitcoins was for gifts/donations (55%), while computer services was also quite high (38%). Only 11% of respondents have bought narcotics (using Bitcoin that is). In fact the community has a contingent of clean-living ascetics, 39% of respondents do not drink, smoke, take drugs, or gamble.
  • http://www.zerohedge.com/news/2013-05-27/mapping-bitcoins-global-adoptionBitcoin is only as strong as the network on which it is based, so the value of connected nodes cannot be overlooked in an analysis of global adoption. The chart below shows a snapshot of the geographical breakdown of connected nodes taken on May 18.This chart represents individual node connections, not total hashing/mining power. We’re working on an article to cover this topic in the depth it deserves, but for now we can see a story consistent with the rest of this analysis. The United States remains the power player, with significant interest from China. The Nordic countries, not represented on the graph due to their relatively low total connections, were represented at an impressive level within the data set relative to their size – as would be expected given the download data shown earlier.
  • MinersJust over half of users have mined bitcoins, most of them as part of a mining pool. The average hash rate (using geometric mean) is 318 MH/s. The average miner has spent $3,188 on a rig, but the spread is huge. The median spend is $500, 35% of miners have spent nothing, while 8% have spent $10,000 or more.How does a miner spend nothing? Well almost 10% of respondents have mined bitcoins on someone else’s hardware, so that’s one way to do it.CommunityAs expected Bitcointalk.org is the dominant platform of discussion, used by 76% of users. Reddit (39%) also had a strong showing, while the classic IRC got a mere 24%. Google+ had a strong showing among early respondents which is now somewhat dwindled, at 18%.The greatest community fear for Bitcoin is “regulatory/legal intervention” (29%) followed by ”reputation problems” (19%). A large number of people answered “Other” and in the free-form field wrote to the effect that Bitcoin was too technically demanding for mainstream use.The most common use of bitcoins was for gifts/donations (55%), while computer services was also quite high (38%). Only 11% of respondents have bought narcotics (using Bitcoin that is). In fact the community has a contingent of clean-living ascetics, 39% of respondents do not drink, smoke, take drugs, or gamble.Overall more people seem to find Bitcoin intellectually rewarding (70% have learned more about cryptography) than socially rewarding (22% have made friends).
  • MinersJust over half of users have mined bitcoins, most of them as part of a mining pool. The average hash rate (using geometric mean) is 318 MH/s. The average miner has spent $3,188 on a rig, but the spread is huge. The median spend is $500, 35% of miners have spent nothing, while 8% have spent $10,000 or more.How does a miner spend nothing? Well almost 10% of respondents have mined bitcoins on someone else’s hardware, so that’s one way to do it.CommunityAs expected Bitcointalk.org is the dominant platform of discussion, used by 76% of users. Reddit (39%) also had a strong showing, while the classic IRC got a mere 24%. Google+ had a strong showing among early respondents which is now somewhat dwindled, at 18%.The greatest community fear for Bitcoin is “regulatory/legal intervention” (29%) followed by ”reputation problems” (19%). A large number of people answered “Other” and in the free-form field wrote to the effect that Bitcoin was too technically demanding for mainstream use.The most common use of bitcoins was for gifts/donations (55%), while computer services was also quite high (38%). Only 11% of respondents have bought narcotics (using Bitcoin that is). In fact the community has a contingent of clean-living ascetics, 39% of respondents do not drink, smoke, take drugs, or gamble.Overall more people seem to find Bitcoin intellectually rewarding (70% have learned more about cryptography) than socially rewarding (22% have made friends).
  • The utilization of bitcoin in the real world, outside of the internet, will be paramount to its broader proliferation. There have been major advancements towards this, such as Kreuzberg, Berlin recently showing the world a significant step forward by deeply integrating bitcoin into the local economy and restaurants in New York City beginning to accept it as well.As a proxy to determine the propensity for a region to bring the bitcoin movement offline, we looked at the number of people participating in bitcoin-oriented meetups across the world. The chart below shows the number of participants in the largest meetups in each city, grouped by country. The usual suspects are all present, with newcomers like Israel and Argentina demonstrating significant real world interest.
