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Cryptocurrency Bitcoin
Tsaschikher Nyamgerel
2015
Overview
• What is cryptocurrency? (Introduction)
• How it works
• How to use it
• Transaction
• Security (Block Chain, Pr...
What is Cryptocurrency?
• Cryptocurrency is electronic money or virtual currency. (Online cash,
digital cur…)
• Bitcoin is...
Who and When?
• Bitcoin is proposed in 2008 by “Satoshi Nakamoto”
• Released Paper is found: bitcoin.org/bitcoin.pdf
• Fir...
Who and When?
It’s name also been suggested that
• Samsung
• Toshiba
• Nakamichi
• Motorola
Are the founders. (But there’s...
How to Use Bitcoin?
• Generate BTC address
• Connect to BTC network
• Update or download transactional block chain
• Send ...
What is Advantage?
• Transactions transact directly with each other without using third party
(no Bank)
• Almost no proces...
How Does Transaction Work?
• Use digital signature for transaction (identity like real signature)
• Binds the sender’s ide...
Identity (Digital Signature)
• Bitcoin uses the digital signature to prove that
signature owner is the “account owner”
– I...
Private Key
• Private key is a single unsigned 256 bit integer (32 bytes)
– Usually picked at “random”
• Needs to be secre...
Public Key
• Elliptic curve multiplication function generate a public key from
private key (compressed 33 and uncompressed...
Account Address
• Bitcoin address is string of digits and characters
and generated from public key
– Using cryptographic h...
Public Key and Address
Generation
Public Key generation
using Elliptic Curve Address generation
using Hash
Digital Signature
• To send money (Transaction)
– User must prove that he is owner of the address
• Which means he has the...
Advantage of Elliptic Curve
• Shorter keys are as strong as long key for RSA
(IEEE paper)
• Low on CPU consumption.
• Low ...
Transaction
• BitCoin is collective entries into a ledger
Transaction
• Every transactions ever happened recorded on one global ledger
• To send money (Alice -> Bob)
– Account has ...
Transaction
• In fact, no records of account balances are kept
• Instead of balances, fund is verified through link to
pre...
Transaction
Now Alice can send 5 bitcoins to Bob
Transaction
Real Transaction exampleInput balance should match with output
Transactions are not encrypted so it is possibl...
Transaction (Chain)
- Each transaction includes its previous transaction
Transaction
• When you install BitCoin wallet
– It downloads every transactions
– Checks each one’s validity all the way b...
Double Spending (Order or
Timestamp)
• A double spend is an attack where the given set of coins is
spent more than 1 trans...
Double Spending
• Double spend (Alice->Bob)
1. Alice send bitcoin to Bob, don’t include fee
2. Receive items
3. Before tra...
Double Spending
• Solution:
– BTC network records all bitcoin transfers in a
ledger (the block chain)
– And ensuring for a...
Block Chain
• Block chain (Public Ledger) is used to order
transactions
– Ordered and timestamped record of transactions
•...
Block Chain
• Node (also computer or miner)
– Collects unconfirmed transactions into a block
– Broadcasts the block to all...
Block Chain (Book and Pages)
• Node
– Collects transactions that are happened at the same time
– And puts them into a one ...
Block Chain
– To add block to the block chain
• Every transactions inside the block paired and then
hashed together like a...
Block Chain
• Every transactions hashed together like a Merkle
tree until it becomes one Merkle Root (Digest)
• Only the M...
Block Chain
• Problem
– Multiple blocks can be created at the same time
• Can’t rely on the order because they may arrive ...
Block Chain
• In this picture,
– Three blocks are happened at the same time and
– Each node build on top of the first one ...
Block Chain
– Current block link gets broken when someone solves
another block (prev picture)
– The general rule is that
•...
Proof of Work (POW)
• Proof of Work
– Is a economic measure to deter spam email and denial of
service (Dos) attacks
– It r...
Proof of Work (Bitcoin)
• Proof of work scheme is SHA-256
• And works relative to a given
– Challenge string (Hashed previ...
Proof of Work
•
Challenge
Proof of Work
When 1 zero added,
work will be doubled
Because 2^5 = 2^4 * 2
Proof Challenge
Hash...
Proof of Work
When resulting zeros are 40 means 2^40 = 1099511627776
When 41 zeros means 2^40 * 2 (doubled)
Proof of Work
• It is impossible to switch block in the middle of the chain
– Because hash value for the new block would b...
