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Did a little searching an could not find an answer to this. A lot of ISPs these days are providing combination router/modem units, and they come with a pre-configured password that is a random string of letters and numbers, such as 1kd94nc9. Are these passwords reasonably secure, or should the end user change it to their own custom password (ignoring the fact that these can be hard for someone to remember)?

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    There is no universal answer. An ISP may or may not have used a process that generates unpredictable passwords. They may or may not store a copy of your password. If you somehow knew the answer for one company, that wouldn't mean you could conclude what a different company does. – Future Security May 18 at 16:38
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They're often not as random as they might appear. The forums posts listed here show many examples of researchers reverse-engineering the algorithms used to generate default router passwords - sometimes, even by disassembling the firmware.

Many manufacturers assume that no one will go to such trouble. These manufacturers often rely on obscurity, using algorithms that are only pseudo-random, and/or derived from the MAC address or other non-random information.

This varies by manufacturer and model, of course - but since it's often very hard to tell, you're almost always better off changing to something that you know is random, and of sufficient length to be beyond run-of-the-mill bruteforce capabilities - say, 15 characters random mixed-case alphanumeric+specials (or often better, the equivalent entropy in a randomly-generated passphrase that's easy to type).

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It is best practice to change the default password of all devices that you use once you finish set up. It is even better to change them periodically following a practice of "cyber/digital hygiene". Regarding the hard to remember part, may I suggest pass phrases instead? Pass phrases is a series of common words (QuickFoxLazy) that actually increase complexity of the password and are easy to remember by creating some bizarre story behind the scene.

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