You can read part 2 here: https://blog.cryptographyengineering.com/2017/01/21/zero-knowledge-proofs-an-illustrated-primer-part-2/

This is as close an "explain this to me like I'm five" tutorial on zero knowledge proofs as you're likely to find. Excellent.

Nice to see this posted on SN. We desperately need to start the discussion about adding ZK (validity) rollups to Bitcoin.

ZK rollups will allow for arbitrary settlement in BTC, which is a huge feature. I.e., you could run entire sidechains or payment networks "off-chain" and have it settle on-chain with much better security guarantees than anything that exists now.

With ZK rollups we could even shrink the blocksize and make the chain easier to run on lower end hardware.

Unfortunately, ZK rollups have already taken off on ETH. The ETH ecosystem obviously does not share the values we have in the Bitcoin ecosystem, but if they have tech like this they could win out (and are currently winning out) on market share for the sorts of applications that require arbitrary settlement. This is not a world we want to live in.

@lightcoin did a great research project on adding zk rollups to bitcoin, details here: https://bitcoinrollups.org/

The post is from 2014 and ZK proofs will never make it into bitcoin because it doesent have the neccesary development culture to pull it off. The "sound money" lobby is basically in control of BTC and they believe it doesent have to change. Unfortunately for Bitcoin other cryptos have grown up now and are accumulating the neccesary network effects to become "sound money" and they will also be able to pull off the zero knowledge proofs.