Using cryptography for confirmation of paid items is what I intend, as cryptography can be used to verify a legitimate payment & point out a fake one.
possible?
You should try to give it a good thinking and see what's the intended workflow and then also explain it to us.
I expected the payments are handled by the cashier with a software and device provided by a bank or payment processor and you probably integrate with that.
Do you want to handle payments yourself? Are they bitcoin payments? Are they also fiat payments too? What you mean by fake payments?
Do you expect your database (with products, prices, tags/barcodes/QR) be ... public/exposed?