A five-round algebraic property of AES and its application to the ALPHA-MAC

We present a five-round algebraic property of the advanced encryption standard (AES), and we show that this algebraic property can be used to analyse the internal structure of ALPHA-MAC whose underlying block cipher is AES. In the proposed property, we modify 20 bytes from 5 intermediate values at some fixed locations in 5 consecutive rounds, and we show that after 5 rounds of operations, such modifications do not change the intermediate result and finally, still produce the same ciphertext. By employing the proposed five-round algebraic property of AES, we provide a method to find second preimages of the ALPHA-MAC based on the assumption that a key or an intermediate value is known. We also show that our idea can also be used to find internal collisions of the ALPHA-MAC under the same assumption.