I am in a dispute regarding a test question in an exam. The question is something like that:
What would happen if one were to use RSA with $n=100$ and $e=13$ to encrypt a message $m$?
a) You would be able to encrypt the message but not decrypt it.
b) You would not be able to encrypt the message.
Both parties agree that the operation $c = m^e \bmod n$ (a transformation known as encryption when using proper RSA) is no longer bijective, as $n$ is not the product of two primes. For example, $m=10$ and $m=20$ would both result in "cryptogram" $c=0$.
I consider that an encryption function must be invertible, as the purpose of encryption is to hide information from non-authorized eyes while allowing authorized parties to retrieve it. The fact that this transformation (which I'd argue could not even be called RSA, as $n$ does not fulfill RSA's rules) is not bijective means that it is not invertible, so it cannot be considered encryption. I would say that, under this assumption, any discussion of encryption/decryption is pointless, and if one answer had to be marked, it should be B: we cannot call $c = m^e \bmod n$ "encryption".
On the other hand, the other party sustains that the only correct answer is A, and that "it is fallacious to believe that encryption must be invertible, as there are many non-invertible encryption schemes". They are not available for questioning, so I cannot seek further clarification about what they meant. I assume they meant cryptographic hashes, but I would not consider them encryption schemes, but cryptographic primitives.
My question is therefore two-fold:
- Am I correct in assuming that it is not wrong to impose the condition that a transformation must at least be invertible in order to be considered encryption?
- If I am correct: Could I be pointed out to some reputable bibliographic source to use to strengthen my case?
- If I am incorrect: Is it because cryptographic hashes are considered encryption schemes or because there truly are non-invertible cryptographic schemes? If so, how do they meaningfully differ from hashes?