  • The utilization of bitcoin in the real world, outside of the internet, will be paramount to its broader proliferation. There have been major advancements towards this, such as Kreuzberg, Berlin recently showing the world a significant step forward by deeply integrating bitcoin into the local economy and restaurants in New York City beginning to accept it as well.As a proxy to determine the propensity for a region to bring the bitcoin movement offline, we looked at the number of people participating in bitcoin-oriented meetups across the world. The chart below shows the number of participants in the largest meetups in each city, grouped by country. The usual suspects are all present, with newcomers like Israel and Argentina demonstrating significant real world interest.
  • At the backbone of the bitcoin movement are a handful of visionary entrepreneurs and prescient investors. To see where the future of bitcoin is being built, we compiled a list of leading bitcoin companies and venture capitalists, focusing on the US as it has by far the greatest number of successful companies and investment capital flow to date.The notion of international collaboration across disparate individuals has never before been achieved at this scale, outside of the internet itself. There is a bright future ahead for bitcoin, and we’re looking forward to helping it unfold.
  • Comparing Bitcoin Desktop ClientsA Bitcoin desktop client is software that you run on your own computer, as compared to an online client which is a service that makes your wallet available online. With a desktop client, your wallet is stored on your computer as a file, which means your wallet is as secure as your computer is. There are several desktop clients available, which vary in the features they have and how easy they are to use. When you first start a desktop client the entire Bitcoin block chain is downloaded to your computer. The block chain is a file that records every transaction that has ever occurred in the Bitcoin network. It is constantly growing in size (it is currently around 7 GB) and can take several hours to fully download and verify, depending on your internet connection speed. You won’t be able to send or receive bitcoins until this process is complete (unless you use a “light-weight” client, like Electrum, or decide to use an online wallet).Bitcoin-QtBitcoin-Qt is the original Bitcoin client, first developed by Satoshi Nakamoto and now developed by the Bitcoin development team. It is considered the “reference” implementation, which means that any other Bitcoin clients are expected to conform to how it works (though other clients are free to offer additional features and modify the look-and-feel).The Bitcoin-Qt client lets you perform all the basic operations you would expect, from creating a wallet to sending and receiving bitcoins. Available for Windows, Linux, and Mac at:http://bitcoin.org/ArmoryThe Armory client offers more advanced features including the ability to run multiple wallets and paper backups of your Bitcoin keys. It also offers “cold storage”, which is the ability to store your bitcoins in a computer that is kept permanently offline and manually synced with your normal computer. Cold storage is a bit of a hassle, but it’s basically hacker-proof.The Armory client requires the Bitcoin-Qt client to already be installed and running. Armory essentially sits on top of Bitcoin-Qt and offers functionality that Bitcoin-Qt doesn’t have. After you’ve gotten started with Bitcoin and become familiar with the terminology, you should definitely check Amory out.Available for Windows, Linux, and Mac at:http://bitcoinarmory.com/Electrum Electrum is a “light-weight” Bitcoin client, which means that, unlike Bitcoin-Qt and Armory, it doesn’t need to download the full block chain before it can start working. Instead, it relies on remote servers that have a copy of the block chain (you can run your own Electrum server if you want). Your wallet file is still stored locally and securely on your own computer.Because it doesn’t download the entire block chain, you can start using Electrum much sooner than other clients, so if you’re in a hurry, Electrum is good place to start.Available for Windows, Linux, Mac, and Android at:http://electrum.org/MultiBitMultiBit is another light-weight client that doesn’t require you to download the entire Bitcoin block chain before you can get started. It’s translated into a growing number of languages, which makes it a good choice if you want a client in a language other than English. A list of which languages it supports can be seen at the MultiBit website.Available for Windows, Linux, and Mac at:
  • http://www.zerohedge.com/news/2013-05-27/mapping-bitcoins-global-adoptionCountries listed in order of cumulative downloadsThe United States is the clear frontrunner in terms of total number of downloads. China had surprisingly few downloads for a country its size until the recent documentary aired by China’s largest state-run broadcaster. As shown in the chart above and echoed elsewhere in our findings, Russia was an early adopter but has since tapered off relative to interest growing elsewhere around the globe.To normalize for country size, we compared total wallet downloads to the population of each country to find penetration into each region. In doing so, we quickly realized the Nordic countries are the clear leaders in bitcoin adoption. As the second chart below indicates, one probable reason for this is the region’s familiarity with and access to technology – all of the Nordic countries rank among the highest in the world for internet penetration.They also all share similar and uniquely successful socioeconomic models based on a strong mutual trust between the citizens and states. So much so that PäiviHeikkinen, Finland’s Head of the Division for Oversight of Financial Markets Infrastructure explicitly responded to a question about whether or not bitcoin is illegal by stating, “Not at all; people can invest in and use any money they prefer.”
