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I was just wondering if, due perhaps to different hashing methods, knowing that the password is the same for a Windows 7 and an Ubuntu system would make either system more vulnerable. The OSs are dual booted from the same laptop using GRUB.

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If you are asking about the scenario that someone knows that a password is the same on two systems using different hash methods and is trying to compare the hash outputs to get the password - that really can't work. Hashes are one-way functions designed so that you can't get the password from the hash. You can't compare the two hashes against each other either. This assumes that the hashing algorithms are good and the hash lengths are long enough for security and that the person is using some sort of decent password.

To explain that, if the hash isn't good and the output long enough, a rainbow attack is possible. Even if you have a very good hash and very long outputs - say 256bit or so - the typical "dumb" passwords like "12345" and "password" and others would be the first hashes to be created and tested against. After that, it is brute force.

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