Not "if then send" -- if that were the case you could detect that your images were matching and then use the system as an oracle to e.g. detect that the databas

Not "if then send" -- if that were the case you could detect that your images were matching and then use the system as an oracle to e.g. detect that the database might contain disfavored political content in addition to whatever they claim it contains. The system was proposed as part of the upload process to your private encrypted cloud storage. So they already have the files. The system was designed so that if there were a sufficient number of hits against an encrypted database then a party possessing a particular private key would learn the private key for the encrypted files, as a passive effect of there being matches. Like if I mutter random letters of my password while entering it, you'd eventually passively learn my password just by hanging around while I logged in each morning. This way any matching is completely undetectable on the users end, at least until the private key possessing parties or the people they share the information with choose to take some action against the user.