View source for Proof of work

{{short description|System that regulates the formation of blocks on a blockchain}}

'''Proof of work''' (also written as '''proof-of-work''', an abbreviated '''PoW''') is a form of [[Cryptography|cryptographic]] [[proof (truth)|proof]] in which one party (the ''prover'') proves to others (the ''verifiers'') that a certain amount of a specific computational effort has been expended.<ref>{{Cite journal |last1=Lachtar |first1=Nada |last2=Andrius |first2=Abdulrahman Abu |last3=Bacha |first3=Anys |last4=Malik |first4=Hafiz |date=2023-10-01 |title=A Cross-Stack Approach Towards Defending Against Cryptojacking |journal=IEEE Computer Architecture Letters |volume=19 |issue=2 |pages=126–129 |doi=10.1109/LCA.2023.3017457 |doi-broken-date=12 March 2025 |s2cid=222070383 |issn=1556-6056|doi-access=free }}</ref> Verifiers can subsequently confirm this expenditure with minimal effort on their part. The concept was first implemented in [[Hashcash]] by [[Moni Naor]] and [[Cynthia Dwork]] in 1993 as a way to deter [[denial-of-service attack]]s and other service abuses such as [[spam (electronic)|spam]] on a network by requiring some work from a service requester, usually meaning processing time by a computer. The term "proof of work" was first coined and formalized in a 1999 paper by [[Markus Jakobsson]] and Ari Juels.{{r|"JaJue1999"}}{{r|"DwoNao1992"}} The concept was adapted to digital tokens by [[Hal Finney (computer scientist)|Hal Finney]] in 2004 through the idea of "reusable proof of work" using the 160-bit secure hash algorithm 1 (SHA-1).<ref>{{Cite web |title=RPOW - Reusable Proofs of Work |url=https://nakamotoinstitute.org/finney/rpow/index.html |access-date=2024-01-17 |website=nakamotoinstitute.org |archive-date=2023-06-19 |archive-url=https://web.archive.org/web/20230619102132/https://nakamotoinstitute.org/finney/rpow/index.html |url-status=live }}</ref>

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 attack|Sybil deterrence mechanisms]]. In the context of [[Cryptocurrency|cryptocurrencies]] they are the most common mechanisms.<ref name="EP-mechanisms">{{Cite web |date=July 2018 |title=Cryptocurrencies and blockchain |url=https://www.europarl.europa.eu/cmsdata/150761/TAX3%20Study%20on%20cryptocurrencies%20and%20blockchain.pdf |access-date=29 October 2020 |website=[[European Parliament]] |quote=the two best-known – and in the context of cryptocurrencies also most commonly used |archive-date=27 June 2023 |archive-url=https://web.archive.org/web/20230627212856/https://www.europarl.europa.eu/cmsdata/150761/TAX3%20Study%20on%20cryptocurrencies%20and%20blockchain.pdf |url-status=live }}</ref>

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 Protocol|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 (economics)|value]] in the form of cryptocurrency.<ref name=":0">{{Cite web |title=Proof of Work Explained in Simple Terms - The Chain Bulletin |url=https://chainbulletin.com/proof-of-work-explained-in-simple-terms |access-date=2023-04-01 |website=chainbulletin.com |language=en |archive-date=2023-04-01 |archive-url=https://web.archive.org/web/20230401162119/https://chainbulletin.com/proof-of-work-explained-in-simple-terms |url-status=live }}</ref><ref>{{Cite news |title=The Only Crypto Story You Need, by Matt Levine |language=en |work=Bloomberg.com |url=https://www.bloomberg.com/features/2022-the-crypto-story/ |access-date=2023-04-01 |archive-date=2023-04-07 |archive-url=https://web.archive.org/web/20230407014836/https://www.bloomberg.com/features/2022-the-crypto-story/ |url-status=live }}</ref>

The purpose of proof-of-work algorithms is not proving that certain [[Work (human activity)|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.<ref name=":0" /> Proof-of-work systems have been criticized by environmentalists for their energy consumption.<ref>{{cite news |last1=Kharif |first1=Olga |title=Analysis {{!}} Bye-Bye, Miners! How Ethereum's Big Change Will Work |url=https://www.washingtonpost.com/business/bye-bye-miners-how-ethereums-big-change-will-work/2021/11/30/234cabda-5201-11ec-83d2-d9dab0e23b7e_story.html |access-date=13 January 2022 |newspaper=[[The Washington Post]] |agency=[[Bloomberg News]] |date=November 30, 2021 |archive-date=2 December 2021 |archive-url=https://web.archive.org/web/20211202031349/https://www.washingtonpost.com/business/bye-bye-miners-how-ethereums-big-change-will-work/2021/11/30/234cabda-5201-11ec-83d2-d9dab0e23b7e_story.html |url-status=live }}</ref>