Proof of Work
• After successfully solving the problem
– Block will be accepted (to the next chain)
• Difficulty of work i...
Bitcoin Network
• The steps to run the network are:
– New transactions are broadcast to all nodes (transaction)
– Each nod...
Network (Safety)
• If two blocks are found at the same time, this will be decided by the
vote
• Vote is not one-IP-address...
Network (Safety)
• Moreover, when two different blocks are found, nodes work on the first
one they received, but save the ...
Network (double spending)
• For attackers perspective:
– Attacker needs to get input from previous block and add his own
(...
How Bitcoin is Generated?
• Reward is given to whoever solves a block
• Which means
– Whenever miners succeed, they are al...
Bitcoin Generation (reward)
Whoever solved the hash can include their
transaction into new block (for reward)
Also collect...
Bitcoin Generation
• Totally 21,000,000 BTC
– Total number of BTC will be generated for reward (Maximum
number of BTC in B...
Bitcoin Generation
• Reward size is cut in half every 210,000 blocks (4 years)
– Every 10 minutes there’s new block genera...
Bitcoin Generation
• At around year 2140, all bitcoins will have
been generated
• BTC are fractional
– Smallest possible u...
Bitcoin Unit
Is it slow? (Transaction)
• Bitcoin transactions are not slow, in fact it is
INSTANT! But confirmations take 10 minutes on...
How to Get Bitcoin?
• There are currently four methods of acquiring
Bitcoins:
1. Mining (Requires large investment)
2. Wir...
Where Do I Store Bitcoin?
• Bitcoins are stored in wallets
– Wallets is a randomly generated string of numbers and
consist...
Local Wallet Example
Sending BTC
Receive using address
Receive using QR code
BTC addresses
BTC vs USD
• Currently there is 14,083,600 BTC generated
• 1 BTC = $234.54 USD ($221 USD 10 days ago)
• Market Cap: 234 * ...
Potential Outcome of BTC
• BTC will either succeed with the mainstream or fail
• If succeed:
– By 2025
• The estimated wor...
Price
– Previous data is from 2013
• Current GDP US$74.31 trillion (from wikipedia)
• Market cap: 0.0044% of the current G...
Fee per day
12 – 17 BTC is used for everyday25 BTC from reward
Number of Transactions
~60.000 – 100.000 and increasing
Number of Transactions per Block
350 – 750 and increasing
Comparison of Crypto-currencies
BitCoin vs LiteCoin
Old data
Price and Market Cap
BitCoin LiteCoin
1 vs USD
$234.50 USD ~1.4 USD ($1.42771)
Market Capacity
$3,299,521,813.80
(~$3.3B U...
Conclusion
• Bitcoin is decentralized cryptocurrency
• Transferred person to person
• No bank or government control
• Low ...
References
• https://bitcoin.org/bitcoin.pdf
• http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2544331
• http://en.wiki...
Thank you
• Questions?
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Bitcoin (Cryptocurrency)

Technical Overview and Security of Bitcoin and Cryptocurrency

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Bitcoin (Cryptocurrency)

  1. 1. Cryptocurrency Bitcoin Tsaschikher Nyamgerel 2015
  2. 2. Overview • What is cryptocurrency? (Introduction) • How it works • How to use it • Transaction • Security (Block Chain, Proof of work) • Statistics • Cryptocurrency comparisons • It’s market and its future • BitCoin vs LiteCoin
  3. 3. What is Cryptocurrency? • Cryptocurrency is electronic money or virtual currency. (Online cash, digital cur…) • Bitcoin is one of the biggest (successful) representation of the Cryptocurrency • Bitcoin has no central authority (Decentralized) (P2P like torrent) – No government involved (no bank) • BTC can be created offline (email address) – Anyone can create (without any permission) – 1461501637330902918203684832716283019655932542976 (2^160) • 21 Million Bitcoins will be created, and or mined • Until year 2140. – Limited or scarce like gold (Deflationary and protected from inflation)
  4. 4. Who and When? • Bitcoin is proposed in 2008 by “Satoshi Nakamoto” • Released Paper is found: bitcoin.org/bitcoin.pdf • First appeared and operated on 1/3/2009 • Completely open source, so anyone can develop his own cryptocurrency (BitCoin, LiteCoin, AltCoin…) • Released open source: github.com/Bitcoin/Bitcoin
  5. 5. Who and When? It’s name also been suggested that • Samsung • Toshiba • Nakamichi • Motorola Are the founders. (But there’s no confirmation) Satoshi Nakamoto
  6. 6. How to Use Bitcoin? • Generate BTC address • Connect to BTC network • Update or download transactional block chain • Send and receive BTC – Offline clients: • Install electrum, armory and hive.. – Online clients: • Register coinbase.com, blockchain.info/wallet..
