Bitcoin and Cryptocurrency Technologies

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Recall that you are free to create as many Bitcoin addresses as you like. With this in mind, you might be wondering whether Bitcoin addresses really are pseudo-identities considering that you can create as many of these pseudonyms as you like. As we’ll see, this still does not make Bitcoin anonymous. In computer science, anonymity refers to pseudonymity together with unlinkability. Unlinkability is a property that’s defined with respect to the capabilities of a specific adversary. Intuitively, unlinkability means that if a user interacts with the system repeatedly, these different interactions should not be able to be tied to each other from the point of view of the adversary in consideration. Sidebar.The distinction between anonymity and mere pseudonymity is something that you might be familiar with from a variety of other contexts. One good example is online forums. On a forum like Reddit, you pick a long-term pseudonym and interact over a period of time with that pseudonym. You could create multiple pseudonyms, or even a new one for every comment, but that would be tedious and annoying and most people don’t do it. So interacting on Reddit is usually pseudonymous but not quite anonymous. 4Chan, by contrast, is an online forum in which users generally post anonymously — with no attribution at all. Bitcoin is pseudonymous, but pseudonymity is not enough if your goal is to achieve privacy. Recall that the block chain is public and anyone can look up all Bitcoin transactions that involved a given address. If anyone is ever able to link your Bitcoin address to your real world identity, then all of your transactions — past, present, and future — will have been linked back to your identity. To make things worse, linking a Bitcoin address to a real-world identity is often easy. If you interact with a Bitcoin business — be it an online wallet servics, exchange, or other merchant — they are usually going to want your real life identity in order to let you transact with them. For example, an exchange might require your credit card details, while a merchant will need your shipping address. Or you might go to a coffee shop and pay for your coffee with bitcoins. Since you're physically present in the store, the barista knows a lot about your identity even if they don't ask for your real name. Your physical identity thus gets tied to one of your Bitcoin transactions, making all the other transactions that involved that address linkable to you. This is clearly not anonymous. Side channels. Even if a direct linkage doesn't happen, your pseudonymous profile can be deanonymizeddue to side channels, or indirect leakages of information. For example, someone may look at a profile of pseudonymous Bitcoin transactions and note at what times of day that user is active. They can correlate this information with other publicly available information. Perhaps they’ll notice that some Twitter user is active during roughly same time intervals, creating a link between the pseudonymous Bitcoin profile and a real-world identity (or at least a Twitter identity). Clearly pseudonymity does not guarantee privacy or anonymity. To achieve those, we require the stronger property of unlinkability as well. 166
Unlinkability. To understand unlinkability in the Bitcoin context more concretely, let’s enumerate some key properties that are required for Bitcoin activity to be unlinkable: 1. It should be hard to link together different addresses of the same user. 2. It should be hard to link together different transactions made by the same user. 3. It should be hard to link the sender of a payment to its recipient. The first two properties are intuitive, but the third one is a bit tricky. If you interpret “a payment” as a Bitcoin transaction, then the third property is clearly false. Every transaction has inputs and outputs, and these inputs and outputs are inevitably going to be in the block chain and publicly linked together. However, what we mean by a payment is not a single Bitcoin transaction, but rather anything that has the effect of transferring bitcoins from the sender to the recipient. It might involve a roundabout series of transactions. What we want to ensure is that it’s not feasible to link the sender and the ultimate recipient of the payment by looking at the block chain. Anonymity set. Even under our broader definition of a payment, the third property seems hard to achieve. Say you pay for a product that costs a certain number of bitcoins and you send that payment through a circuitous route of transactions. Somebody looking at the block chain will still be able to infer something from the fact that a certain number of bitcoins left one address and roughly the same number of bitcoins (minus transaction fees, perhaps) ended up at some other address. Moreover, despite the circuitous route, the initial sending and the ultimate receiving will happen in roughly the same time period because the merchant will want to receive payment without too much of a delay. Because of this difficulty, we usually don't try to achieve complete unlinkability among all possible transactions or addresses in the system, but rather something more limited. Given a particular adversary, the anonymity setof your transaction is the set of transactions which the adversary cannot distinguish from your transaction. Even if the adversary knows you made a transaction, they can only tell that it’s one of the transactions in the set, but not which one it is. We try to maximize the size of the anonymity set — the set of other addresses or transactions amongst which we can hide. Calculating the anonymity set is tricky. Since the anonymity set is defined with respect to a certain adversary or set of adversaries, you must first concretely define what your adversary model is. You have to reason carefully about what that adversary knows, what they don't know, and what is it that we are trying to hide from the adversary — that is, what the adversary cannotknow for the transaction to be considered anonymous. There's no general formula for doing this. It requires carefully analyzing each protocol and system on a case-by-case basis. Taint analysis. In the Bitcoin community, people often carry out intuitive analyses of anonymity services without rigorous definitions. Taint analysisis particularly popular: it’s a way of calculating how “related” two addresses are. If bitcoins sent by an address S always end up at another address R, whether directly or after passing through some intermediate addresses, then S and R will have a high taint score. The formula accounts for transactions with multiple inputs and/or outputs and specifies how to allocate taint. 167