==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.<ref>{{Cite web |last=Back |first=Adam |date=August 2002 |title=Hashcash - A Denial of Service Counter-Measure |url=http://www.hashcash.org/papers/hashcash.pdf}}</ref> 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<!-- *not* hash collisions...  --> to prove that computation was done, as a goodwill token to send an [[e-mail]]. For instance, the following header represents about 2<sup>52</sup> hash computations to send a message to <code>calvin@comics.net</code> 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 <code>X-Hashcash:</code> 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:{{ref|a}}

 0000000000000756af69e2ffbdb930261873cd71

Whether PoW systems can actually solve a particular denial-of-service issue such as the spam problem is subject to debate;<ref name="LauClay2004">{{cite journal
 | first1 = Ben | last1 = Laurie | first2 = Richard | last2 = Clayton
 | title  = Proof-of-work proves not to work | journal = Workshop on the Economics of Information Security 2004 |date=May 2004
}}</ref><ref name="LiuCa2006">{{cite web | first1 = Debin | last1 = Liu | first2 = L. Jean | last2 = Camp | title = Proof of Work can work - Fifth Workshop on the Economics of Information Security | url = http://www.econinfosec.org/archive/weis2006/prog.html | date = June 2006 | access-date = 2015-12-29 | archive-date = 2017-08-20 | archive-url = https://web.archive.org/web/20170820195332/http://www.econinfosec.org/archive/weis2006/prog.html | url-status = live }}</ref> 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.<ref name="LauClay2004" />

== Evolution of Proof-of-Work Algorithms ==
Proof of work traces its theoretical origins to early efforts to combat digital abuse, evolving significantly over time to address security, accessibility, and broader applications beyond its initial anti-spam purpose. The idea first emerged in 1993 as a deterrent for junk mail, but it was [[Satoshi Nakamoto]]’s 2008 whitepaper, "Bitcoin: A Peer-to-Peer Electronic Cash System,"<ref>{{Cite journal |last=Wright |first=Craig S |date=2008 |title=Bitcoin: A Peer-to-Peer Electronic Cash System |url=https://www.ssrn.com/abstract=3440802 |journal=SSRN Electronic Journal |language=en |doi=10.2139/ssrn.3440802 |issn=1556-5068}}</ref> that solidified proof of work's potential as a cornerstone of blockchain networks. This development reflects the rising demands for secure, trustless systems.

The earliest appearance of proof of work was in 1993, when [[Cynthia Dwork]] and [[Moni Naor]] proposed a system to curb junk email by requiring senders to perform computationally demanding tasks. In their paper, "Pricing via Processing or Combatting Junk Mail,"<ref>{{Citation |last1=Dwork |first1=Cynthia |title=Pricing via Processing or Combatting Junk Mail |date=1993 |work=Advances in Cryptology — CRYPTO’ 92 |volume=740 |pages=139–147 |editor-last=Brickell |editor-first=Ernest F. |url=http://link.springer.com/10.1007/3-540-48071-4_10 |access-date=2025-02-27 |place=Berlin, Heidelberg |publisher=Springer Berlin Heidelberg |language=en |doi=10.1007/3-540-48071-4_10 |isbn=978-3-540-57340-1 |last2=Naor |first2=Moni}}</ref> they outlined methods such as computing modular square roots, designed to be challenging to solve yet straightforward to verify, establishing a foundational principle of proof of work’s asymmetry. This asymmetry is the crucial to the effectiveness of proof of work, ensuring that tasks like sending spam are costly for attackers, while verification remains efficient for legitimate users.

This conceptual groundwork found practical use in 1997 with [[Adam Back]]’s Hashcash, a system that required senders to compute a partial hash inversion of the [[SHA-1]] algorithm, producing a hash with a set number of leading zeros. Described in Back’s paper "Hashcash: A Denial of Service Counter-Measure,"<ref>{{Cite journal |last=Duke |first=David |date=May 2002 |title=What is the difference between Denial-of-Service (DoS) and Distributed-Denial-of-Service (DDoS)? |url=https://doi.org/10.1016/s1353-4858(02)05008-0 |journal=Network Security |volume=2002 |issue=5 |pages=4 |doi=10.1016/s1353-4858(02)05008-0 |issn=1353-4858}}</ref> Hashcash imposed a computational cost to deter spam while allowing recipients to confirm the work effortlessly, laying a critical foundation for subsequent proof of work implementations in cryptography and blockchain technology.

