The problem is highlighted in the following statement:
Unfortunately the designers of Mifare Classic did not follow this principle. Instead, they chose to combine a secret algorithm with a relatively short 48-bit key. This is a problem because once you know the algorithm it’s possible for an attacker to search the entire 48-bit key space, and therefore to forge cards, in a matter or days or weeks. With 48 key bits, there are only about 280 trillion possible keys, which sounds like a lot to the person on the street but isn’t much of a barrier to today’s computers.
An extremely healthy discussion is going on in the comments section of the afore-mentioned blog post of Ed.
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