Bitcoin and Cryptocurrency Technologies

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Commitment scheme.A commitment scheme consists of two algorithms: ● ● com := commit(msg, nonce) The commit function takes a message and secret random value, called a nonce, as input and returns a commitment. verify(com, msg, nonce) The verify function takes a commitment, nonce, and message as input. It returns true if com== commit(msg, nonce) and false otherwise. We require that the following two security properties hold: ● ● Hiding: Given com, it is infeasible to find msg Binding: It is infeasible to find two pairs (msg, nonce)and (msg’, nonce’)such that msg ≠ msg’and commit(msg, nonce) == commit(msg’, nonce’) To use a commitment scheme, we first need to generate a random nonce. We then apply the commit function to this nonce together with msg, the value being committed to, and we publish the commitment com. This stage is analogous to putting the sealed envelope on the table. At a later point, if we want to reveal the value that they committed to earlier, we publish the random nonce that we used to create this commitment, and the message, msg. Now, anybody can verify that msg was indeed the message committed to earlier. This stage is analogous to opening up the envelope. Every time you commit to a value, it is important that you choose a new random value nonce.In cryptography, the term nonceis used to refer to a value that can only be used once. The two security properties dictate that the algorithms actually behave like sealing and opening an envelope. First, given com, the commitment, someone looking at the envelope can’t figure out what the message is. The second property is that it’s binding. This ensures that when you commit to what’s in the envelope, you can’t change your mind later. That is, it’s infeasible to find two different messages, such that you can commit to one message, and then later claim that you committed to another. So how do we know that these two properties hold? Before we can answer this, we need to discuss how we’re going to actually implement a commitment scheme. We can do so using a cryptographic hash function. Consider the following commitment scheme: commit(msg, nonce):= H(nonce ‖ msg) where nonceis a random 256‐bit value To commit to a message, we generate a random 256‐bit nonce. Then we concatenate the nonce and the message and return the hash of this concatenated value as the commitment. To verify, someone will compute this same hash of the nonce they were given concatenated with the message. And they will check whether that’s equal to the commitment that they saw. Take another look at the two properties that we require of our commitment schemes. If we substitute the instantiation of commit and verify as well as H(nonce ‖ msg) for com, then these properties 28
ecome: ● ● Hiding: Given H(nonce ‖ msg), it is infeasible to find msg Binding: It is infeasible to find two pairs (msg, nonce)and (msg’, nonce’)such that msg ≠msg’ and H(nonce ‖ msg) == H(nonce’ ‖ msg’) The hiding property of commitments is exactly the hiding property that we required for our hash functions. If keywas chosen as a random 256‐bit value then the hiding property says that if we hash the concatenation of keyand the message, then it’s infeasible to recover the message from the hash 1 output. And it turns out that the binding property is implied by the collision‐resistant property of the underlying hash function. If the hash function is collision‐resistant, then it will be infeasible to find distinct values msg and msg’ such that H(nonce ‖ msg) = H(nonce’ ‖ msg’)since such values would indeed be a collision. Therefore, if His a hash function that is collision‐resistant and hiding, this commitment scheme will work, in the sense that it will have the necessary security properties. Property 3: Puzzle friendliness. The third security property we’re going to need from hash functions is that they are puzzle‐friendly. This property is a bit complicated. We will first explain what the technical requirements of this property are and then give an application that illustrates why this property is useful. Puzzle friendliness.A hash function H is said to be puzzle‐friendly if for every possible n‐bit output value y, if k is chosen from a distribution with high min‐entropy, then it is infeasible to find xsuch that H(k ‖ x) = y in time significantly less than 2 n . Intuitively, what this means is that if someone wants to target the hash function to come out to some particular output value y, that if there’s part of the input that is chosen in a suitably randomized way, it’s very difficult to find another value that hits exactly that target. Application: Search puzzle.Now, let’s consider an application that illustrates the usefulness of this property. In this application, we’re going to build a search puzzle, a mathematical problem which requires searching a very large space in order to find the solution. In particular, a search puzzle has no shortcuts. That is, there’s no way to find a valid solution other than searching that large space. 1 The reverse implications do not hold. That is, it’s possible that you can find collisions, but none of them are of the form H(nonce ‖ msg) == H(nonce’ ‖ msg’). For example, if you can only find a collision in which two distinct nonces generate the same commitment for the same message, then the commitment scheme is still binding, but the underlying hash function is not collision‐resistant. 29
Page 1 and 2: Bitcoin and Cryptocurrency Technolo
Page 3 and 4: Preface — The Long Road to Bitcoi
Page 5 and 6: work, there is also the issue of co
Page 7 and 8: Finally, CyberCash has the dubious
Page 9 and 10: This was the first serious digital
Page 11 and 12: and so on — powers of two. That w
Page 13 and 14: Figure 3 shows the user side of the
Page 15 and 16: initial cost to acquire all the equ
Page 17 and 18: the system is to record the relativ
Page 19 and 20: original design. However, after Bit
Page 21 and 22: A final reason that’s often cited
Page 23 and 24: Chapter 1: Introduction to Cryptogr
Page 25 and 26: Figure 1.2 Because the number of
Page 27: Property 2: Hiding The second pr
Page 31 and 32: SHA‐256 uses a compression functi
Page 33 and 34: Figure 1.5 Block chain.A block c
Page 35 and 36: Figure 1.7 Merkle tree. In a Mer
Page 37 and 38: throughout this book. 1.3 Digital S
Page 39 and 40: Figure 1.9 Unforgeability game.
