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# hw2-12 - CMPT 404 Cryptography Exercises on Pseudorandom...

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CMPT 404 — Cryptography Exercises on Pseudorandom Generators, Functions and Permuta- tions. Due: Thursday, March 1st (at the beginning of the class) 1. (a) Which of the following functions are superpolynomial: - 2 n ; - n log n ; - n log n ? (b) Prove that for every superpolynomial function T the function ( T ( n 1 3 )) 1 3 n 3 is also superpoly- nomial. 2. (optional) This exercise will unable to test your favorite pseudorandom generator. The test is based on a well known property of random integers: Given two randomly chosen integers m and n , the probability they are relatively prime (their greatest common divisor is 1) is 6 π 2 . Use this property in a program to determine statistically the value of π . The program should call the random number generator from the system library to generate the random integers. It should loop through a large number of random numbers to estimate the probability that two numbers are relatively prime. From this find an approximate value of π . Report the type/name of the random number generator(s), the number of pairs of numbers in your sample, and the approximate value of π . 3. Suppose you have a true random bit generator where each bit in the generated stream has the same probability of being a 0 or 1 as any other bit in the stream and that the bits are not correlated; that is the bits are generated from identical independent distribution. However,

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