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2 a = Question 2: Let n= pq for two different primes p and q. This exercise shows that we can use the RSA even if gcd(M, n) + 1 (M is a message). 1. Let j be a multiple of 0(n). Show that for M such that gcd(M, n) #1, Mi+1 = M mod p and Mi+1 = M mod q = M a 2. Let e and d be the be the encryption and decryption for RSA modulo n. Show that Med = M mod n for any M. = 3. Explain why this means that we can use the RSA also if gcd(M, n) + 1. 4. Explain why is gcd(M, n) 1 highly likely for a large n=p.q. = =