If I got it right, chosen ciphertext security implies also CPA security. In other words, attacker can submit plaintexts to the challenger (along with ciphertexts).
I do not understand why encryption system (E,D) where D(k,0)=0 is considered as ciphertext secure.
Imagine CPA security game where an attacker just submits two plaintexts, m0 = 0 and m1 = (any value != 0). In that case if poor challenger returns 0 then we are certain that we're in experiment 0 and win CPA game.
What I am missing here?