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Prob. 5 (20pts) (Birthday attack) A birthday attack is a type of cryptographic attack that exploits the mathematics behind the birthday problem in probability theory. It can be used to find collisions in a cryptographic hash function. Suppose that we have a hash function which, when supplied with a random input, returns one of 256 equally likely values. The attack generates n random inputs, supplies them into the hash function, and obtains n returned values (each is chosen from the 256 possible values uniformly at random). Use MATLAB or other programming language, compute and plot the probability of at least two returned values being the same (i.e., collision happens), for n = 1 to 30, (Submit your math formula, the code, and a nice-looking plot.)
Please write down the equation for calculating the probability & use c language for programming part.
Thank you!
math   Statistics-And-Probability   
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