Probability of collision when using a 32 bit hash

Question

I have a 10 character string key field in a database. I\'ve used CRC32 to hash this field but I\'m worry about duplicates. Could somebody show me the probability of collisio

Answer 1

In the case you cite, at least one collision is essentially guaranteed. The probability of at least one collision is about 1 - 3x10^-51. The average number of collisions you would expect is about 116.

In general, the average number of collisions in k samples, each a random choice among n possible values is:

The probability of at least one collision is:

In your case, n = 2³² and k = 10⁶.

The probability of a three-way collision in your case is about 0.01. See the Birthday Problem.

Answer 2

Duplicate of Expected collisions for perfect 32bit crc

The answer referenced this article: http://arstechnica.com/civis/viewtopic.php?f=20&t=149670

Found the image below from: http://preshing.com/20110504/hash-collision-probabilities