Like companies that provide a service and charge you monthly automatically? How are the credit card numbers stored safely so everyone doesn’t know your number? I understand password hashing on servers. Is it similar to that?
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When done right (big emphasis on the done right part), the company that is charging you say Patreon, doesn’t keep all of your information, they might keep the last 4 of your card number, name and zip code for example.
Simplifying a lot, They pass the rest onto a payment processor who then does the transaction and returns something to say it was successful. Patreon can than use that return value to charge you next month, basically hey remember that transaction? yea can you do it again, here is the proof it was authorized.
The rules governing all this are called **pci compliance** and are pretty complicated and require a lot of checks which is why most companies use a payment processor like paypal, stripe, visa etc
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