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Proof of work is the concept which makes things difficult for the fraudulent note to catch up with the Ow-nest notes.

Ideally the purpose of Proof-of-work
• Produce a challenge to the user / computer
• The user / computer has to produce the challenge result to submit some value.
• Essentially showing the Proof of Some Work Done.
• And eliminate entities which are slow or not capable enough to generate the proof of work
The idea behind Proof of Work is:
• Find or generate a Value which is:
- Difficult to generate (In terms of CPU Power)
- And yet easily verifiable.

BlockChain Solve Problem

For example, proof Of Work in Blockchain
• Proof of Work : Block Should have n leading 0.
For example:   n = 4, hash should have 4 leading zeros.

0000AB23EF23DD223432FC0390040438DF.....

How to Get Such Proof of Work ?

Generate Nonce, (may be by Bruteforce) such that :
• Combination of Nonce and Block Data generates the leading zeros.
• As per the difficulty of the challenge (Value of n)
• More the value of n more the difficulty.

Significance of Proof of Work
• Signifies that the computation required is exponential to the number of leading zeros required.
• Once the CPU effort has been expended to make satisfy proof of work the block cannot be changed.
• Until redoing the proof of work.
• And as the blocks are chained, redoing will require entire chain to be redone.
A Validity of Proof-of-Work
• Even if Attacker tries to catch up and produce the Proof-of-Work faster, the added block will be assessed again when new block is added
• Chain with longest proof of work will be accepted.
• Parallel chains are formed.
• Other Block will be rejected (Called the Dangling)
• If majority of the nodes are honest, they will grow and outpace the any competing chains.
• To modify any block
- The attacker would have to redo all the proof of work for all the blocks from that block till the last block.
- And catch up and surpass work of the honest nodes
• As per the original paper of Satashi Nakamoto:
- There is a premises that as number of blocks increase, the probability of slower attacker catching up diminishes.