(multiplicative one-time pad). We may also define a multiplication mod variation of the one-time pad. This is a cipher = (, ), defined over (,,), where : = : = : = {1, . . . , 1}, where p is a prime. Encryption and decryption are defined as follows: (,) : = (,) : = 1 . Here, 1 denotes the multiplicative inverse of modulo . a) Verify the correctness property for this cipher [5 pts] b) Prove that it is perfectly secure [10 pts]