# El Gamal encryption scheme and symmetric encryption scheme

Consider the El Gamal encryption scheme, a symmetric encryption scheme (KG,E,D), and the following hybrid encryption scheme having an encryption algorithm that, on input a public key (G,q,g,h), where h=g^x, returns (c1,c2). For which of the following c1,c2 values (and assuming a suitable definition of the key generation and decryption algorithms) does the hybrid encryption scheme satisfy indistinguishability in the presence of chosen message attack?

A.c1=g^y, c2=E(k,m), where k = g and y is random
B.c1=g^y, c2=E(k,m), where k = h and y is random
C.c1=g^y, c2=E(k,m), where k = g^y and y is random
D.c1=g^y, c2=E(k,m), where k = h^y and y is random


I think the answer should be one of C and D, but not sure which one. Can anyone explain which one is the correct and why other three are not? Thanks so much!

• look at C a second time. Is there any secret involved? – DrLecter Apr 13 '14 at 8:48