Squared RSA Prove the identity a^p (p^-1) = 1 (mod p^2), where a is relatively prime to p and p is prime. Now consider the RSA scheme: the public key is (N = p^2 q^2, 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. x^ed = x (mod N). Continuing the previous part, prove that the scheme is unbreakable, i.e. your scheme is at least as difficult as ordinary RSA. Squared RSA Prove the identity a^p (p^-1) = 1 (mod p^2), where a is relatively prime to p and p is prime. Now consider the RSA scheme: the public key is (N = p^2 q^2, 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. x^ed = x (mod N). Continuing the previous part, prove that the scheme is unbreakable, i.e. your scheme is at least as difficult as ordinary RSA