An RSA cryptosystem has open parameters n, e and trapdoor parameters d, p, q, f(n), where p, q are..

An RSA cryptosystem has open parameters n, e and trapdoor parameters d, p, q, f(n), where p, q are primes and ed = 1 (mod f(n)). a) Determine how many numbers in {0, 1, . . . , f(n)} that are possible values for e if p = 2p1 + 1 and q = 2q1 + 1 where p1 and q1 are primes. b) The prime number theorem states that the number of primes not exceeding N is approximately N/ ln N. Thus the number of primes is relatively dense compared to nonprimes. Therefore for generation of p and q we may adopt the following strategy: test the prime p with some primality test and then choose q close to p with same primality tests. This ensures that p and q are about the same size. Can you use this method to generate primes for RSA crypto system ? Motivate your answer. c) Prove that D(E(M)) = M for the case gcd(M, n) = 1