Nt2580 Birthday Attack Extra Credit

In: Computers and Technology

Submitted By sbharadwa
Words 638
Pages 3
A birthday attack is a type of cryptographic attack that exploits the mathematics behind the birthday problem in probability theory. This attack can be used to abuse communication between two or more parties. The attack depends on the higher likelihood of collisions found between random attack attempts and a fixed degree of permutations (pigeonholes), as described in the birthday problem/paradox.

Understanding the problem
As an example, consider the scenario in which a teacher with a class of 30 students asks for everybody's birthday, to determine whether any two students have the same birthday (corresponding to a hash collision as described below [for simplicity, ignore February 29]). Intuitively, this chance may seem small. If the teacher picked a specific day (say September 16), then the chance that at least one student was born on that specific day is, about 7.9%. However, the probability that at least one student has the same birthday as any other student is around 70% (using the formula for n = 30).

The Mathematics
Given a function, the goal of the attack is to find two different inputs such that a pair is called a collision. The method used to find a collision is simply to evaluate the function for different input values that may be chosen randomly or pseudorandomly until the same result is found more than once. Because of the birthday problem, this method can be rather efficient. Specifically, if a function yields any of different outputs with equal probability and is sufficiently large, then we expect to obtain a pair of different arguments. Then we look to evaluating the function for about different arguments on average. We consider the following experiment. From a set of H values we choose n values uniformly at random thereby allowing repetitions. Let p (n; H) be the probability that during this experiment at least one value is chosen more than…...

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