I'll be talking about digital signatures which is the basis for such things. I assume basic understanding of asymmetric cryptography and hashing.

Basically, you hash the content you want to verify with a secure hashing function and encrypt the value with your private key. You can now append this encrypted value to the content or just release it alongside it.

To now verify this content they can use your public key to decrypt your signature and get the original hash value, and compare it to their own. To get that, they just need to hash the content themselves with the same function.

So by signing their videos with the white house private key and publishing their public key somewhere, you can verify the video's authenticity like that.

For a proper understanding check out DSA :)

Click the padlock in your browser, and you'll be able to see that this webpage (if you're using lemmy.world) was encrypted by a server that has been verified by Google Trust Services to be a server which is controlled by lemmy.world. In addition, your browser will remember that... and if you get a page from the same server that has been verified by another cloud provider, the browser (should) flag that and warn you it might be

The idea is you'll be able to view metadata on an image and see that it comes from a source that has been verified by a third party such as Google Trust Services.

How it works, mathematically... well, look up "asymmetric cryptography and hashing". It gets pretty complicated and there are a few different mathematical approaches. Basically though, the white house will have a key, that they will not share with anyone, and only that key can be used to authorise the metadata. Even Google Trust Services (or whatever cloud provider you use) does not have the key.

There's been a lot of effort to detect fake images, but that's really never going to work reliably. Proving an image is valid, however... that can be done with pretty good reliability. An attack would be at home on Mission Impossible. Maybe you'd break into a Whitehouse photographer's home at night, put their finger on the fingerprint scanner of their laptop without waking them, then use their laptop to create the fake photo... delete all traces of evidence and GTFO. Oh and everyone would know which photographer supposedly took the photo, ask them how they took that photo of Biden acting out of character, and the real photographer will immediately say they didn't take the photo.