Here the link to the NIPoPoWs paper
The jargon and complexity of the topic is too difficult for me to parse.
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By definition, NiPoPoWs are lightweight proofs for Proof-of-Work blockchains. In a nutshell, they operate by taking advantage of the fact that every so often, a block of highly unusual likelihood is mined. Here’s a quick summary:
In PoW, a miner is elected Block leader when they win a lottery by producing a block hash with a certain difficulty level. Let’s say (for arguments sake) the chances of producing such a block are 1/100. Every so often, a miner will produce a block hash with an unusually high unlikelihood (I.e. 1/10,000 chance). NiPoPoWs take advantage of this “super-unlikelihood” by recognizing these super blocks are produced at a regular cadence. So instead of validating the entire blockchain, one only needs to validate the superblocks, which may be a much smaller subset of the rest of the blocks.
Another way to think about this: lets say there is an engine running and you know that a every 1000 engine cycles, the piston makes an unusual noise. If I ask you to count how long 5000 cycles takes, instead of counting 5000 engine cycles, you can just count 5 of the “unusual” cycles.
Here’s a more beginner friendly article on the topic.