  7. 7. What is Advantage? • Transactions transact directly with each other without using third party (no Bank) • Almost no processing fees • No bank or government control – Which means no identity revelation and no freezing account • Transactions are computationally impractical to reverse (to protect sellers from fraud) • Implement escrow mechanisms (to protect buyers) • Very difficult and expensive to hack (Hacking 10 minutes cost around half billion USD)
  8. 8. How Does Transaction Work? • Use digital signature for transaction (identity like real signature) • Binds the sender’s identity to the transaction • Detail of transaction is broadcasted to all the nodes of the p2p network • Receiver can get assurance from network about transaction (balance match, not spent..) based on cryptographic proof before it gets verified or even payed – Owner has money in his account and didn’t spend it • Distributed network also give assurance for double spent
  9. 9. Identity (Digital Signature) • Bitcoin uses the digital signature to prove that signature owner is the “account owner” – In other words, owner owns private key • “Private Key” is used to create the signature • “Public Key” is used to verify the signature – This allows anybody can verify digital signature if they have its public key (account address)
  10. 10. Private Key • Private key is a single unsigned 256 bit integer (32 bytes) – Usually picked at “random” • Needs to be secret (all the time) – When you lose your private key, you’ll lose your all bitcoins in that account • Owner of the private key can spend corresponding account bitcoins (funds) • The private key used to generate – “Digital Signatures” • Signature is required to spend bitcoins (of the account) – “Public Keys” • Public key is used to verify signatures and generate account address Private key
  11. 11. Public Key • Elliptic curve multiplication function generate a public key from private key (compressed 33 and uncompressed 65) • No need to be secret – Used for verifying account owner • “Account address” is generated from public key – Using a one-way cryptographic hash function • Used to verify the “Digital Signatures” – Using this digital signature he can transact bitcoin (without revealing private key) • Verifying digital signature, we can now that he has a private key (owner or not) Public key
  12. 12. Account Address • Bitcoin address is string of digits and characters and generated from public key – Using cryptographic hash (SHA256) • Shared with anyone who wants to send you bitcoins • User can have many addresses – 1461501637330902918203684832716283019655932542976 (possible bitcoin addresses) •
  13. 13. Public Key and Address Generation Public Key generation using Elliptic Curve Address generation using Hash
  14. 14. Digital Signature • To send money (Transaction) – User must prove that he is owner of the address • Which means he has the private key – To do that user generate “digital signature” from • Transaction message • His private key Signature = f(private key, transaction message) – Nodes in the network can verify using this signature that • He is the owner of the account and • He can spend money (from that account) accept or reject = verify(transaction message, public key, signature) – BitCoin Digital Signature uses • Elliptic Curve Digital Signature Algorithm (ECDSA) (en.wikipedia.org/wiki/Elliptic_Curve_Digital_Signature_Algorithm) Transaction message is Hashed message so result will be constant. Signature = f(private key, Hash(M))
  15. 15. Advantage of Elliptic Curve • Shorter keys are as strong as long key for RSA (IEEE paper) • Low on CPU consumption. • Low on memory usage. • RSA relies on the hardness of factorization (Studied for 2500 years) • While Elliptic cure depends on discrete logarithm (25 years of research)
  16. 16. Transaction • BitCoin is collective entries into a ledger
  17. 17. Transaction • Every transactions ever happened recorded on one global ledger • To send money (Alice -> Bob) – Account has to have enough money • To verify money in the account – We need to verify previous transactions • That fund is also verified through links to previous transactions • All transactions are written on the global ledger • Alice has 5 bitcoins – Means someone sent to Alice 5 bitcoins before – “Input” should be 5 BTC – “Output” can’t exceed 5 BTC
  18. 18. Transaction • In fact, no records of account balances are kept • Instead of balances, fund is verified through link to previous transactions • Inputs should match the balance – To making sure that Alice can send 5 BTC • Owning BTC means, – There are transactions that point to your account – And haven’t spent
  19. 19. Transaction Now Alice can send 5 bitcoins to Bob
  20. 20. Transaction Real Transaction exampleInput balance should match with output Transactions are not encrypted so it is possible to browse and view http://blockexplorer.com ScriptSig contains: Signature + Public Key Type: Address and PubKey
