Difficulty Bitcoin

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Hashcash. A very similar idea called hashcash was independently invented in 1997 by Adam Back, a postdoctoral researcher at the time who was part of the cypherpunk community. Cypher-punks were activists who opposed the power of governments and centralized institutions, and sought to create social and political change through cryptography. Back was practically oriented: he released hashcash first as software,2 and five years later in 2002 released an Internet draft (a standardization document) and a paper.4

Hashcash is much simpler than Dwork and Naor's idea: it has no trapdoor and no central authority, and it uses only hash functions instead of digital signatures. It is based on a simple principle: a hash function behaves as a random function for some practical purposes, which means the only way to find an input that hashes to a particular output is to try various inputs until one produces the desired output. Further, the only way to find an input that hashes into an arbitrary set of outputs is again to try hashing different inputs one by one. So, if I challenged you to find an input whose (binary) hash value begins with 10 zeros, you would have to try numerous inputs, and you would find that each output had a 1/210 chance of beginning with 10 zeros, which means that you would have to try on the order of 210 inputs, or approximately 1,000 hash computations.

As the name suggests, in hashcash Back viewed proof of work as a form of cash. On his webpage he positioned it as an alternative to David Chaum's DigiCash, which was a system that issued untraceable digital cash from a bank to a user.3 He even made compromises to the technical design to make it appear more cashlike. Later, Back made comments suggesting that bit-coin was a straightforward extension of hashcash. Hashcash is simply not cash, however, because it has no protection against double spending. Hashcash tokens cannot be exchanged among peers.

Meanwhile, in the academic scene, researchers found many applications for proof of work besides spam, such as preventing denial-of-service at-tacks,25 ensuring the integrity of Web analytics,17 and rate-limiting password guessing online.38 Incidentally, the term proof of work was coined only in 1999 in a paper by Markus Jakobsson and Ari Juels, which also includes a nice survey of the work up until that point.24 It is worth noting that these researchers seem to have been unaware of hashcash but independently started to converge on hash-based proof of work, which was introduced in papers by Eran Gabber et al.18 and by Juels and Brainard.25 (Many of the terms used throughout this paragraph did not become standard terminology until long after the papers in question were published.)

Proof of work and digital cash: A catch-22. You may know that proof of work did not succeed in its original application as an anti-spam measure. One possible reason is the dramatic difference in the puzzle-solving speed of different devices. That means spammers will be able to make a small investment in custom hardware to increase their spam rate by orders of magnitude. In economics, the natural response to an asymmetry in the cost of production is trade—that is, a market for proof-of-work solutions. But this presents a catch-22, because that would require a working digital currency. Indeed, the lack of such a currency is a major part of the motivation for proof of work in the first place. One crude solution to this problem is to declare puzzle solutions to be cash, as hashcash tries to do.

More coherent approaches to treating puzzle solutions as cash are found in two essays that preceded bit-coin, describing ideas called b-money13 and bit gold43 respectively. These proposals offer timestamping services that sign off on the creation (through proof of work) of money, and once money is created, they sign off on transfers. If disagreement about the ledger occurs among the servers or nodes, however, there isn't a clear way to resolve it. Letting the majority decide seems to be implicit in both authors' writings, but because of the Sybil problem, these mechanisms are not very secure, unless there is a gatekeeper who controls entry into the network or Sybil resistance is itself achieved with proof of work.

back to top Putting It All Together

Understanding all these predecessors that contain pieces of bitcoin's design leads to an appreciation of the true genius of Nakamoto's innovation. In bit-coin, for the first time, puzzle solutions don't constitute cash by themselves. Instead, they are merely used to secure the ledger. Solving proof of work is performed by specialized entities called miners (although Nakamoto underestimated just how specialized mining would become).

Miners are constantly in a race with each other to find the next puzzle solution; each miner solves a slightly different variant of the puzzle so that the chance of success is proportional to the fraction of global mining power that the miner controls. A miner who solves a puzzle gets to contribute the next batch, or block, of transactions to the ledger, which is based on linked timestamping. In exchange for the service of maintaining the ledger, a miner who contributes a block is rewarded with newly minted units of the currency. With high likelihood, if a miner contributes an invalid transaction or block, it will be rejected by the majority of other miners who contribute the following blocks, and this will also invalidate the block reward for the bad block. In this way, because of the monetary incentives, miners ensure each other's compliance with the protocol.

Bitcoin neatly avoids the double-spending problem plaguing proof-of-work-as-cash schemes because it eschews puzzle solutions themselves having value. In fact, puzzle solutions are twice decoupled from economic value: the amount of work required to produce a block is a floating parameter (proportional to the global mining power), and further, the number of bitcoins issued per block is not fixed either. The block reward (which is how new bitcoins are minted) is set to halve every four years (in 2017, the reward is 12.5 bitcoins/block, down from 50 bitcoins/block). Bit-coin incorporates an additional reward scheme—namely, senders of transactions paying miners for the service of including the transaction in their blocks. It is expected the market will determine transaction fees and miners' rewards.

