# Finding colliding messages for AES decryption

I'm doing a school problem where I'm supposed to find a colliding message in a hashing algorithm that is weak-collision resistant.

The hashing algorithm is AES with a key & message size of 128.

### The problem

Given $$m$$ (message), $$k$$ (key), find some $$m$$' such that $$AES_{Decrypt}(k, m) = AES_{Decrypt}(k,m')$$

I've talked to my classmates about this and they tell me that it's really simple, basically a one-liner, if you understand encryption.

Clearly, there's something I'm missing.

• Welcome to Cryptography. It is nice to you have said it is homework. Now, what are your thoughts? Note: I've edited your question, key is before the message. If anything is incorrect, please edit. – kelalaka Nov 10 at 14:48
• Are you sure that this is the assignment? Keyed AES is a pseudo-random permutation or PRP. That means that - by definition - this cannot hold. Different ciphertext blocks always decrypt to different plaintext blocks... @kelalaka It says message size is 128 bits; so a single block. I infer direct use of the block cipher. – Maarten Bodewes Nov 10 at 16:21
• Please do use the same account ... creating two separate accounts with the same name is not a good idea. Flag a moderator if you don't know how to do this. – Maarten Bodewes Nov 10 at 16:28
• No! we don't have $E_k(a+b)=E_k(a)+E_k(b)$ for AES. This is a homomorphism – kelalaka Nov 10 at 17:28