  21. 21. Transaction (Chain) - Each transaction includes its previous transaction
  22. 22. Transaction • When you install BitCoin wallet – It downloads every transactions – Checks each one’s validity all the way back to the first transaction ever made – If you use bitcoin wallet with TOR network (which hides IP address) you can use BTC without revealing anything but public key
  23. 23. Double Spending (Order or Timestamp) • A double spend is an attack where the given set of coins is spent more than 1 transactions • So, there is no guarantee that first transaction comes before second one – Because transactions are passed through the network node-by- node • We can’t trust timestamp also – Because anyone can lie about the time a transaction was created • This opens up the potential fraud
  24. 24. Double Spending • Double spend (Alice->Bob) 1. Alice send bitcoin to Bob, don’t include fee 2. Receive items 3. Before transaction confirms • Send the same bitcoin to herself include a fee 4. Miner (node) picks up the transaction with the fee and the one without fee will disappear (already spent) • This will happen only if there’s same block chain happened (Rare)
  25. 25. Double Spending • Solution: – BTC network records all bitcoin transfers in a ledger (the block chain) – And ensuring for all transferred bitcoins that they haven't been previously spent – Block chain: • Is used to order transactions (TimeStamp) • While transaction chain keeps track of how ownership changes
  26. 26. Block Chain • Block chain (Public Ledger) is used to order transactions – Ordered and timestamped record of transactions • One block of block chain: – Includes many transactions that considered to have happened at the same time • Transactions not yet in a block are called “unconfirmed” or unordered
  27. 27. Block Chain • Node (also computer or miner) – Collects unconfirmed transactions into a block – Broadcasts the block to all nodes
  28. 28. Block Chain (Book and Pages) • Node – Collects transactions that are happened at the same time – And puts them into a one block – Then link to the block chain • If we think global ledger is the BOOK – One block is the page of that book – Multiple transactions listed in that page • Miners (nodes) goal is – Take this page – Add to the global ledger BOOK
  29. 29. Block Chain – To add block to the block chain • Every transactions inside the block paired and then hashed together like a Merkle Tree
  30. 30. Block Chain • Every transactions hashed together like a Merkle tree until it becomes one Merkle Root (Digest) • Only the Merkle root included in the block’s hash • Finally resulting one block hash combined with the block chain (linked together) • Item here represents transaction Block Chain (Digest) New Block
  31. 31. Block Chain • Problem – Multiple blocks can be created at the same time • Can’t rely on the order because they may arrive in different order • Solution – Vote the blocks and whichever wins will be selected • How to vote? – Every nodes need to solve problem in order to vote • Which makes it difficult to vote (from fake votes) • Proof of work – That puzzle is called proof of work – Which measures (proves) computing power is used or not
  32. 32. Block Chain • In this picture, – Three blocks are happened at the same time and – Each node build on top of the first one it received – Other nodes may have received the blocks in a different order and will be generating on the first block they received. •
  33. 33. Block Chain – Current block link gets broken when someone solves another block (prev picture) – The general rule is that • Node always immediately switch to the longest branch available. – The Proof of Work (Reversing hash with certain threshold) • Makes it rare for blocks to be solved at the same time (Time Stamp) • And even more rare for this to happen multiple times in a row. – The probability of a single hash succeeding is: • 0.0000000000000000000047086771693440932602401694830052 125
  34. 34. Proof of Work (POW) • Proof of Work – Is a economic measure to deter spam email and denial of service (Dos) attacks – It requires computing power before being allowed to use service • Key feature – Work must be hard to compute – But easy to verify • Bitcoin Proof of work is – Similar to Adam Back’s Hashcash – Used for block generation
  35. 35. Proof of Work (Bitcoin) • Proof of work scheme is SHA-256 • And works relative to a given – Challenge string (Hashed previous block chain) – And proof (Nonce or random guess) • Given challenge string, node needs to find proof that when hashed, result begins with a number of zero bits (Threshold). • Hash(Proof + Challenge) = 000..0XXX..X – Depending on the zeros computation time would be doubled