Nakamoto's genius, then, was not any of the individual components of bitcoin, but rather the intricate way in which they fit together to breathe life into the system. The timestamping and Byzantine agreement researchers didn't hit upon the idea of incentivizing nodes to be honest, nor, until 2005, of using proof of work to do away with identities. Conversely, the authors of hashcash, b-money, and bit gold did not incorporate the idea of a consensus algorithm to prevent double spending. In bitcoin, a secure ledger is necessary to prevent double spending and thus ensure that the currency has value. A valuable currency is necessary to reward miners. In turn, strength of mining power is necessary to secure the ledger. Without it, an adversary could amass more than 50% of the global mining power and thereby be able to generate blocks faster than the rest of the network, double-spend transactions, and effectively rewrite history, overrunning the system. Thus, bitcoin is bootstrapped, with a circular dependence among these three components. Nakamoto's challenge was not just the design, but also convincing the initial community of users and miners to take a leap together into the unknown—back when a pizza cost 10,000 bitcoins and the network's mining power was less than a trillionth of what it is today.

Public keys as identities. This article began with the understanding that a secure ledger makes creating digital currency straightforward. Let's revisit this claim. When Alice wishes to pay Bob, she broadcasts the transaction to all bitcoin nodes. A transaction is simply a string: a statement encoding Alice's wish to pay Bob some value, signed by her. The eventual inclusion of this signed statement into the ledger by miners is what makes the transaction real. Note that this doesn't require Bob's participation in any way. But let's focus on what's not in the transaction: conspicuously absent are Alice and Bob's identities; instead, the transaction contains only their respective public keys. This is an important concept in bitcoin: public keys are the only kinds of identities in the system. Transactions transfer value from and to public keys, which are called addresses.

In order to "speak for" an identity, you must know the corresponding secret key. You can create a new identity at any time by generating a new key pair, with no central authority or registry. You do not need to obtain a user name or inform others that you have picked a particular name. This is the notion of decentralized identity management. Bitcoin does not specify how Alice tells Bob what her pseudonym is—that is external to the system.

Although radically different from most other payment systems today, these ideas are quite old, dating back to David Chaum, the father of digital cash. In fact, Chaum also made seminal contributions to anonymity networks, and it is in this context that he invented this idea. In his 1981 paper, "Untraceable Electronic Mail, Return Addresses, and Digital Pseudonyms,"9 he states: "A digital 'pseudonym' is a public key used to verify signatures made by the anonymous holder of the corresponding private key."
Now, having message recipients be known only by a public key presents an obvious problem: there is no way to route the message to the right computer. This leads to a massive inefficiency in Chaum's proposal, which can be traded off against the level of anonymity but not eliminated. Bitcoin is similarly exceedingly inefficient compared with centralized payment systems: the ledger containing every transaction is maintained by every node in the system. Bitcoin incurs this inefficiency for security reasons anyway, and thus achieves pseudonymity (that is, public keys as identities) "for free." Chaum took these ideas much further in a 1985 paper,11 where he presents a vision of privacy-preserving e-commerce based on pervasive pseudonyms, as well as "blind signatures," the key technical idea behind his digital cash.

The public-keys-as-identities idea is also seen in b-money and bit gold, the two precursor essays to bitcoin discussed earlier. However, much of the work that built on Chaum's foundation, as well as Chaum's own later work on ecash, moved away from this idea. The cypherpunks were keenly interested in privacy-preserving communication and commerce, and they embraced pseudonyms, which they called nyms. But to them, nyms were not mere cryptographic identities (that is, public keys), but rather, usually email addresses that were linked to public keys. Similarly, Ian Goldberg's dissertation, which became the basis of much future work on anonymous communication, recognizes Chaum's idea but suggests that nyms should be human-memorable nicknames with certificates to bind them.20 Thus Bitcoin proved to be the most successful instantiation of Chaum's idea.

back to top The Blockchain

So far, this article has not addressed the blockchain, which, if you believe the hype, is bitcoin's main invention. It might come as a surprise to you that Nakamoto doesn't mention that term at all. In fact, the term blockchain has no standard technical definition but is a loose umbrella term used by various parties to refer to systems that bear varying levels of resemblance to bit-coin and its ledger.

