What does Proof of X mean? What are the types?

Many of you do not know the behind-the-scenes of how transactions are verified and blocks are generated. This thread will explain the various ways and concepts that this is done. In my next thread I will talk about Ethereum adopting Proof of Stake and how they will aim to keep it safe.

Proof of Work

Proof of Work is defined as an economic measure to deter denial of service attacks and other service abuses such as spam on a network by requiring some work from the service requester, usually meaning processing time by a computer. Proof of Work is not a new concept. For additionally reading on the history of it, read here. Coins like Bitcoin use Proof of Work.

Simply put in terms of crypto currency, this means that calculations are required by the network nodes in order to form a distributed ledger. This process is called mining.

A distributed ledger is a decentralized system that can agree on and keep track of the correct amount a wallet has by providing a history of every single transaction.

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The Purpose of Mining

Mining is the process in which Proof of Work is generated. Before we go into the exact purpose of mining, we need to address what a Block is. A block is a permanent storage of record that includes a group of data of all or some transactions that have not yet been included in previous blocks.

The main purpose of mining is to verify the legitimacy of a transaction and prove that it is not a double spend. A double spend is when the same coins are spent more than once. Since mining is a strenuous process, miners are rewarded for their work upon successful completion of mining a block. Rewards vary by coin and can change over time.

Explaining like I am five, here is what happens:
A transaction is made and included with other transactions in a Block;
Miners verify every transaction in the block are legitimate;
In order to do this they must solve a mathematical problem;
Rewards are handed out to the miner that successfully solved the problem;
All legitimate transactions are stored in the mined block on the blockchain.

Due to the strenuous computation nature Proof of Work, it can become an expensive process.

Proof of Stake

Proof of Stake is an alternative to Proof of Work and aims to achieve distributed consensus. The idea was first discussed on bitcointalk in 2011 and first used with Peercoin. There are many different alternatives and solutions in itself, so we will talk about the basics of PoS.

Instead of having miners prove each and every transaction is legitimate, proof of stake requires that a person stake (hold or lockup) coins and validate ownership. There are different ways the new block creator are selected to avoid centralization or more than 51% ownership taking control. We will talk about this next.
Randomized Block Selection

Nxt and Blackcoin use randomization to predict the next block creator. They do this by using an algorithm to look for the lowest hash value in combination with the size of the stake. Since all stakes are public, the nodes can predict which stake will create the next block.

Read the whitepaper here.
Coin Age Selection

Coin age refers to the age of transaction inputs.

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Coin age is equal to the number of coins sent times the average age on these coins. Age is measured in days. Age is reset to zero whenever a coin is sent AND whenever a coin provides a signature. Coin age could be used to calculate mandatory fees, block reward or proofhash target.

Unspent coins must wait 30 days before they can begin competing to generate the next block. Coins like Novacoin and Peercoin use this method.

The reward for staking will either come from new coins generated by inflating the current supply, called minting, or they may come from recycled transaction fees, called forging.

The Differences from Proof of Work
Proof of Stake is more efficient. Electricity and hardware is not needed.
More people are encouraged to run nodes due to efficiency.
Proof-of-stake is not ideal for a distributed consensus protocol.
The "Nothing At Stake" problem. This can be avoided in different ways.
Variations of Proof of Stake
Proof of Stake Anonymous (PoSA)

First introduced by Cloakcoin, transactions are cloaked by other users who receive a reward for aiding in the anonymization of the transaction. Other users provide inputs and outputs to the transaction and make it impossible to determine the source and destination of the transaction.

Read the whitepaper here.
Delegated Proof of Stake (DPoS)

Delegated Proof of Stake was first seen on Bitshares blockchain. The way it works is it has users vote for "delegates" who are then given the power to earn profit from running a full node. This method is supposed to be more efficient and protect users from unwanted regulatory interference.

Read the whitepaper here.
Proof of Importance (POI)

An expansion by NEM called Proof of Importance was introduced to promote economic activity. Each account is assigned an importance score that proxies its aggregate importance to the economy. This method helps make sure that all the computers on the network agree with each other and can stop people from spending coins they do not have. Users who are "important" can "harvest" and earn rewards.

Read the whitepaper here.
Proof of Storage

Proof of Storage was first formulated in 2013. Coins like Storj use Proof of Storage. Instead of using a blockchain, the network uses a blocktree. Also instead of seeing every single transaction listed, the user will only see transactions that are relevant to them. Each node on the blocktree contains a blockchain. As of right now there is no known practical publicly verifiable proof of storage, and no known scheme for independently verifying that a privately verifiable audit was issued or answered as claimed.

Read the whitepaper here.
Proof of Stake Time (PoST)

First to use this is Vericoin. Proof of Stake Time uses coin age, but instead of using the amount of coins to calculate age, they use the period of time the coins have been held at the specific address. This method was implemented to avoid making the rich, richer, which many Proof of Stake methods do.

Read the whitepaper here.
Proof of Stake Velocity (PoSV)

Reddcoin is the first to introduce this method. Proof of Stake Velocity rewards users based on how many coins they have and how actively they use them.

Read the whitepaper here.

Proof of Activity

Proof of Activity (POA) was first proposed in 2012 as an alternative to Proof of Stake. It is a method that compliments Proof of Work and helps prevent a 51% Attack, which is when a user or pool controls 51% or more of a network's mining hashrate. Proof of Activity, in short, selects a random peer from the network to sign a new block. This method requires continuous data exchange. In order to reduce traffic, the block "template" does not include the transaction list and is instead added by the last signer.

Read the whitepaper here.

Proof of Burn (PoB)

Proof of Burn is exactly what it is called. You are providing proof that you have burned some of your coins in the process of sending a transaction to an address that is unspendable. This method only works with coins mined from Proof of Work crypto currencies. Users will try to burn the most amount of coins to hopefully "win" the block reward. Most times Proof of Burn has been introduced to seed other coins by destroying the value of one.

You can read more on the concept here.

Proof of Capacity (PoC)

Crypto currencies that utilize Proof of Capacity, also known as Proof of Space, use Hard Drive Mining to validate new blocks. Burst coin was the first to introduce this concept. Proof of Work miners burn resources whereas Proof of Capacity allows you to use allotted space on your hard drive to mine. An algorithm is used to create chunks of data called plots by repeatedly hashing public keys. The more space that you have, the more likely you are to mine a block.

Proof of Checkpoint (PoC)

Proof of Checkpoint is a hybrid system that utilizes any Proof of Stake system with a Proof of Work system. The idea of this concept is to mitigate attacks on the Proof of Stake system; however, it is still subject to an attack on a node that has been offline for an extended period of time and can in turn be used to provide false information about the blockchain.

Every x amount of blocks on the Proof of Stake system requires a Proof of Work block to be mined. Each Proof of Work block contains no transactions and are directly linked to both the Proof of Work network and the Proof of Stake network.

End Note

If anything in this thread needs to be corrected, please let me know. Additionally if there is a concept I have not talked about, please let me know so I can do some research on it and add it to the thread! Everything I have talked about are quick overviews of the concepts. I wanted this thread to be easy for members to educate themselves. For the technical aspects on the various concepts, please read the whitepapers that I have linked.