Verifying the integrity of ciphertext using the cleartext hash?

Question

I want to be able to verify the integrity of a ciphertext by providing the cleartext hash, for this to work it would need to:

$$hash(crypt(cleartext)) = f(hash(cleartext))$$

Where $f$ is an arbitrary function mapping the cleartext hash to the ciphertext hash.

Is there such a pair?

Update: I'm trying to prove the integrity to the receiver while delaying the key exchange until I'm ready to commit (send him the decryption details). The hash that proves the integrity comes from another source entirely.

Answer 1

There really isn't such a function $f$; encryption algorithms attempt to generate what looks like random bitstrings (at least, it looks that way to anyone who doesn't know the key), and because the plaintexts and the ciphertexts look unrelated, their hashes are also going to look unrelated.

On the other hand, what is the problem you're trying to solve? When you say 'verify the integrity of a ciphertext', who is doing the verification?

• Are you trying to allow the decryptor to verify that the message he got was the message that the encryptor sent without someone modifying it in the middle? If that's the case, the standard way of addressing it is with a Message Authentication Code

• Are you attempting to allow the encryptor to verify that the encryption process proceeded properly? About the only ways to do that are to either run the encryption process again (with the same IV) and compare, or attempt to decrypt the ciphertext and compare.

• Are you trying to allow someone in the middle (without the keys) to verify that a specific ciphertext happens to be a specific plaintext? Well, that would be an unusual requirement; I don't have any bright ideas on that one.