Discrete mathematics

2 Squared RSA (a) Prove the identitya-1 (mod p). where a is relatively prime to p and p is prime. (b) Now consider the RSA scheme: the public key is (N = p-r,e) for primes p and q, with e relatively prime to p(p-1)q(q-1). The private key is d = e-1 (mod p(p-1)q(q-1). Prove that the scheme is correct, i.e . xd-x (mod N). , You may assume that is relative ly prime to both p and g c) Continuing the previous part, prove that the scheme is unbreakable, i.e. your scheme is at least as difficult to break as ordinary RSA