# Existence of a NIZK proof demonstrating that a ciphertext does not encrypt some specified plaintexts

Given a (El Gamal, for instance) ciphertext, can I (efficiently) prove that the ciphertext does not decrypt to plaintexts in a small set? For instance, given ciphertext $$c = Enc(pk,2; r)$$, can I (efficiently) prove that the ciphertext does not decrypt to a plaintext in set $$S = \{0,1\}$$?

I could use plaintext equality tests. For instance, I could construct ciphertexts $$Enc(pk,0; 1)$$ and $$Enc(pk,1; 1)$$, and use plaintext equality tests to show that neither of those ciphertexts is plaintext equivalent to ciphertext $$c$$. But, can I do better in terms of complexity?