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Proof of work

Proof of work is a physics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Proof of work rather than just read about it. In short: Proof of work (also written as proof-of-work, and abbreviated PoW) is a form of cryptographic proof in which one party (the prover) proves to others (the verifiers) that a certain amount of a specific computational effort has been expended. Verifiers can subsequently confirm this expenditure with minimal effort on their part.

Proof of work — main illustration
Proof of work — illustration

Key takeaways

  • Proof of work belongs to physics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Proof of work to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Proof of work from memory before moving on to harder problems.

Reference excerpt

Proof of work (also written as proof-of-work, and abbreviated PoW) is a form of cryptographic proof in which one party (the prover) proves to others (the verifiers) that a certain amount of a specific computational effort has been expended. Verifiers can subsequently confirm this expenditure with minimal effort on their part. The concept was first proposed by Moni Naor and Cynthia Dwork in 1993 as a way to deter denial-of-service attacks and other service abuses such as spam on a network by requiring some work from a service requester, usually meaning processing time by a computer. Extending the work of Cynthia Dwork and Moni Naor, Adam Back formally described a proof of work system called Hashcash as a protection against email spam in 1997. The term "proof of work" was coined and formalized in a 1999 paper by Markus Jakobsson and Ari Juels. The concept was adapted to digital tokens by Hal Finney in 2004 through the idea of "reusable proof of work" using the 160-bit secure hash algorithm 1 (SHA-1). Proof of work was later popularized by Bitcoin as a foundation for consensus in a permissionless decentralized network, in which miners compete to append blocks and mine new currency, each miner experiencing a success probability proportional to the computational effort expended. PoW and PoS (proof of stake) remain the two best known Sybil deterrence mechanisms. In the context of cryptocurrencies they are the most common mechanisms. A key feature of proof-of-work schemes is their asymmetry: the work – the computation – must be moderately hard (yet feasible) on the prover or requester side but easy to check for the verifier or service provider. This idea is also known as a CPU cost function, client puzzle, computational puzzle, or CPU pricing function. Another common feature is built-in incentive-structures that reward allocating computational capacity to the network with value in the form of cryptocurrency. The purpose of proof-of-work algorithms is not proving that certain work was carried out or that a computational puzzle was "solved", but deterring manipulation of data by establishing large energy and hardware-control requirements to be able to do so. Proof-of-work systems have been criticized by some environmentalists who argue that it generates externalities that are not reflected in market electricity prices which do not compensate for the economic and social benefits. The interruptible load characteristics of proof-of-work mining provide demand-response services and support the integration of variable renewable energy under certain market and grid conditions.

Background The concept of Proof of Work (PoW) has its roots in early research on combating spam and preventing denial-of-service attacks. One of the earliest implementations of PoW was Hashcash, created by British cryptographer Adam Back in 1997. It was designed as an anti-spam mechanism that required email senders to perform a small computational task, effectively proving that they expended resources (in the form of CPU time) before sending an email. This task was trivial for legitimate users but would impose a significant cost on spammers attempting to send bulk messages. Hashcash's system was based on the concept of finding a hash value that met certain criteria, a task that required computational effort and thus served as a "proof of work." The idea was that by making it computationally expensive to send large volumes of email, spamming would be reduced. One popular system, used in Hashcash, uses partial hash inversions to prove that computation was done, as a goodwill token to send an e-mail. For instance, the following header represents about 252 hash computations to send a message to calvin@comics.net on January 19, 2038:

X-Hashcash: 1:52:380119:calvin@comics.net:::9B760005E92F0DAE

It is verified with a single computation by checking that the SHA-1 hash of the stamp (omit the header name X-Hashcash: including the colon and any amount of whitespace following it up to the digit '1') begins with 52 binary zeros, that is 13 hexadecimal zeros:[1]

0000000000000756af69e2ffbdb930261873cd71

Whether PoW systems can actually solve a particular denial-of-service issue such as the spam problem is subject to debate; the system must make sending spam emails obtrusively unproductive for the spammer, but should also not prevent legitimate users from sending their messages. In other words, a genuine user should not encounter any difficulties when sending an email, but an email spammer would have to expend a considerable amount of computing power to send out many emails at once. Proof-of-work systems are being used by other, more complex cryptographic systems such as Bitcoin, which uses a system similar to Hashcash.

… excerpt ends here. Continue reading the full article.

Illustrations

Proof of work illustration
Proof of work: Bitcoin electricity consumption as of 2021[34]
Bitcoin electricity consumption as of 2021[34]

Worked examples

Example 1 — a first encounter with Proof of work

Start with the simplest possible case. Write down what Proof of work claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Proof of work before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Proof of work ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Proof of work

In research
Proof of work appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Proof of work in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Proof of work is common in secondary-school and first-year university syllabi. It links to neighbouring topics Cryptocurrencies, Energy consumption, so understanding it makes those chapters shorter.
In everyday life
Look for Proof of work outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Proof of work in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Proof of work means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Proof of work out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Proof of work in simple terms?

Proof of work (also written as proof-of-work, and abbreviated PoW) is a form of cryptographic proof in which one party (the prover) proves to others (the verifiers) that a certain amount of a specific computational effort has been expended. Verifiers can subsequently confirm this expenditure with m…

Why does Proof of work matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Proof of work?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Proof of work.

Tags

  • Cryptocurrencies
  • Energy consumption

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