It is often said that breaking RSA is equivalent to factoring the modulus, n.
a. Prove that if n can be factored, one can determine the private key d from the modulus n and the public key e.
b. Show that it is not necessary to factor n in order to determine the private key d from the modulus n and the public key e.
c. Show that it is not necessary to factor n in order to determine the plaintext m from a given ciphertext c, the public key e, and the modulus n.