  • http://www.zerohedge.com/news/2013-05-27/mapping-bitcoins-global-adoptionCountries listed in order of cumulative downloadsThe United States is the clear frontrunner in terms of total number of downloads. China had surprisingly few downloads for a country its size until the recent documentary aired by China’s largest state-run broadcaster. As shown in the chart above and echoed elsewhere in our findings, Russia was an early adopter but has since tapered off relative to interest growing elsewhere around the globe.To normalize for country size, we compared total wallet downloads to the population of each country to find penetration into each region. In doing so, we quickly realized the Nordic countries are the clear leaders in bitcoin adoption. As the second chart below indicates, one probable reason for this is the region’s familiarity with and access to technology – all of the Nordic countries rank among the highest in the world for internet penetration.They also all share similar and uniquely successful socioeconomic models based on a strong mutual trust between the citizens and states. So much so that PäiviHeikkinen, Finland’s Head of the Division for Oversight of Financial Markets Infrastructure explicitly responded to a question about whether or not bitcoin is illegal by stating, “Not at all; people can invest in and use any money they prefer.”
  • http://www.zerohedge.com/news/2013-05-27/mapping-bitcoins-global-adoptionThere is a correlation of 0.7 between a country’s bitcoin downloads per capita and internet penetration
  • Searches and software downloads show interest, but the true story unfolds when money enters the picture, so looking at exchange volumes across currencies offers even deeper insight into the evolving bitcoin narrative.As would be expected, USD still dominates trading volume, but mapped against other currencies we can see a consistent declining trend as other countries and their currencies enter the picture in larger amounts.USD as a share of total bitcoin trading volume has fallen from near 100% to approximately 80% over the past two years. The most notable gain from is from CNY (Chinese Yuan), which grew from approximately 0.4% of total volume in April 2012 to an impressive 4.7% in April 2013.Within the still-dominant USD trading, there is a healthy trend of diversification away from Mt. Gox towards alternative exchanges. As shown in the chart below, alternative exchanges have gained traction on the DDoS-susceptible leader in the space – a trend likely to continue after their recent loss of Dwolla as an account funding source and investigation by the Department of Homeland Security. Worth noting, the chart below should be viewed as an approximation, as data for exchanges that have shut down over the years was not available for this analysis.
  • Searches and software downloads show interest, but the true story unfolds when money enters the picture, so looking at exchange volumes across currencies offers even deeper insight into the evolving bitcoin narrative.As would be expected, USD still dominates trading volume, but mapped against other currencies we can see a consistent declining trend as other countries and their currencies enter the picture in larger amounts.USD as a share of total bitcoin trading volume has fallen from near 100% to approximately 80% over the past two years. The most notable gain from is from CNY (Chinese Yuan), which grew from approximately 0.4% of total volume in April 2012 to an impressive 4.7% in April 2013.Within the still-dominant USD trading, there is a healthy trend of diversification away from Mt. Gox towards alternative exchanges. As shown in the chart below, alternative exchanges have gained traction on the DDoS-susceptible leader in the space – a trend likely to continue after their recent loss of Dwolla as an account funding source and investigation by the Department of Homeland Security. Worth noting, the chart below should be viewed as an approximation, as data for exchanges that have shut down over the years was not available for this analysis.
