How to validate the purchase of a premium app?

The mobile(ios, android) game I'm making is premium (aka you buy it once, no iap) and has online functionalities. To connect online, I want to make sure that it was legally purchased. Presumably the store would authenticate the purchase before signing into my app and using my backend. Is there any simple way of doing this? I've only ever made f2p games before, not sure how premium works and can't find any info on this.

Thanks!