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 five intermediate values at some fixed locations in five consecutive rounds, and we show that after five 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.