  • Bitcoin & Bitcoin Mining

    1. 1. BitcoinandBitcoin MiningIntroductionLab ofProfessor Hidetoshi ShimodairaZehady Abdullah KhanBachelor 4th year,Mathematical Science Course,Department of Information andComputer Sciences,School Of Engineering Science,Osaka University.12013-06-12
    2. 2. ContentsIntroduction of Bitcoin.What is Bitcoin Mining?Different Mining Methods.Pool-Hopping Problem.Introduction of Hopping-Proof Methods.2According to mainly two papers:1. Bitcoin: A peer-to-peer electronic cash systemS. Nakamoto, Tech Report, 20092. Analysis of Bitcoin Pooled Mining Reward SystemsMeni Rosenfeld - Distributed, Parallel, and Cluster Computing,2011
    3. 3. BitcoinBitcoinDigitalCurrencyPublic KeyCryptographyInternetSecurityCryptographyFinancialTransactionE-CashComplex NetworkIntro3
    4. 4. What is Bitcoin? A digital currency Unit: BTC (1 BTC = 110 USD). Buy or sell goods. Differences Decentralized and Distributed. Low fee & Fast Transaction. Anonymous: Address <=> Address transaction. Value increase (Only 21,000,000 Bitcoin) How do you get and use bitcoin? Bitcoin exchanges to buy and sell bitcoin. Bitcoin wallets to use bitcoin to receive or send bitcoin.4
    5. 5. How Bitcoin looks like? Not a physical object like gold or paper-money. A chain of digital signatures in a block-chain. Block header Transactions Block Reward(B) 25 bitcoin per valid block Halves every 4 year How do you count your bitcoin? Bitcoin wallet collects/remembers all the transactions associated withyou.5
    6. 6. Block: Human Readable format6
    7. 7. Block Confirmation: Proof of Work Current target(Tcur): “Bits” field Maximum target(Tmax):0x00000000FFFF0000000000000000000000000000000000000000000000000000 Condition of Block confirmation Hash of block header Tcur Block Difficulty(D): (2016 Blocks / every 2 week) Which hash will validate the block ? A Hash validating a block is a Rare Event SHA256 chooses any 256-bit number from 0 ~ 2^2567£Nonce ChangeA completelydifferent hash of theblock headerD =TmaxTcurSHA 256CryptographicHash FunctionBlock HeaderHash of Block header(256 bit Number)
    8. 8. Block Validation Probability 0x00000000FFFF0000000000000000000000000000000000000000000000000000The offset for difficulty 1 is and for difficulty D is The expected number of hashes we need to calculate to find ablock with difficulty D is Every hash has a probability of to validate a block.8208 bits16bitsTmax1232D(216-1)2208 (216-1)2208D2256(216-1)2208D=2256D(216-1)2208=248D(216-1)» 232D
    9. 9. Bitcoin Mining Intro If your hash rate is h and you mine for time , on average thenumber of found blocks is D = Difficulty, h = miner’s hashrate Exp- Ananda buys a mining computer with h = 1Ghash/s = 10^9hash/s . If he mines for a day(86,400 s) when D = 1690906 and B=50BTCFound Blocks = ht / ( 2^32 * D) = 0.0119 blocks = 0.0119 * B = 0.595BTC Classification of mining Solo Mining: Mining alone. Pooled Mining: Mining with other miners in a mining pool.9N =th232Dt
    10. 10. Solo Mining as a Poisson Process Number of trial is depends on miner’s hash rate h p: Probability of success(very small). n: Number of blocks found by a miner mining for time t with hash rate h results in on average blocks. n follows the Poisson distribution P0(λ) where λis the parametercalled intensity. P: Payout P= N x 1B = N x 25 x 11500¥ (1B = 1block = 25 BTC) Exp: Ananda has V[P]=0.0119B2 , σ = 5.454B, About 3 months to find a block in solo mining. The process is completely random and memoryless. May wait on average 3 more months.10l =th232DE[P] = lB =htB232D, V[P] = lB2=htB2232D, s = V[P]th232D
    11. 11. Pooled Mining Joint effort & reward distribution. H: Total hash rate of all miners. Single miner’s hash rate h = qH (0<q<1) E[Pp]: Total average payout of the pool E[Ps]: Single miner’s payout in pooled mining V[Ps]: Single miner’s variance in pooled mining11E[Pp ]=HtB232DE[Ps ]= qHtB232D=hHHtB232D=htB232D= l = E[P]V[Ps ]= q2HtB232D= qhtB232D= ql < l =V[p]