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Bitcoin and Cryptocurrency Technolo
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Preface — The Long Road to Bitcoi
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work, there is also the issue of co
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Finally, CyberCash has the dubious
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This was the first serious digital
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and so on — powers of two. That w
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Figure 3 shows the user side of the
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initial cost to acquire all the equ
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the system is to record the relativ
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original design. However, after Bit
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A final reason that’s often cited
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Chapter 1: Introduction to Cryptogr
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Figure 1.2 Because the number of
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Property 2: Hiding The second pr
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ecome: ● ● Hiding: Given H(
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SHA‐256 uses a compression functi
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Figure 1.5 Block chain.A block c
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Figure 1.7 Merkle tree. In a Mer
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throughout this book. 1.3 Digital S
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Figure 1.9 Unforgeability game.
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andomness just in making a signatur
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1.5 A Simple Cryptocurrency Now let
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The first key idea is that a design
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Figure 1.13 A PayCoins Transa
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Perusing the NIST standard that def
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Chapter 2: How Bitcoin Achieves Dec
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state of the system. The implicatio
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consensus is somewhat pessimistic,
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Implicit Consensus. This assumpt
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Figure 2.2 A double spend attempt.
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In general, the more confirmations
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Figure 2.4 The block reward is c
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puzzle‐friendliness property from
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possible outcomes, and the probabil
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theory problem that’s not easily
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this interlocking interdependence b
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Further reading The Bitcoin whitepa
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Chapter 3: Mechanics of Bitcoin Thi
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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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Page 117 and 118: Figure 4.5: Proof of liabilities.
Page 119 and 120: crypto and we won’t cover it here
Page 121 and 122: Figure 4.8: Payment process involvi
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Page 131 and 132: Chapter 5: Bitcoin Mining This chap
Page 133 and 134: In most cases you'll try every sing
Page 135 and 136: You can see in Figure 5.3 that over
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Page 141 and 142: Disadvantages of GPU mining. GPU
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Page 145 and 146: Figure 5.10: Evolution of mining
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Page 149 and 150: Still, if we could replace Bitcoin
Page 151 and 152: Figure 5.11: Illustration of uncert
Page 153 and 154: Figure 5.13: Mining rewards. Thr
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Page 157 and 158: By April 2015, the situation looks
Page 159 and 160: Figure 5.15 Forking attack.A mal
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Page 165: Chapter 6: Bitcoin and Anonymity
Page 169 and 170: eason is that use cases that we cla
Page 171 and 172: But this reveals something. The tra
Page 173 and 174: the other hand, are often not new a
Page 175 and 176: Figure 6.5. Labeled clusters.
Page 177 and 178: Luckily, this is a problem of commu
Page 179 and 180: they are unhappy with anonymity pro
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Page 191 and 192: We start with Bitcoin itself, which
Page 193 and 194: An alternative design to Zerocoin i
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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
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To drive home the mismatch between
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Conclusion to the book Some people
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