Answer completely and carefully based on cryptography for thumbs up.

(f) In the Elgamal encryption algorithm the public encryption key (p, a, ) is published, whereas the value a E Z*_1 (the discrete logarithm of in base a modulo p) is kept secret. The plaintext x is encrypted by choosing a random k e ZM-1. The cryptotext is an element in Zp * Zcalculated as (ak, xk). Explain why Elgamal is not perfectly secure when the public key (p, a, ) is known. (f) In the Elgamal encryption algorithm the public encryption key (p, a, ) is published, whereas the value a E Z*_1 (the discrete logarithm of in base a modulo p) is kept secret. The plaintext x is encrypted by choosing a random k e ZM-1. The cryptotext is an element in Zp * Zcalculated as (ak, xk). Explain why Elgamal is not perfectly secure when the public key (p, a, ) is known