    12. 12. Pooled Mining f: Fee/Block, B = Block reward. Operator’s fee for a block = fB. Actual Reward for the pool miners = B – fB = (1-f)B. In a pool Each miner submits shares into the pool. Share: Hash of a block header calculated by a miner which isless than Tcur assuming D=1 (e.g. Tcur = Tmax). Each hash has a probability of to be a share in the pool. Each share has a probability p = to validate a block. For a single share, a miner’sExpected payout = Expected contribution to total reward = pB1212321D
    13. 13. Pooled Mining Reward System A pool has the potential to improve the variance of a miner. Dividing a reward in a fair way is difficult.Existing pool reward systems13PooledMiningSimpleRewardSystemsProportionalPay-per-shareScore-basedSystemsSlush’sMethodGeometricMethodPay-per-last-N-shares
    14. 14. Proportional Pool14
    15. 15. Proportional Pool (1-f)B is distributed in proportion to the number of shares in aRound. Round: Round is the time between two success (2 blocks). n: Number of shares submitted by a miner during a round. N: Total number of shares during the round. Miner’s payout = Assumption: Fixed number of miners in a proportional system. N follows a negative binomial distribution with success ratep=1/D.15nN1- f( )B#trial = #success+ # failureP(N) =#success+ # failure-1#success -1æèçöø÷ p#success-1(1- p)# failurep
    16. 16. Proportional Pool: Expected Value &Variance After the success in the previous round, in the next round, wehave N-1 failed shares before the final successful share.16#success = 2 # failure = (N -1)P(N) =2 +(N -1)-12 -1æèçöø÷ p2-1(1- p)N-1p =N1æèçöø÷ p2-1(1- p)N-1p= Np2(1- p)N-1Reward for a share, w =BN(ignoring fees)Expected PayoutE[w]= E[BN]=BNNp2(1- p)N-1= p2BN=1¥å (1- p)K= pBK=0¥å
    17. 17. Proportional Pool: Expected Value &Variance After the success in the previous round, in the next round, wehave N-1 shares before the final success share. Exp : if D = 1.5 x 106, Variance per share of a miner in a pool is 1.13 x 105 timesless than the variance in solo mining.17
    18. 18. Pool-Hopping Problem18 Pool-Hopping: Some miners leave pool early to increasetheir profit but that decrease the profit of continuous miners. N: Total Number of shares follows a geometric distributionwith parameter p. Given that, I shares already submitted, then N > I.P(N) = p(1- p)N-1P(N | N > I) =0 N £ Ip(1- p)N-I-1N > IìíïîïE[w | N > I] =p(1- p)N-I-1BNN=I+1¥å (w =BN)If I is small,e.g. shares submitted at the very start,E[w | N > I] » -pBln p = pBln D > pB
    19. 19. Simplification…19
    20. 20. Pool-hopping Amplification factor20 Represents the amplification factor when xD = (pI )(1/p)=Ishares have already been submitted. Monotonically decreasing function. A pool hopper will mine if x < x0 and mine solo when x >x0. The payout of the honest miners will be less thanexpected because of hopping by pool hoppers.f(x):= exp(x)E1(x)x » 0, f (x) » -ln x -g ,where g is Euler gamma constantx » ¥, f (x) »1x +1f (x) =1 represents solo mining for x0 = 0.4348182 » 43.5%
    21. 21. Pay-per-share Pool21
    22. 22. Pay-per-share pool(PPS) A hopping-proof method. Reward is given per share. When a participant submits a share, he is immediatelyrewarded with (1-f)pB independent of found blocks . Operator keeps all the rewards for found blocks. PPS is a deterministic value known in advance. Properties: Offers zero variance in the reward per share. No waiting time. No losses due to pool-hopping. But operator is taking the risk What if no blocks are found? Chance of bankruptcy.22
    23. 23. Marcov chain Modeling in PPS pool When will the PPS pool go bankrupt? Goal: Estimate the financial reserves that the pool operatorshould keep to prevent pool bankruptcy. Pool operator’s balance can be modeled as the Markovchain where each submitted share corresponds to a step.23Xt+1 - Xt =-(1- f )pB + B w.p. p-(1- f )pB w.p. 1-pìíïîïE[Xt - Xt-1]= {-(1- f )pB+ B}p+{-(1- f )pB}(1- p) = fpBE[(Xt - Xt-1)2]= -p2B2+ pB2+ f 2p2B2V[Xt - Xt-1]= pB2- p2B2» pB2