Page 41 and 42: andomness just in making a signatur
Page 43 and 44: 1.5 A Simple Cryptocurrency Now let
Page 45 and 46: The first key idea is that a design
Page 47 and 48: Figure 1.13 A PayCoins Transa
Page 49 and 50: Perusing the NIST standard that def
Page 51 and 52: Chapter 2: How Bitcoin Achieves Dec
Page 53 and 54: state of the system. The implicatio
Page 55 and 56: consensus is somewhat pessimistic,
Page 57 and 58: Implicit Consensus. This assumpt
Page 59 and 60: Figure 2.2 A double spend attempt.
Page 61 and 62: In general, the more confirmations
Page 63 and 64: Figure 2.4 The block reward is c
Page 65 and 66: puzzle‐friendliness property from
Page 67 and 68: possible outcomes, and the probabil
Page 69 and 70: theory problem that’s not easily
Page 71 and 72: this interlocking interdependence b
Page 73 and 74: Further reading The Bitcoin whitepa
Page 75 and 76: Chapter 3: Mechanics of Bitcoin Thi
Page 77 and 78: In this example, Alice specifies tw
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3.2 Bitcoin Scripts Each transactio
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the Bitcoin language and one has to
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exactly the same script, which is i
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in the normal case, this isn’t th
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Technically all of these transactio
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The header mostly contains informat
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in turn sends it to all of its peer
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Figure 3.10 Block propagation ti
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that actually affect them. So they
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that the old version would accept a
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Exercises 1. Transaction validation
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Chapter 4: How to Store and Use Bit
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software can automatically turn the
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The cryptographic magic that makes
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may never know (or care) who the co
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Given this stringent requirement, s
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There is a formula called Lagrange
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Ideally, the site will encrypt thos
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seen exchanges that fail due to bre
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Figure 4.5: Proof of liabilities.
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crypto and we won’t cover it here
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Figure 4.8: Payment process involvi
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transaction can't create coins, but
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of U.S. dollars per day pass throug
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Now if you look at a particular sec
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alance of 500,000 BTC. It then sign
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Chapter 5: Bitcoin Mining This chap
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In most cases you'll try every sing
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You can see in Figure 5.3 that over
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steady‐state, the period to find
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TARGET=(65535
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Disadvantages of GPU mining. GPU
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may be the fastest turnaround time
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Figure 5.10: Evolution of mining
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Hopefully, over time the embodied e
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Still, if we could replace Bitcoin
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Figure 5.11: Illustration of uncert
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Figure 5.13: Mining rewards. Thr
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Some mining hardware even supports
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By April 2015, the situation looks
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Figure 5.15 Forking attack.A mal
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Temporary block‐withholding attac
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the transaction from address X
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Chapter 6: Bitcoin and Anonymity
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Unlinkability. To understand unl
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eason is that use cases that we cla
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But this reveals something. The tra
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the other hand, are often not new a
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Figure 6.5. Labeled clusters.
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Luckily, this is a problem of commu
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they are unhappy with anonymity pro
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Fees should be all-or-nothing. M
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Somebody looking at this transactio
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a single transaction that combines
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just minting one doesn’t automati
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Efficiency. Recall the statement
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We start with Bitcoin itself, which
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An alternative design to Zerocoin i
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elieve the same thing. So consensus
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of developers who maintain Bitcoin
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The interesting case is if the fork
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eing effectively bankrupt. As of ea
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In an important sense it doesn't ma
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of illegal items becomes potentiall
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arrest. So although Ulbricht was th
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kind of business that will handle l
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een enough time for sellers to buil
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The text refers to “activities in
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A book that looks at the history of
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It’s easy to see how Bitcoin’s
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Why might memory‐hard and memory
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Until recently, it wasn’t known i
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meaning the exponential growth peri
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Next, consider the problem that SET
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In Permacoin, each miner Msto
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Interestingly, these concerns have
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they can perform the signatures on
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schemes also require a small amount
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to provide an effective solution, t
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Chapter 9: Bitcoin as a Platform In
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means that if you actuallydo
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CommitCoin exploits this property.
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features without needing to change
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would just look like a dollar bill.
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you. In particular, you can’t use
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To solve this problem we can once a
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NBA draft lottery.One example th
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that there’s no way for anyone to
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to predict the low‐level fluctuat
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design, because miners have to veri
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Here's another example, this time f
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You can also trade shares for futur
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Order books.The final piece o
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Chapter 10: Altcoins and the Crypto
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Attracting miners has special impor
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with the launch date of the altcoin
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Namecoin is technically interesting
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10.3 Relationship Between Bitcoin a
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Switching costs are certainly not z
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If our altcoin is merge‐mined, we
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When we think about a rational mine
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DepositA [Altcoin block chain] Refu
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Sidechains. The sidechains vision i
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lock themselves could tell us. This
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written in bytecode and executed by
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Bitcoin. In particular, there are c
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The simple binary Merkle tree used
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Chapter 11: Decentralized Instituti
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Bitcoin, Alice can remotely transfe
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only these signatures of limited fo
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11.3 Template for Decentralization
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Sidebar: trust.Some people in th
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competition among intermediaries. P
Page 305 and 306:
To drive home the mismatch between
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Conclusion to the book Some people
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