The probability of a collision is found by a standard formula: p = 1 - k! / N
k-1(N-k)!, where k is the number of hashes generated (100x10
10x10
3) and N is the number of possible hashes (2
160).
This is a difficult number to calculate, but there is a good approximation: p = 1 - e
-k(k-1)/2NBut even that value is difficult to compute because of the precision needed. Here is another approximation p = k
2/2N.
So the answer is that the probability of at least one collision is approximately 7x10
-19 or 0.00000000000000007%
See:
http://preshing.com/20110504/hash-collision-probabilities