They're not magical. They're just smart use of cryptography.

Ashton Kutcher's foundation Thorn https://en.wikipedia.org/wiki/Thorn_(organization) does a lot of work in this space. They have hashed content databases, they have suspected and watchlisted IP addresses, etc...

I don't know why I'm being downvoted. This is an active area of cryptography research, and I've applied these types of content checks in real life. You can maintain good privacy and still help combat child pornography.

Sometimes HN takes digital cynicism a step too far.

Checking the images you upload to icloud against a database of CSAM image hashes is what Apple is updating people’s phones to do. I actually don’t really see the issue and I don’t think the average consumer will care about this one bit. apple has always been able to see your icloud backups in plan text anyway