Bitcoin and Cryptocurrency Technologies

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This is where the zero-knowledge proof comes in. At any point, there will be many commitments on the block chain — let’s call them c 1 ,c 2 ,...,c n . Here are the steps that go into spending a zerocoin with serial number S to redeem a new basecoin: ● Create a special “spend” transaction that contains S, along with a zero-knowledge proof of the statement: “I know rsuch that Commit(S, r)is in the set {c 1 ,c 2 ,...,c n }”. ● Miners will verify your zero-knowledge proof which establishes your abilityto open one of the zerocoin commitments on the block chain, without actually opening it. ● Miners will also check that the serial number S has never been used in any previous spend transaction (since that would be a double-spend). ● The output of your spend transaction will now act as a new basecoin. For the output address, you should use an address that you own. Figure 6.13: Spending a zerocoin. The spend transaction reveals the serial number S committed by the earlier mint transaction, along with a zero-knowledge proof that S corresponds to someearlier mint transaction. Unlike a mint transaction (or a normal Bitcoin/basecoin transaction), the spend transaction has no inputs, and hence no signature. Instead the zero-knowledge proof serves to establish its validity. Once you spend a zerocoin, the serial number becomes public, and you will never be able to redeem this serial number again. And since there is only one serial number for each zerocoin, it means that each zerocoin can only be spent once, exactly as we required for security. Anonymity. Observe that ris kept secret throughout; neither the mint nor the spend transaction reveals it. That means nobody knows which serial number corresponds to which zerocoin. This is the key concept behind Zerocoin’s anonymity. There is no link on the block chain between the mint transaction that committed a serial number S and the spend transaction that later revealed S to redeem a basecoin. This is a magical-sounding property that is possible through cryptography but we wouldn't get in a physical, envelope-based system. It’s as if there are a bunch of sealed envelopes on a table with different serial numbers, and you can prove that a particular serial number is one of them, without having to reveal which one and without having to open any envelopes. 188
Efficiency. Recall the statement that’s proved in a spend transaction: “I know rsuch that Commit(S, r)is in the set {c 1 ,c 2 ,...,c n }”. This sounds like it would be horribly inefficient to implement, because the size of the zero-knowledge proofs would grow linearly as nincreases, which is the number of zerocoins that have everbeen minted. Remarkably, Zerocoin manages to make the size of these proofs only logarithmic in n. Note that even though the statementto be proved has a linear length, it doesn’t need to be included along with the proof. The statement is implicit; it can be inferred by the miners since they know the set of all zerocoins on the block chain. The proof itself can be much shorter. Nevertheless, compared to Bitcoin, Zerocoin still adds quite a sizable overhead, with proofs about 50 kB in size. Trusted setup.One of the cryptographic tools used in building Zerocoin (RSA accumulators) which require a one-time trusted setup. Specifically, a trusted party needs to choose two large primes pand qand publish N=p·qwhich is a parameter that everybody will use for the lifetime of the system. Think of Nlike a public key, except for all of Zerocoin as opposed to one particular entity. As long as the trusted party destroys any record of pand q, the system is believed to be secure. In particular, this rests on the widely-believed assumption that it’s infeasible to factoring a number that’s a product of two large primes. But if anyoneknows the secret factors pand q(called the “trapdoor”), then they’d be able to create new zerocoins for themselves without being detected. So these secret inputs must be used once in generating the public parameters and then securely destroyed. There’s an interesting sociological problem here. It’s not clear how an entity could choose Nand convince everybody that they have securely destroyed the factors pand qthat were used during the setup. There have been been various proposals for how to achieve this, including “threshold cryptography” techniques that allow a set of delegates to jointly compute Nin such a way that as long as any one of them deletes their secret inputs, the system will remain secure. It’s also possible to use a slightly different cryptographic construction to avoid the trusted setup. Specifically, it has been shown that simply generating a very large random value for Nis secure with high probability, because the number probably cannot be completely factored. Unfortunately this carries a huge efficiency hit and is thus not considered practical. Zerocash. Zerocash is a different anonymous cryptocurrency that builds on the concept of Zerocoin but takes the cryptography to the next level. It uses a cryptographic technique called zero-knowledge SNARKs (zk-SNARKS) which are a way of making zero-knowledge proofs much more compact and efficient to verify. The upshot is that the efficiency of the system overall gets to a point where it becomes possible to run the whole network without needing a basecoin. All transactions can be done in a zero-knowledge manner. As we saw, Zerocoin supports regular transactions for when you don’t need unlinkability, augmented with computationally expensive transactions that are used only for mixing. The mix transactions are of fixed denominations and splitting and merging of values can happen only in Basecoin. In Zerocash, that distinction is gone. The transaction amounts are now inside the commitments and no longer visible on the block chain. The cryptographic proofs ensure that the splitting and merging happens correctly and that users can’t create zerocash out of thin air. 189
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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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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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Page 141 and 142: Disadvantages of GPU mining. GPU
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Page 145 and 146: Figure 5.10: Evolution of mining
Page 147 and 148: Hopefully, over time the embodied e
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 and 166: Chapter 6: Bitcoin and Anonymity
Page 167 and 168: Unlinkability. To understand unl
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
Page 181 and 182: Fees should be all-or-nothing. M
Page 183 and 184: Somebody looking at this transactio
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Page 187: just minting one doesn’t automati
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Page 213 and 214: The text refers to “activities in
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Page 223 and 224: meaning the exponential growth peri
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Page 227 and 228: In Permacoin, each miner Msto
Page 229 and 230: Interestingly, these concerns have
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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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