A birthday attack (Links to an external site.) is a type of cryptographic attack that exploits the mathematics behind the birthday problem in probability theory (Links to an external site.).
Birthday matching is a good model for collisions between items randomly inserted into a hash table.
What is the probability that some birthday is shared by two people in a class of n randomly and independently selected students? To work this out, we’ll assume that the probability that a randomly chosen student has a given birthday is 1/d (of course we still work with 365 day calendars!)
Start with :
There are d^n sequences of n birthdays, and under our assumptions, these are equally likely.
There are
(d)(d-1)(d-2)...(d-(n-1)) length n sequences of distinct birthdays.
That means the probability that everyone has a different birthday is;
................................................................................do the math and show;
e − ( n ( n − 1 ) ) 2 d
2. Now show that it implies that to use a hash function that maps n items into a hash table of size d, you can expect many collisions if n^2 is more than a small fraction of d.
This is how Birthday attacks work!
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