4. Consider the following cryptographic system. Alice chooses two large primes p and q and publishes N p. It is assumed that N is hard to factor. Alice also chooses three random numbers g modulo N and and r2 modulo (p- 1)(1) and computes (Alice takes care to choose and r2 so that neither g nor g2 is congruent to 1 modulo N) Her public key is the triple (N, g1.92) and she keeps p, q, g, Ti, and r2 private Now Bob wants to send a message m E Z/NZ to Alice. He chooses two random integers s1 and s2 modulo N and compute CEmgi' mod N and c2-mga2 mod N Bob sends the ciphertext (c1, c2) to Alice. Alice then decrypts by using the Chinese remainder theorem to solve the pair of con gruences (a) Prove that Alice's solution is equal to Bob's plaintext m modulo N (b) Show that Eve can use the public information to (quickly) find the factors p and q of N. Hence, show that this system is not secure