Discussing example applications that benefit from a blockchain will help clarify the different uses of the term. First, consider a database backend for transactions among a consortium of banks, where transactions are netted at the end of each day and accounts are settled by the central bank. Such a system has a small number of well-identified parties, so Nakamoto consensus would be overkill. An on-blockchain currency is not needed either, as the accounts are denominated in traditional currency. Linked time-stamping, on the other hand, would clearly be useful, at least to ensure a consistent global ordering of transactions in the face of network latency. State replication would also be useful: a bank would know that its local copy of the data is identical to what the central bank will use to settle its account. This frees banks from the expensive reconciliation process they must currently perform.

Second, consider an asset-management application such as a registry of documents that tracks ownership of financial securities, or real estate, or any other asset. Using a blockchain would increase interoperability and decrease barriers to entry. We want a secure, global registry of documents, and ideally one that allows public participation. This is essentially what the timestamping services of the 1990s and 2000s sought to provide. Public blockchains offer a particularly effective way to achieve this today (the data itself may be stored off-chain, with only the metadata stored on-chain). Other applications also benefit from a timestamping or "public bulletin board" abstraction, most notably electronic voting.

Let's build on the asset-management example. Suppose you want to execute trades of assets via the block-chain, and not merely record them there. This is possible if the asset is issued digitally on the blockchain itself, and if the blockchain supports smart contracts. In this instance, smart contracts solve the "fair exchange" problem of ensuring that payment is made if and only if the asset is transferred. More generally, smart contracts can encode complex business logic, provided that all necessary input data (assets, their prices, and so on) are represented on the blockchain.
This mapping of blockchain properties to applications allows us not only to appreciate their potential, but also to inject a much-needed dose of skepticism. First, many proposed applications of blockchains, especially in banking, don't use Nakamoto consensus. Rather, they use the ledger data structure and Byzantine agreement, which, as shown, date to the 1990s. This belies the claim that blockchains are a new and revolutionary technology. Instead, the buzz around blockchains has helped banks initiate collective action to deploy shared-ledger technology, like the parable of "stone soup." Bitcoin has also served as a highly visible proof of concept that the decentralized ledger works, and the Bitcoin Core project has provided a convenient code base that can be adapted as necessary.

Second, blockchains are frequently presented as more secure than traditional registries—a misleading claim. To see why, the overall stability of the system or platform must be separated from endpoint security—that is, the security of users and devices. True, the systemic risk of block-chains may be lower than that of many centralized institutions, but the endpoint-security risk of blockchains is far worse than the corresponding risk of traditional institutions. Block-chain transactions are near-instant, irreversible, and, in public block-chains, anonymous by design. With a blockchain-based stock registry, if a user (or broker or agent) loses control of his or her private keys—which takes nothing more than losing a phone or getting malware on a computer—the user loses his or her assets. The extraordinary history of bitcoin hacks, thefts, and scams does not inspire much confidence—according to one estimate, at least 6% of bitcoins in circulation have been stolen at least once.39

back to top Concluding Lessons

The history described here offers rich (and complementary) lessons for practitioners and academics. Practitioners should be skeptical of claims of revolutionary technology. As shown here, most of the ideas in bitcoin that have generated excitement in the enterprise, such as distributed ledgers and Byzantine agreement, actually date back 20 years or more. Recognize that your problem may not require any breakthroughs—there may be long-forgotten solutions in research papers.

Academia seems to have the opposite problem, at least in this instance: a resistance to radical, extrinsic ideas. The bitcoin white paper, despite the pedigree of many of its ideas, was more novel than most academic research. Moreover, Nakamoto did not care for academic peer review and did not fully connect it to its history. As a result, academics essentially ignored bitcoin for several years. Many academic communities informally argued that Bitcoin could not work, based on theoretical models or experiences with past systems, despite the fact it was working in practice.

We have seen repeatedly that ideas in the research literature can be gradually forgotten or lie unappreciated, especially if they are ahead of their time, even in popular areas of research. Both practitioners and academics would do well to revisit old ideas to glean insights for present systems. Bitcoin was unusual and successful not because it was on the cutting edge of research on any of its components, but because it combined old ideas from many previously unrelated fields. This is not easy to do, as it requires bridging disparate terminology, assumptions, and so on, but it is a valuable blueprint for innovation.

Practitioners would benefit from being able to identify overhyped technology. Some indicators of hype: difficulty identifying the technical innovation; difficulty pinning down the meaning of supposedly technical terms, because of companies eager to attach their own products to the bandwagon; difficulty identifying the problem that is being solved; and finally, claims of technology solving social problems or creating economic/political upheaval.

In contrast, academia has difficulty selling its inventions. For example, it's unfortunate that the original proof-of-work researchers get no credit for bitcoin, possibly because the work was not well known outside academic circles. Activities such as releasing code and working with practitioners are not adequately rewarded in academia. In fact, the original branch of the academic proof-of-work literature continues today without acknowledging the existence of bitcoin! Engaging with the real world not only helps get credit, but will also reduce reinvention and is a source of fresh ideas.