Bitcoin, launched in 2009 by Satoshi Nakamoto, marked a pivotal shift by adapting Hashcash’s proof of work for cryptocurrency. Nakamoto’s Bitcoin whitepaper outlined a system using the [[SHA-2|SHA-256]] algorithm, where miners compete to solve cryptographic puzzles to append blocks to the blockchain, earning rewards in the process. Unlike Hashcash’s static proofs, Bitcoin’s proof of work algorithm dynamically adjusts its difficulty based on the time taken to mine the previous block, ensuring a consistent block time of approximately 10 minutes, creating a tamper-proof chain. This innovation transformed proof of work from a standalone deterrent into a consensus mechanism for a decentralized network, emphasizing financial incentives over computational effort.

However, Bitcoin was not perfect. Miners began exploiting Bitcoin's proof of work with specialized hardware like [[Application-specific integrated circuit|ASICs]]. Initially mined with standard [[Central processing unit|CPUs]], Bitcoin saw a rapid transition to [[GPUs]] and then to ASIC, which vastly outperformed general hardware in solving SHA-256 puzzles. This gave ASICs miners an overwhelming advantage, rendering casual participants insignificant, which undermines Bitcoin's initial vision of a decentralized network accessible to all.

To address Bitcoin’s increasing reliance on specialized hardware, proof of work evolved further with the introduction of [[Litecoin]] in 2011, which adopted the [[Scrypt]] algorithm. Developed by [[Colin Percival]] and detailed in the technical specification "The scrypt Password-Based Key Derivation Function,"<ref>{{Cite report |url=https://doi.org/10.17487/rfc7914 |title=The scrypt Password-Based Key Derivation Function |last1=Percival |first1=C. |last2=Josefsson |first2=S. |date=August 2016 |publisher=RFC Editor|doi=10.17487/rfc7914 }}</ref> Scrypt was designed as a memory-intensive algorithm, requiring significant RAM to perform its computations. Unlike Bitcoin’s SHA-256, which favored powerful ASICs, Scrypt aimed to level the playing field by making mining more accessible to users with general-purpose hardware through heightened memory demands. However, over time, advancements in hardware led to the creation of Scrypt-specific ASICs, shifting the advantage back toward specialized hardware and reducing the algorithm's goal for decentralization.

== Variants ==
There are two classes of proof-of-work protocols.

* '''Challenge–response''' protocols assume a direct interactive link between the requester (client) and the provider (server). The provider chooses a challenge, say an item in a set with a property, the requester finds the relevant response in the set, which is sent back and checked by the provider. As the challenge is chosen on the spot by the provider, its difficulty can be adapted to its current load. The work on the requester side may be bounded if the challenge-response protocol has a known solution (chosen by the provider), or is known to exist within a bounded search space.

[[Image:Proof of Work challenge response.svg|550px|center]]

* '''Solution–verification''' protocols do not assume such a link: as a result, the problem must be self-imposed before a solution is sought by the requester, and the provider must check both the problem choice and the found solution. Most such schemes are unbounded probabilistic iterative procedures such as Hashcash.

[[Image:Proof of Work solution verification.svg|550px|center]]

Known-solution protocols tend to have slightly lower variance than unbounded probabilistic protocols because the variance of a [[Uniform distribution (continuous)|rectangular distribution]] is lower than the variance of a [[Poisson distribution]] (with the same mean).{{Explain|date=February 2018|reason=What is a variance in this context? Why is the known-solution protocol related to a Poisson distribution and not some other distribution?}} A generic technique for reducing variance is to use multiple independent sub-challenges, as the average of multiple samples will have a lower variance.

There are also fixed-cost functions such as the time-lock puzzle.

Moreover, the underlying functions used by these schemes may be:
* '''CPU-bound''' where the computation runs at the speed of the processor, [[Moore's law|which greatly varies in time]], as well as from high-end server to low-end portable devices.<ref>[https://web.archive.org/web/20110125110235/http://downloadsquad.switched.com/2009/07/20/how-powerful-was-the-apollo-11-computer How powerful was the Apollo 11 computer?], a specific comparison that shows how different classes of devices have different processing power.</ref>
* '''Memory-bound'''<ref name="ABuMaWo2003"/><ref name="DwoGoNao2003"/><ref name="Coe2005"/><ref name="Tro2014"/> where the computation speed is bound by main memory accesses (either latency or bandwidth), the performance of which is expected to be less sensitive to hardware evolution.
* '''Network-bound'''<ref name="Abliz09"/> if the client must perform few computations, but must collect some tokens from remote servers before querying the final service provider. In this sense, the work is not actually performed by the requester, but it incurs delays anyway because of the latency to get the required tokens.

