Collision Probability in MD5

Question

In the worst case, I have 180 million values ​​in the cache (15 minute window before they fade out), and MD5 has 2 ^ 128 values. What is the probability of a collision? or better yet, is there a webpage somewhere to answer this question or a rough estimate? This is skalo, so I know my chances.

Answer 1

The probability is 1-m! / (Mⁿ (mn)!), Where m = 2¹²⁸ and n = 180,000,000.

Running via Wolfram on-line exceeds available computing time!

If you have SmallTalk installed locally, you can run this:

|m n p|

m := 2 raisedTo:128.
n := 180000000.
p := (1-(m factorial/((m raisedTo:n)*(m-n)factorial)))asFloat.

Transcript show:p printString;cr.

​​ , , 128 2.6 × 10¹⁰, 1 10¹⁸, 140 × , . , , "".

, n "m 1-e ^{-n 2/2m} , m n , 4.76 × 10⁻ ²³ 1 2.10 × 10²² .

, , FOOBAR, , , 15 , , .