How Unique is CRC16 Value?

Question

I'm developing an OpenSource .NET Licensing Engine. This engine use hardware id (harddisk serial number) as lock and CRC16 this value to get shorten identifier.

Example value is MAXTOR ST3100, 476300BE and CRC16 result is 3FF0

My concern is how often 2 diffrent value get same CRC16 value, or should I use CRC32 instead ?

Answer 1

Probability of collision between 2 items = 1 ⁄ 0x10000 = 0.00152%...

But if you have more than 2 items, see the Birthday Problem -- it gets a lot more likely:
You just need 300 items to get a 50% probability of collision.

http://www.texify.com/img/%5CLARGE%5C%21%5CLARGE%5C%21%5Cleft%281%20-%20%5Cfrac%7B0%7D%7B2%5E%7B16%7D%7D%5Cright%29%5Cleft%281%20-%20%5Cfrac%7B1%7D%7B2%5E%7B16%7D%7D%5Cright%29%5Cleft%281%20-%20%5Cfrac%7B2%7D%7B2%5E%7B16%7D%7D%5Cright%29%5Cleft%281%20-%20%5Cfrac%7B3%7D%7B2%5E%7B16%7D%7D%5Cright%29%5Ccdots%5Cleft%281%20-%20%5Cfrac%7BN%7D%7B2%5E%7B16%7D%7D%5Cright%29%3D%2050%25%20%5C%5C%20N%20%5Capprox%20300.gif

Answer 2

As CRC16 is a 16-bit value, I'd say that the chance is around 1 in 65536.

Answer 3

No hashing method generates unique values, collisions being guaranteed at some point. The closest bet based on your requirements is simply to use the harddisk serial number as-is.

Hackers will crack it easily though.