Consider the following public key encryption scheme. The public key is (G, q, g, h) and the private key is x, generated exactly as in the El Gamal encryption shceme.

Consider the following public-key encryption scheme. The public key is (G, q, g, h) and the private key is x, generated exactly as in the El Gamal encryption scheme In order to encrypt a bit b, the sender does the following: (a) If b-0 then chose uniformly y E Zq and compute cg' and c- h. The cipher text is C1, C2) (b) If b = 1 then choose independent uniform y, z E Zq, compute ci-gy and c2-g" and set the ciphertext equal to C1, C2 Show that it is possible to decrypt efficiently given knowledge of x