A proof of work is a piece of data which is difficult (costly, time-consuming) to produce but easy for others to verify and which satisfies certain requirements. Producing a proof of work can be a random process with low probability so that a lot of trial and error is required on average before a valid proof of work is generated. Bitcoin uses the Hashcash proof of work system.

One application of this idea is using Hashcash as a method to preventing email spam, requiring a proof of work on the email's contents (including the To address), on every email. Legitimate emails will be able to do the work to generate the proof easily (not much work is required for a single email), but mass spam emailers will have difficulty generating the required proofs (which would require huge computational resources).

Hashcash proofs of work are used in Bitcoin for block generation. In order for a block to be accepted by network participants, miners must complete a proof of work which covers all of the data in the block. The difficulty of this work is adjusted so as to limit the rate at which new blocks can be generated by the network to one every 10 minutes. Due to the very low probability of successful generation, this makes it unpredictable which worker computer in the network will be able to generate the next block.

For a block to be valid it must hash to a value less than the current target; this means that each block indicates that work has been done generating it. Each block contains the hash of the preceding block, thus each block has a chain of blocks that together contain a large amount of work. Changing a block (which can only be done by making a new block containing the same predecessor) requires regenerating all successors and redoing the work they contain. This protects the block chain from tampering.

The most widely used proof-of-work scheme is based on SHA-256 and was introduced as a part of Bitcoin. Some other hashing algorithms that are used for proof-of-work include Scrypt, Blake-256, CryptoNight, HEFTY1, Quark, SHA-3, scrypt-jane, scrypt-n, and combinations thereof.

Example

Let's say the base string that we are going to do work on is "Hello, world!". Our target is to find a variation of it that SHA-256 hashes to a value smaller than 2^240. We vary the string by adding an integer value to the end called a nonce and incrementing it each time, then interpreting the hash result as a long integer and checking whether it's smaller than the target 2^240. Finding a match for "Hello, world!" takes us 4251 tries.

"Hello, world!0" => 1312af178c253f84028d480a6adc1e25e81caa44c749ec81976192e2ec934c64 = 2^252.253458683 "Hello, world!1" => e9afc424b79e4f6ab42d99c81156d3a17228d6e1eef4139be78e948a9332a7d8 = 2^255.868431117 "Hello, world!2" => ae37343a357a8297591625e7134cbea22f5928be8ca2a32aa475cf05fd4266b7 = 2^255.444730341 ... "Hello, world!4248" => 6e110d98b388e77e9c6f042ac6b497cec46660deef75a55ebc7cfdf65cc0b965 = 2^254.782233115 "Hello, world!4249" => c004190b822f1669cac8dc37e761cb73652e7832fb814565702245cf26ebb9e6 = 2^255.585082774 "Hello, world!4250" => 0000c3af42fc31103f1fdc0151fa747ff87349a4714df7cc52ea464e12dcd4e9 = 2^239.61238653

4251 hashes on a modern computer is not very much work (most computers can achieve at least 4 million hashes per second). Bitcoin automatically varies the target (and thus the amount of work required to generate a block) to keep a roughly constant rate of block generation.

In Bitcoin the hash value is also used as a reference to the block itself, so somebody might say that their transaction has been mined into block with hash 0000c3af42fc31103f1fdc0151fa747ff87349a4714df7cc52ea464e12dcd4e9 . The header of a block contains the Merkle tree which depends on the included transactions. This includes the generation transaction, a transaction "out of nowhere" to our own address, which in addition to providing the miner with incentive to do the work, also ensures that every miner hashes a unique data set.

List of algorithms

Traditional proof of work

hashcash with double iterated SHA256 hashcash with scrypt internal hash Momentum birthday collision Cuckoo Cycle proof of work https://github.com/tromp/cuckoo Various other proof of works functions

Proof of X

References

Distribution of nonces and hashes