Finally, some PoW systems offer '''shortcut''' computations that allow participants who know a secret, typically a private key, to generate cheap PoWs. The rationale is that mailing-list holders may generate stamps for every recipient without incurring a high cost. Whether such a feature is desirable depends on the usage scenario.

== List of proof-of-work functions ==
Here is a list of known proof-of-work functions:
<!-- include a brief description, references, comparison... -->
* [[Quadratic residue|Integer square root modulo]] a large prime<ref name="DwoNao1992">{{cite book | first1 = Cynthia | last1 = Dwork | author1-link = Cynthia Dwork | first2 = Moni | last2 = Naor | title = Advances in Cryptology — CRYPTO' 92 | chapter = Pricing via Processing or Combatting Junk Mail | series = Lecture Notes in Computer Science | volume = 740 | author2-link = Moni Naor | publisher = Springer | year = 1993 | pages = 139–147 | chapter-url = http://www.wisdom.weizmann.ac.il/~naor/PAPERS/pvp.ps | doi = 10.1007/3-540-48071-4_10 | isbn = 978-3-540-57340-1 | doi-access = free | access-date = 2012-09-10 | archive-date = 2017-11-26 | archive-url = https://web.archive.org/web/20171126072840/http://www.wisdom.weizmann.ac.il/~naor/PAPERS/pvp.ps | url-status = live }}</ref>{{Dubious|Modular square roots|date=May 2019}}
* Weaken [[Fiat–Shamir heuristic|Fiat–Shamir]] signatures<ref name="DwoNao1992"/>
* Ong–Schnorr–Shamir signature broken by Pollard<ref name="DwoNao1992"/>
* Partial hash inversion<ref name="Ba1997">{{cite web | first = Adam | last = Back | url = http://hashcash.org/ | title = HashCash | access-date = 2005-03-02 | archive-date = 2017-09-29 | archive-url = https://web.archive.org/web/20170929102830/http://www.hashcash.org/ | url-status = live }} A popular PoW system. First announced in March 1997.</ref><ref name="GaJaMaMa1998">{{cite book |last1=Gabber |first1=Eran |last2=Jakobsson |first2=Markus |last3=Matias |first3=Yossi |last4=Mayer |first4=Alain J. |year=1998 |chapter=Curbing junk e-mail via secure classification |chapter-url=https://www.researchgate.net/publication/2737730 |archive-url=https://web.archive.org/web/20231204123901/https://www.researchgate.net/publication/2737730_Curbing_Junk_E-Mail_via_Secure_Classification |url-status=dead |archive-date=December 4, 2023 |title=Financial Cryptography|series=Lecture Notes in Computer Science |volume=1465 |pages=198–213 |doi=10.1007/BFb0055484 |isbn=978-3-540-64951-9 }}</ref>{{r|"JaJue1999"}} This paper formalizes the idea of a proof of work and introduces "the dependent idea of a [[bread pudding protocol]]", a "re-usable proof-of-work" (RPoW) system.<ref name="WaRei2003">{{cite journal | first1 = Xiao-Feng | last1 = Wang | first2 = Michael | last2 = Reiter | title = Defending against denial-of-service attacks with puzzle auctions | journal = IEEE Symposium on Security and Privacy '03 | date = May 2003 | url = http://cs.unc.edu/~reiter/papers/2003/SP.pdf | access-date = 2013-04-15 | archive-date = 2016-03-03 | archive-url = https://web.archive.org/web/20160303220133/http://cs.unc.edu/~reiter/papers/2003/SP.pdf | url-status = dead }}</ref>
* Hash sequences<ref name="FraMa1997">{{cite book | first1 = Matthew K. | last1 = Franklin | author1-link = Matthew K. Franklin | first2 = Dahlia | last2 = Malkhi | title = Financial Cryptography | chapter = Auditable metering with lightweight security | author2-link = Dahlia Malkhi | volume = 1318 | pages = [https://archive.org/details/financialcryptog0000fcco/page/151 151–160] | year = 1997 | doi = 10.1007/3-540-63594-7_75 | series = Lecture Notes in Computer Science | isbn = 978-3-540-63594-9 | chapter-url-access = registration | chapter-url = https://archive.org/details/financialcryptog0000fcco/page/151 }} Updated version May 4, 1998.</ref>
* Puzzles<ref name="JueBrai1999">{{cite journal
 | first1 = Ari | last1 =  Juels | first2 = John | last2 = Brainard
