security - Difference between Hashing a Password and Encrypting it

The current top-voted to this question states:

Another one that's not so much a security issue, although it is security-related, is complete and abject failure to grok the difference between hashing a password and encrypting it. Most commonly found in code where the programmer is trying to provide unsafe "Remind me of my password" functionality.

What exactly is this difference? I was always under the impression that hashing was a form of encryption. What is the unsafe functionality the poster is referring to?

Answer

Hashing is a one way function (well, a mapping). It's irreversible, you apply the secure hash algorithm and you cannot get the original string back. The most you can do is to generate what's called "a collision", that is, finding a different string that provides the same hash. Cryptographically secure hash algorithms are designed to prevent the occurrence of collisions. You can attack a secure hash by the use of a rainbow table, which you can counteract by applying a salt to the hash before storing it.

Encrypting is a proper (two way) function. It's reversible, you can decrypt the mangled string to get original string if you have the key.

The unsafe functionality it's referring to is that if you encrypt the passwords, your application has the key stored somewhere and an attacker who gets access to your database (and/or code) can get the original passwords by getting both the key and the encrypted text, whereas with a hash it's impossible.

People usually say that if a cracker owns your database or your code he doesn't need a password, thus the difference is moot. This is naïve, because you still have the duty to protect your users' passwords, mainly because most of them do use the same password over and over again, exposing them to a greater risk by leaking their passwords.