Prove that if Alice’s public exponent e is 3 and an adversary obtains Alice’s secret exponent d, where 0 < d < Φ(n), then the adversary can factor Alice’s modulus n in time polynomial in the number of bits in n. (Although you are not asked to prove it, you may be interested to know that this result remains true even if the condition e = 3 is removed. See Miller [255].)