 | title =  Client puzzles: A cryptographic defense against connection depletion attacks | journal =  NDSS 99 | year = 1999 }}</ref>
* [[Diffie–Hellman key exchange|Diffie-Hellman]]–based puzzle<ref name="WaJueHaFe2004">{{cite journal | first1 = Brent | last1 = Waters | first2 = Ari | last2 = Juels | first3 = John A. | last3 = Halderman | first4 = Edward W. | last4 = Felten | author4-link = Edward Felten | title = New client puzzle outsourcing techniques for DoS resistance | journal = 11th ACM Conference on Computer and Communications Security | year = 2004 | url = http://www.cs.utexas.edu/~bwaters/publications/papers/outsource_paper.pdf | access-date = 2019-08-06 | archive-date = 2021-04-21 | archive-url = https://web.archive.org/web/20210421083218/https://www.cs.utexas.edu/~bwaters/publications/papers/outsource_paper.pdf | url-status = live }}</ref>
* Moderate<ref name="ABuMaWo2003">{{cite journal
 | first1 = Martín | last1 =  Abadi | author1-link = Martín Abadi | first2 = Mike | last2 =  Burrows | first3 = Mark | last3 = Manasse | first4 = Ted | last4 = Wobber
 | title = Moderately hard, memory-bound functions
 | volume =  5 | number = 2 | pages = 299–327 | year = 2005 | url = https://www.researchgate.net/publication/220169842
}}</ref>
* Mbound<ref name="DwoGoNao2003">{{cite book
 | first1 = Cynthia | last1 =  Dwork | author1-link = Cynthia Dwork | first2 =  Andrew | last2 =  Goldberg | author2-link = Andrew V. Goldberg | first3 = Moni | last3 = Naor | title = Advances in Cryptology - CRYPTO 2003 | chapter = On Memory-Bound Functions for Fighting Spam | author3-link = Moni Naor
 |  volume = 2729 |  pages= 426–444 | publisher =  Springer | year = 2003
| doi = 10.1007/978-3-540-45146-4_25 | series = Lecture Notes in Computer Science | isbn = 978-3-540-40674-7 | doi-access = free }}</ref>
* Hokkaido<ref name="Coe2005">{{cite journal
 | first =  Fabien
 | last =  Coelho
 | title =  Exponential memory-bound functions for proof of work protocols
 | journal =  Cryptology ePrint Archive, Report
 | url =  http://eprint.iacr.org/2005/356
 | year =  2005
 | access-date =  2007-11-04
 | archive-date =  2018-04-09
 | archive-url =  https://web.archive.org/web/20180409043045/https://eprint.iacr.org/2005/356
 | url-status =  live
 }}</ref>
* Cuckoo Cycle<ref name="Tro2014">{{cite book
 |first        = John
 |last         = Tromp
 |title        = Financial Cryptography and Data Security
 |chapter      = Cuckoo Cycle: A Memory Bound Graph-Theoretic Proof-of-Work
 |chapter-url  = https://eprint.iacr.org/2014/059.pdf
 |volume       = 8976
 |publisher    = Springer
 |pages        = 49–62
 |year         = 2015
 |doi          = 10.1007/978-3-662-48051-9_4
 |series       = Lecture Notes in Computer Science
 |isbn         = 978-3-662-48050-2
 |access-date  = 2015-09-30
 |archive-date = 2017-07-05
 |archive-url  = https://web.archive.org/web/20170705204246/https://eprint.iacr.org/2014/059.pdf
 |url-status   = live
}}</ref>
* [[Merkle tree]]–based<ref name="Coe2007">{{cite journal
 |first        = Fabien
 |last         = Coelho
 |title        = An (almost) constant-effort solution-verification proof-of-work protocol based on Merkle trees
 |journal      = Cryptology ePrint Archive, Report
 |url          = http://eprint.iacr.org/2007/433
 |year         = 2007
 |access-date  = 2007-11-25
 |archive-date = 2016-08-26                       
 |archive-url  = https://web.archive.org/web/20160826093458/http://eprint.iacr.org/2007/433
 |url-status   = live
}}</ref>
* [[Guided tour puzzle protocol]]<ref name="Abliz09">{{cite book
 | first1 = Mehmud | last1 =  Abliz | first2 = Taieb | last2 = Znati
 | title = 2009 Annual Computer Security Applications Conference | chapter = A Guided Tour Puzzle for Denial of Service Prevention | pages = 279–288 | location =  Honolulu, HI |date=December 2009 | doi = 10.1109/ACSAC.2009.33 | isbn = 978-1-4244-5327-6 | citeseerx = 10.1.1.597.6304 | s2cid = 14434713 }}</ref>
* partial match od a hash function{{citation needed|date=February 2025}}

