Introduction to Cryptography with Coding Theory, 3rd Edition

7.6 Password Security

When you log in to a computer and enter your password, the computer checks that your password belongs to you and then grants access. However, it would be quite dangerous to store the passwords in a file in the computer. Someone who obtains that file would then be able to open anyone’s account. Making the file available only to the computer administrator might be one solution; but what happens if the administrator makes a copy of the file shortly before changing jobs? The solution is to encrypt the passwords before storing them.

Let $f(x)$ be a one-way function. This means that it is easy to compute $f(x)$, but it is very difficult to solve $y=f(x)$ for $x$. A password $x$ can then be stored as $f(x)$, along with the user’s name. When ...