"Well, where do you store your private DPG then?"
Private DPGs are generators of passwords locations to which (URLs) are known only to users.
Private DPGs as well as public DPGs do not store passwords in any place.
"And what happens when that computer fails?"
Private DPGs are hosted on multiple servers in multiple countries, so if some fail other will work.
In a very unlikely event if all servers will be down a user will have portable offline versions, which can be run on any computer.
"And how do you give billions of users worldwide each their own unique cryptographically secure DPG?"
It is a simple combinatorics. If there will be 100 trillions people on the planet, they will have private DPGs which will generate unique set of passwords for each of them.
"If you have an algorithm that generates the same passwords for the same input every single time, the end result is the same as storing them in a file."If you have an algorithm that generates the same passwords for the same input every single time, the end result is the same as storing them in a file.
When your passwords are in a file, it can be hacked and decrypted.
When we have an algorithm, even if it is a public algorithm, there are too many inputs to test to discover your output passwords. You will spends millions of years with quantum computers to brute-force such algorithm.
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