== Proof of useful work (PoUW) ==

At the [[International Association for Cryptologic Research|IACR]] conference Crypto 2022 researchers presented a paper describing Ofelimos, a blockchain protocol with a [[Consensus (computer science)|consensus mechanism]] based on "proof of useful work" (PoUW). Rather than miners consuming energy in solving complex, but essentially useless, puzzles to validate transactions, Ofelimos achieves consensus while simultaneously providing a decentralized [[Mathematical optimization|optimization problem solver]]. The protocol is built around Doubly Parallel Local Search (DPLS), a local search algorithm that is used as the PoUW component. The paper gives an example that implements a variant of [[WalkSAT]], a local search algorithm to solve Boolean problems.<ref>{{Cite web |last=Fitzi |first=Matthias |title=Combinatorial Optimization via Proof-of-Useful-Work |url=https://crypto.iacr.org/2022/papers/538804_1_En_12_Chapter_OnlinePDF.pdf |access-date=9 September 2022 |website=IACR conference Crypto 2022 |archive-date=9 September 2022 |archive-url=https://web.archive.org/web/20220909071908/https://crypto.iacr.org/2022/papers/538804_1_En_12_Chapter_OnlinePDF.pdf |url-status=live }}</ref>

== Bitcoin-type proof of work ==
In 2009, the Bitcoin network went online. Bitcoin is a proof-of-work digital currency that, like Finney's RPoW, is also based on the Hashcash PoW. But in Bitcoin, double-spend protection is provided by a decentralized P2P protocol for tracking transfers of coins, rather than the hardware trusted computing function used by RPoW. Bitcoin has better trustworthiness because it is protected by computation. Bitcoins are "mined" using the Hashcash proof-of-work function by individual miners and verified by the decentralized nodes in the P2P Bitcoin network. The difficulty is periodically adjusted to keep the [[Blockchain#Block time|block time]] around a target time<ref name="whitepaper">{{Cite web |last=Nakamoto |first=Satoshi |date=24 May 2009 |title=Bitcoin: A Peer-to-Peer Electronic Cash System |url=https://bitcoin.org/bitcoin.pdf |url-status=live |archive-url=https://web.archive.org/web/20140320135003/https://bitcoin.org/bitcoin.pdf |archive-date=20 March 2014 |access-date=21 April 2025}}</ref>

=== Energy consumption ===
[[File:Bitcoin electricity consumption.svg|thumb|Bitcoin electricity consumption as of 2021<ref name="cbeci">{{Cite web|url=https://www.cbeci.org/|title=Cambridge Bitcoin Electricity Consumption Index (CBECI)|website=www.cbeci.org|access-date=2020-02-20|archive-date=2020-03-02|archive-url=https://web.archive.org/web/20200302001747/https://www.cbeci.org/|url-status=live}}</ref>]]
Since the creation of Bitcoin, proof-of-work has been the predominant design of [[peer-to-peer]] cryptocurrency. Studies have estimated the total energy consumption of cryptocurrency mining.<ref>{{cite web |title=Cambridge Bitcoin Electricity Consumption Index |url=https://www.cbeci.org/ |publisher=Cambridge Center For Alternative Finance |access-date=30 September 2020 |archive-date=29 September 2020 |archive-url=https://web.archive.org/web/20200929201811/https://cbeci.org/ |url-status=live }}</ref> The PoW mechanism requires a vast amount of computing resources, which consume a significant amount of electricity. 2018 estimates from the [[University of Cambridge]] equate Bitcoin's energy consumption to that of [[Energy in Switzerland|Switzerland]].<ref name="EP-mechanisms"/>

=== History modification ===
Each block that is added to the blockchain, starting with the block containing a given transaction, is called a confirmation of that transaction. Ideally, merchants and services that receive payment in the cryptocurrency should wait for at least one confirmation to be distributed over the network, before assuming that the payment was done. The more confirmations that the merchant waits for, the more difficult it is for an attacker to successfully reverse the transaction in a blockchain—unless the attacker controls more than half the total network power, in which case it is called a [[51% attack]].<ref name="51%">{{cite news |author1=Michael J. Casey |author2=Paul Vigna |title=Short-Term Fixes To Avert "51% Attack" |url=https://blogs.wsj.com/moneybeat/2014/06/16/bitbeat-a-51-attack-what-is-it-and-could-it-happen/ |access-date=30 June 2014 |work=Money Beat |publisher=Wall Street Journal |date=16 June 2014 |archive-date=15 August 2020 |archive-url=https://web.archive.org/web/20200815203333/https://blogs.wsj.com/moneybeat/2014/06/16/bitbeat-a-51-attack-what-is-it-and-could-it-happen/ |url-status=live }}</ref>