  36. 36. Proof of Work • Challenge Proof of Work When 1 zero added, work will be doubled Because 2^5 = 2^4 * 2 Proof Challenge Hash 0000000…0xxxxxxxxx…x Threshold zeros Keep inserting Random bits Prev BC Hash
  37. 37. Proof of Work When resulting zeros are 40 means 2^40 = 1099511627776 When 41 zeros means 2^40 * 2 (doubled)
  38. 38. Proof of Work • It is impossible to switch block in the middle of the chain – Because hash value for the new block would be different – And reference would no longer point to it • Which means block cannot be solved before the previous block is solved
  39. 39. Proof of Work • After successfully solving the problem – Block will be accepted (to the next chain) • Difficulty of work is adjusted by network so that block can be generated every 10 minutes – When many miners (nodes) joined to the network proof of work become more difficult – Otherwise, it will become easier • That is the reason transaction confirmation take 10 minutes on average (SAFETY reason)
  40. 40. Bitcoin Network • The steps to run the network are: – New transactions are broadcast to all nodes (transaction) – Each node collects new transactions put it into a block and works on finding a difficult proof-of-work for its block (problem solving) – When a node finds a proof-of-work it broadcasts the block to all nodes (block) – Nodes accept the block only if all transactions in it are valid and not already spent – Nodes express their acceptance of the block by working on creating the next block in the chain and using the hash of the accepted block as the previous hash
  41. 41. Network (Safety) • If two blocks are found at the same time, this will be decided by the vote • Vote is not one-IP-address-one-vote but rather one-CPU-one-vote • In the network, there is other nodes (CPU) will also solve and result (vote) will be the same as one of them • One with the most vote will be accepted • Modifying a past block, attacker have to redo all the proof of work of the previous blocks
  42. 42. Network (Safety) • Moreover, when two different blocks are found, nodes work on the first one they received, but save the other branch in case it becomes longer • Link will be broken when the next POW is found and other link becomes longer • And nodes that are working on the other branch will then switch to the longer one. • Majority of decision is represented by the longest chain, which has the greatest POW effort invested • Outrunning block chain is same as the winning the lottery many consecutive times – Because hash is collision resistance (Hard to find)
  43. 43. Network (double spending) • For attackers perspective: – Attacker needs to get input from previous block and add his own (fake) transaction. – Then compute the next blocks until he catches the honest block chain. – Honest chain generates new block every 10 minutes. – The race between the honest chain and attacker chain can be characterized as a Binomial Random Walk. – Probability is analogous to a Gambler’s Ruin problem Waiting for 10 minutes makes transaction more secure!
  44. 44. How Bitcoin is Generated? • Reward is given to whoever solves a block • Which means – Whenever miners succeed, they are allowed include in that transaction block special transaction for themselves. • That is coin-based transaction and this is how new coins get included in the BTC system. • This is the reward for work associated with adding a new transaction block to the existing transaction block chain for Bitcoin – Because these nodes are using a lot of computational power (Hardware and electricity) to come up with these proofs • Moreover, succeeded miner also get to collect the transaction fees that are specified in the transaction records
  45. 45. Bitcoin Generation (reward) Whoever solved the hash can include their transaction into new block (for reward) Also collects all transactions fees inside of that block
  46. 46. Bitcoin Generation • Totally 21,000,000 BTC – Total number of BTC will be generated for reward (Maximum number of BTC in BTC network) – BTC system is public, so anyone knows how many BTC have been generated • 25 BTC reward – Current BTC reward for solving new block (This was 50 at the beginning) • Transaction Fees – After all BTC generated, reward will depends on the transaction fees
  47. 47. Bitcoin Generation • Reward size is cut in half every 210,000 blocks (4 years) – Every 10 minutes there’s new block generated – So 1 block * 6 (hour) * 24 * 365 * 4 = 210,240 • Every 2016 blocks proof of work is normalized (2 weeks) – Estimated time: 10 min * 6 (hour) * 24 (day) * 14 = 2016 – When blocks are generated faster than 2 weeks, proof of work becomes harder – Otherwise it becomes easier (fewer miners)
  48. 48. Bitcoin Generation • At around year 2140, all bitcoins will have been generated • BTC are fractional – Smallest possible unit is: 0.0000 0001 BTC (Satoshi) – All other units • Bits or μBTC – 0.000001 • mBTC - 0.001..
