NIZK proof for Order-preserving encryption Suppose a cipher c=Enc(K,m), where Enc() is the order-preserving encryption scheme. Can NIZK be used to prove that c does indeed encrypt m? The Schnorr NIZK is based on discrete logarithms equality. I don't know if it can be used for order-preserving encryption.

Thank you!
You cannot prove that a ciphertext (produced by an order-preserving encryption scheme) encrypts a particularly plaintext in zero-knowledge, because verification of such a proof would necessarily leak the plaintext. 

Perhaps you want to instead prove that the ciphertext is well-formed (i.e., produced by the scheme)? This is possible in the context of site's definition of [OPE][1], namely, a method of encrypting data so that it's possible to make efficient inequality comparisons on the encrypted items without decrypting them, since El Gamal conforms to this definition (see [plaintext equality tests][2]), and NIZK proof systems can be used to prove various properties about El Gamal ciphertexts.

EDIT. The comments note that: 


I assumed (possibly incorrectly) that the message was not to be revealed, and
The site's definition of OPE is incomplete.


I've proposed an edit to the site's definition of OPE. This answer only applies to the original definition.