=== ASICs and mining pools ===
Within the Bitcoin community there are groups working together in [[mining pool]]s.<ref>[https://blockchain.info/pools Overview of the Bitcoin mining pools] {{Webarchive|url=https://web.archive.org/web/20200421095500/https://blockchain.info/pools |date=2020-04-21 }} on blockchain.info</ref> Some miners use [[application-specific integrated circuit]]s (ASICs) for PoW.<ref>[https://www.digitaltrends.com/computing/what-is-an-asic-miner/ What is an ASIC miner] {{Webarchive|url=https://web.archive.org/web/20180522171206/https://www.digitaltrends.com/computing/what-is-an-asic-miner/ |date=2018-05-22 }} on digitaltrends.com</ref> This trend toward mining pools and specialized ASICs has made mining some cryptocurrencies economically infeasible for most players without access to the latest ASICs, nearby sources of inexpensive energy, or other special advantages.<ref>{{cite web|last=Vorick|first=David|title=The State of Cryptocurrency Mining|url=https://blog.sia.tech/the-state-of-cryptocurrency-mining-538004a37f9b|date=13 May 2018|access-date=28 October 2020|archive-date=10 March 2020|archive-url=https://web.archive.org/web/20200310021448/https://blog.sia.tech/the-state-of-cryptocurrency-mining-538004a37f9b|url-status=live}}</ref>

Some PoWs claim to be ASIC-resistant,<ref>[https://github.com/tevador/randomx tevador/RandomX: Proof of work algorithm based on random code execution] {{Webarchive|url=https://web.archive.org/web/20210901070625/https://github.com/tevador/randomx |date=2021-09-01 }} on Github</ref> i.e. to limit the efficiency gain that an ASIC can have over commodity hardware, like a GPU, to be well under an order of magnitude. ASIC resistance has the advantage of keeping mining economically feasible on commodity hardware, but also contributes to the corresponding risk that an attacker can briefly rent access to a large amount of unspecialized commodity processing power to launch a [[51% attack]] against a cryptocurrency.<ref>{{cite journal|title=Cryptocurrency Value and 51% Attacks: Evidence from Event Studies|author1=Savva Shanaev|author2=Arina Shuraeva|author3=Mikhail Vasenin|author4=Maksim Kuznetsov|url=https://jai.pm-research.com/content/22/3/65.short|journal=The Journal of Alternative Investments|year=2019|volume=22|number=3|pages=65–77|doi=10.3905/jai.2019.1.081|s2cid=211422987|access-date=2020-10-28|archive-date=2021-02-06|archive-url=https://web.archive.org/web/20210206092143/https://jai.pm-research.com/content/22/3/65.short|url-status=live}}</ref>

=== Security Weaknesses ===

==== Majority Attack (51% attack) ====

By design, Bitcoin's Proof of Work consensus algorithm is vulnerable to Majority Attacks (51% attacks). Any miner with over 51% of mining power is able to control the canonical chain until their hash power falls below 50%. This allows them to reorg the blockchain, double-spend, censor transactions, and completely control block production.{{citation needed|date=March 2025}}

==== Asymmetric Economic Security ====

Bitcoin has asymmetric security where Bitcoin miners control its security, but they aren't the same people who hold Bitcoin. Unlike with Proof of Stake, there is much weaker economic incentive for those who control security to protect the network under Proof of Work. Historically, many Proof of Work networks with low security budgets have fallen under 51% attacks.,<ref>{{cite web |title=51% attacks |url=https://dci.mit.edu/51-attacks |website=51% attacks - MIT Digital Currency |date=10 July 2020 |access-date=17 March 2025}}</ref> which highlights PoW's asymmetric security.

The amount of protection provided by PoW mining is close to the security budget of the network, which is roughly equal to the total block reward. With each additional halving, Bitcoin's security budget continues to fall relative to its market cap. In the past, Bitcoin developers were hopeful that transaction fees would rise to replace the declining block subsidy, but this has not been the case as transaction fees still only generate 1% of the total block reward.<ref>{{cite web |title=Bitcoin transaction fee ratio |url=https://cryptoquant.com/asset/btc/chart/fees-and-revenue/fees-to-reward-ratio |website=Bitcoin: Fees to Reward Ratio |access-date=17 March 2025}}</ref> There are concerns that Bitcoin's security is unsustainable in the long run due to the declining security budget caused by its halvings.