  49. 49. Bitcoin Unit
  50. 50. Is it slow? (Transaction) • Bitcoin transactions are not slow, in fact it is INSTANT! But confirmations take 10 minutes on average (New block generation time) • Confirmation is supposed to take care of double spending problem • If customer buys small stuff like coffee customer doesn't have to wait at all. The merchant simply takes the risk
  51. 51. How to Get Bitcoin? • There are currently four methods of acquiring Bitcoins: 1. Mining (Requires large investment) 2. Wiring in fiat currency to an BTC exchange (www.coinbase.com) 3. Buying from an individual 4. Selling items for BTC
  52. 52. Where Do I Store Bitcoin? • Bitcoins are stored in wallets – Wallets is a randomly generated string of numbers and consists of: private key and public key • There are three different types of Wallets: 1. Online wallet service • Create and remember passwords for our behalf (coinbase.com) 2. Local wallet or offline wallet • Download and install on our computer (We need to download all block chains on your computer ~ over 20GB) 3. Paper wallet • Keys are generated offline and printed on a physical piece of paper
  53. 53. Local Wallet Example Sending BTC Receive using address Receive using QR code BTC addresses
  54. 54. BTC vs USD • Currently there is 14,083,600 BTC generated • 1 BTC = $234.54 USD ($221 USD 10 days ago) • Market Cap: 234 * 14,083,600 ~ $3.3B Billion USD (3.1 10 days ago) • Price bubble 1 BTC ~ $1000 USD
  55. 55. Potential Outcome of BTC • BTC will either succeed with the mainstream or fail • If succeed: – By 2025 • The estimated world GDP is expected to be around $71T in the year 2025 • “If” BTC can establish a 0.1% Market Cap or $71B and 25% are used for transactions, then market price of one Bitcoin would be about.. ($14,947) (Old data from end of the 2013) • Rule #1 of investing: (Because of “if”) – Invest only what you can afford to lose! • Bitcoin is still experimental, so its future cannot be predicted by anyone.
  56. 56. Price – Previous data is from 2013 • Current GDP US$74.31 trillion (from wikipedia) • Market cap: 0.0044% of the current GDP • 100.000 - 300.000 BTC are used for the transaction (every day) (0.0045% used for the transaction) from 3.3B – Saving (not using) – When it becomes 0.1% and – 25% of them used for the transaction • 1 BTC ~ $15.000 USD • Price depends on Market capacity • And number of transaction used • Value of the bank balance is set by supply and demand of the market
  57. 57. Fee per day 12 – 17 BTC is used for everyday25 BTC from reward
  58. 58. Number of Transactions ~60.000 – 100.000 and increasing
  59. 59. Number of Transactions per Block 350 – 750 and increasing
  60. 60. Comparison of Crypto-currencies
  61. 61. BitCoin vs LiteCoin Old data
  62. 62. Price and Market Cap BitCoin LiteCoin 1 vs USD $234.50 USD ~1.4 USD ($1.42771) Market Capacity $3,299,521,813.80 (~$3.3B USD) 100% $55,143,333.40 (~$55M USD) 1.67% # of Transactions 106,955 4,505
  63. 63. Conclusion • Bitcoin is decentralized cryptocurrency • Transferred person to person • No bank or government control • Low transaction fees • Bitcoin solves “double spend” problem through distributed network – Proof of work – Hash • Open to anyone – Public ledger – Block chain • Very difficult and expensive to hack – Winning a lottery consecutive times in 10 minutes • Transparent (open source)
  64. 64. References • https://bitcoin.org/bitcoin.pdf • http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2544331 • http://en.wikipedia.org/wiki/Proof-of-work_system • https://en.bitcoin.it/wiki/Proof_of_work • https://bitcoin.org/en/developer-guide#payment-processing • http://alphapixel.com/sites/default/files/download/BitCoinPresentation.p df • https://www.stlouisfed.org/~/media/Files/PDFs/DWTF/Bitcoin-3-31- 14.pdf • http://www.imponderablethings.com/2013/07/how-bitcoin-works-under- hood.html • https://www.tbs-certificates.co.uk/FAQ/en/sha256.html • www.khanacademy.org/economics-finance-domain/core-finance/money- and-banking/bitcoin • http://www.coindesk.com/price/
  65. 65. Thank you • Questions?

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