    24. 24. Marcov chain Modeling in PPS pool(continued) By the central limit theorem, Long term behavior of thestochastic process is equivalent to the following form with thesame expectation fpB and variance pB2. Scaling the initial condition by a factor of , we get thefollowing equivalence.24pBXt+1 - Xt =+ pB w.p.(1+f p)2- pB w.p.(1-f p)2ìíïïîïïXt+1 - Xt =+1 w.p.(1+f p)2-1 w.p.(1-f p)2ìíïïîïï
    25. 25. Bankruptcy Recurrence Equation an: Probability to ever reach 0 (represents bankruptcy). Given: We start in state n and denoting By conditioning on the first step we can get recurrence eqn. The characteristic polynomial of this eqn. is General solution: Boundary Conditions: , we have Thus,25q = (1+ f p)/ 2an = qan+1 +(1-q)an-1ql2-l +(1-q)a0 =1,a¥ = 0an = A+ B((1-q)/ q)nA = 0,B =1an =1-qqæèçöø÷n=1- f p1+ f pæèççöø÷÷n» e-2 fn p
    26. 26. Safe reserve for a PPS pool R: Starting reserve of the pool operator. δ: Probability that the pool will ever go bankrupt. To maintain a bankruptcy probability at most , pool shouldreserve at least Exp1: B = 50 BTC,δ=1/1000,f = 5% , R=3454 BTC Exp2: If operator fixes f=1%,he has R = 500BTC,then Probability of bankruptcy δ= 81.9%26d = a RpB» exp -2 fR ppBæèççöø÷÷ = exp-2 fRBæèçöø÷R =Bln(1/d)2 f
    27. 27. Hopping Immunity Theorem It’s impossible to stop hopping if you pay rewards tounsuccessful shares. Theorem: Suppose, difficulty D and block reward B are fixed. Let a reward method distribute (1-f)B among shares inthe round according to a deterministic function of theround length and the share index.27Expected Reward per share at thetime of submission is always (1-f)pBThe entire reward is always given to thelast share submitted .
    28. 28. Methods not discussed PPS is not that good. Hopping-proof methods. First attempt done in Slush’s pool using exponentialscore function to give scores to the miners. Not completely hopping-proof. Other Score based methods Geometric method. Pay-per-last-N-shares. Some other advanced method.28
    29. 29. Things I want to research Statistical analysis of pooled mining. Statistical analysis of transaction graphs. Integrate or Develop better mining pools.29
    30. 30. Bibliography Bitcoin: A Peer-to-Peer Electronic Cash System- S. Nakamoto, Tech Report, 2009 Analysis of Bitcoin Pooled Mining Reward Systems- Meni Rosenfeld - Distributed, Parallel, and Cluster Computing,2011 On Bitcoin and Red Balloons- M. Babaioff, S. Dobzinski, S. Oren, and A. Zohar, SIGEcom(Special InterestGroup on ecommerce) Exchanges, 10(3), 2011 Quantitative Analysis of the Full Bitcoin Transaction Graph- D. Ron and A. Shamir, Financial Cryptography 2013 Bitter to Better — How to Make Bitcoin a Better Currency- S. Barber, X. Boyen, E. Shi, and E. Uzun, Financial Cryptography 2012 Cryptographic hash-function basics: Definitions, implications, andseparations for preimage resistance, second-preimage resistance,and collision resistance- P Rogaway, T Shrimpton - Fast Software Encryption, 2004 - Springer30
    31. 31. The End31
    32. 32. Bitcoin Global NodesCharts32
    33. 33. Bitcoin DemographicsCharts33
    34. 34. Bitcoin PurchaseCharts34
    35. 35. Roles in Bitcoin NetworkCharts35
    36. 36. Things happened because of bitcoinCharts36
    37. 37. Real world/Offline interactionYou can buy and Purchase with BTC!!!Charts37
    38. 38. Offline Bitcoin meetups in USACharts38
    39. 39. Companies and Venture CapitalCharts39
    40. 40. ‹#›
    41. 41. Bitcoin Software DownloadGraphs41
    42. 42. Bitcoin PenetrationGraphs42
    43. 43. Downloads vs Penetrationvs Internet AccessGraphs43
    44. 44. Global Search Traffic44 Graphs
    45. 45. Trading Volume45 Graphs
    46. 46. Trading Volume46 Graphs
    47. 47. Bitcoin Volatility247
    48. 48. Is everything positive ? NO Bitcoin can topple governments, destabilizeeconomies, and create uncontrollable globalbazaars for contraband. Bitcoins will facilitate transactions for criminals, online poker players, tax-evaders, pornographers, drug dealers, and other unsavory types tired of carrying around aVermeer. Bitcoin is just like knife or hammer. You can kill oryou can use it the most efficient,profitable way !!!!48

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