Suppose that RSA is used to send a message m to three recipients, who have relatively prime encryption moduli n1, n2, and n3. All three recipients use the same encryption exponent e = 3, a once-popular choice as it makes encryption very fast. Show that someone who intercepts all three encrypted messages c1 = m3 mod n1, c2 = m3 mod n2, and c3 = m3 mod n1 can efficiently decipher m. Hint: The Chinese remainder theorem implies that you can efficiently find a c such that c = c1 mod n1, c = c2 mod n2, and c = c3 mod n3. Assume this, and show that it implies c = m3 mod n1n2n3. Then note m3 1n2n3.