Question: This is a topic in Computer Science called Cryptography Exercise 3: The following exercises are on prime numbers. a) Use the Miller-Rabin Primality Test to

This is a topic in Computer Science called Cryptography

Exercise 3: The following exercises are on prime numbers. a) Use the Miller-Rabin Primality Test to test whether n = 157 is a prime. Choose the random value a = 8. (4 marks) b) Eve is given a large composite number n = pxq. She attempts a brute force approach to finding a factor of n by testing whether p divides n for p = 2,3,5,7,... until she finds a factor pln. Prove that Eve has to test at most 26/2+1 bln 2 factors until she findspin, where b = log2(n) is the approximate number of bits inn. Hint: Use the Prime Number Theorem to approximate the number of tests required. [3 marks] c) Assume Eve has a computer that can check 100 million factors in a second. How many days could it potentially take Eve to find a prime factor for a number n with b = 100? Use the estimate from b). [2 marks]

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