Bitcoin and Cryptocurrency Technologies

lock themselves could tell us. This is shown in Figure 10.7, each block would contain a pointer both
to its predecessor as well as to the most recent block that satisfied ​hash < target / 4​.
How far can we push this? Can we pick arbitrarily large multiples? Not really. The logic here is similar
to pooled mining, but in reverse. In pooled mining, the pool operator verifies shares, which are blocks
with a lowered difficulty (that is, a higher target value). Miners find many more shares than blocks, so
the operator must do extra work to verify them. The benefit of doing so is the ability to estimate the
miner’s hash power much more accurately — the variance of the estimate is lower.
Here we see the opposite tradeoff. As we do less and less work to estimate the total amount of work
that has gone into building the chain, our estimate will have a greater and greater variance. Here’s an
example. Suppose ​N=4​, so that without the skiplist solution, we’d check that there are 4 blocks that
satisfy ​hash < target​. The expected amount of work that an adversary must do to fool us is 4 times the
average amount of work needed to find a block.
Suppose the adversary only does half this amount of work. If we do the math, it turns out that this
adversary has a 14% chance of finding 4 blocks that satisfy ​hash < target​. On the other hand, with a
skiplist solution with a factor of 4, the adversary’s task would be to find a single block that satisfies
hash < target/4​. In this scenario, the lazy adversary who only does half the expected amount of work
will be able to fool us with a probability of 40% instead of 14%.
10.7 Ethereum and Smart Contracts
We have seen several ways to use Bitcoin’s scripting language to support interesting applications,
such as an escrowed payment transaction. We’ve also seen how Bitcoin script is somewhat limited,
with a small instruction set that isn’t Turing‐complete. As a result, some new altcoins propose adding
application‐specific functionality. Namecoin was the first example but many others have proposed
cryptocurrencies much like Bitcoin but supporting gambling, stock issuance, prediction markets, and
so on.
What if, instead of needing to launch a new system to support every application, we built a
cryptocurrency that could support ​any​application we might dream up in the future? This what
Turing‐completeness is all about: to the best of our knowledge, a Turing‐complete programming
language lets you specify any functionality that is possible to be specified by any other computer. To
some extent, the situation today harkens back to the early days of computers themselves in the
1940s: increasingly complicated machines were being built for various specific applications during
World War II (such as brute‐forcing keys used by mechanical cipher machines or determining firing
trajectories for naval artillery), motivating researchers to build the first reprogrammable
general‐purpose computers that could be used for any conceivable applications.
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