== Environmental concerns ==
{{See also|Environmental impact of bitcoin}}
Miners compete to solve crypto challenges on the bitcoin blockchain, and their solutions must be agreed upon by all nodes and reach consensus. The solutions are then used to validate transactions, add blocks and generate new bitcoins. Miners are rewarded for solving these puzzles and successfully adding new blocks. However, the Bitcoin-style mining process is very energy intensive because the proof of work is shaped like a lottery mechanism. The underlying computational work has no other use but to provide security to the network that provides open access and has to work in adversarial conditions. Miners have to use a lot of energy to add a new block containing a transaction to the blockchain. The energy used in this competition is what fundamentally gives Bitcoin its level of security and resistance to attacks. Also, miners have to invest computer hardwares that need large spaces as fixed cost.<ref>{{Cite journal |last1=Ciaian |first1=Pavel |last2=Kancs |first2=d’Artis |last3=Rajcaniova |first3=Miroslava |date=2021-10-21 |title=The economic dependency of bitcoin security |journal=Applied Economics |language=en |volume=53 |issue=49 |pages=5738–5755 |doi=10.1080/00036846.2021.1931003 |s2cid=231942439 |issn=0003-6846|doi-access=free |hdl=10419/251105 |hdl-access=free }}</ref>

In January 2022 Vice-Chair of the [[European Securities and Markets Authority]] Erik Thedéen called on the EU to ban the proof of work model in favor of the [[proof of stake]] model due its lower energy emissions.<ref>{{Cite web|last=Bateman|first=Tom|date=2022-01-19|title=Ban proof of work crypto mining to save energy, EU regulator says|url=https://www.euronews.com/next/2022/01/19/eu-regulator-calls-for-a-ban-on-proof-of-work-bitcoin-mining-to-save-renewable-energy|access-date=2022-01-22|website=euronews|language=en|archive-date=2022-04-19|archive-url=https://web.archive.org/web/20220419190031/https://www.euronews.com/next/2022/01/19/eu-regulator-calls-for-a-ban-on-proof-of-work-bitcoin-mining-to-save-renewable-energy|url-status=live}}</ref>

In November 2022 the state of [[New York (state)|New York]] enacted a two-year moratorium on cryptocurrency mining that does not completely use [[renewable energy]] as a power source for two years. Existing mining companies will be [[grandfathered]] in to continue mining without the use of renewable energy but they will not be allowed to expand or renew permits with the state. No new mining companies that do not completely use renewable energy will be allowed to begin mining.<ref>{{Cite web |last=Sigalos |first=MacKenzie |title=New York governor signs first-of-its-kind law cracking down on bitcoin mining — here's everything that's in it |url=https://www.cnbc.com/2022/11/23/new-york-governor-signs-law-cracking-down-on-bitcoin-mining.html |access-date=2022-12-04 |website=CNBC |date=23 November 2022 |language=en |archive-date=2022-12-03 |archive-url=https://web.archive.org/web/20221203180017/https://www.cnbc.com/2022/11/23/new-york-governor-signs-law-cracking-down-on-bitcoin-mining.html |url-status=live }}</ref>

== See also ==
* [[Bitcoin]]
* [[Bitmessage]]
* [[Cryptocurrency]]
* [[Proof of authority]]
* [[Proof of burn]]
* [[Proof of personhood]]
* [[Proof of space]]
* [[Proof of stake]]
* [[Proof of elapsed time]]
* [[Consensus (computer science)]]

== Notes ==
* {{note|a}}On most Unix systems this can be verified with <code>echo -n 1:52:380119:calvin@comics.net:::9B760005E92F0DAE | openssl sha1</code>

== References ==
{{Reflist|30em|refs=
<ref name="JaJue1999">{{cite journal
 | first1 = Markus | last1 =  Jakobsson | first2 = Ari | last2 = Juels
 | title = Proofs of Work and Bread Pudding Protocols
 | journal = Secure Information Networks: Communications and Multimedia Security | pages = 258–272 | publisher = Kluwer Academic Publishers | year =1999
| doi = 10.1007/978-0-387-35568-9_18 | doi-access = free }}</ref>
}}

{{Bitcoin}}
{{Cryptocurrencies|state=expanded}}
{{Cryptography navbox | hash}}
{{Portal bar|Free and open-source software|Internet|Numismatics}}
{{Authority control}}

{{DEFAULTSORT:Proof-of-work system}}
[[Category:Cryptography]]
[[Category:Cryptocurrencies]]
[[Category:Energy consumption]]