Which library to use when you want to create password for a door lock system that can be used only once

I don’t see a library for this purpose , you need to have a go at coding .

Post up your code !

You are likely to have memory issues storing 60 passwords with a Nano/UNO and might need to look at maybe NanoEvery .
Your program is going to have to look through all the remaining passwords for a match , which may also be time consuming . If you are new to programming this may be a bit hard to get a good algorithm .

Have a go at writing something with say 3 passwords - put them in an array , then you can use the array position to determine if that password has been used - see how it goes and assess what the difficulties might be .