Meet-in-the-Middle Attacks on Reduced-Round QARMA-64/128

QARMA is a new family of lightweight tweakable block ciphers which is used in the Pointer Authentication of ARMv8.3-A. In this paper, we apply meet-in-the-middle attack to QARMA-64 and QARMA-128 including the outer whitening keys. First, we observe that a linear relation exists between four cells out of the eight input/output cells in the MixColumns operation. Then, the idea of canceling the state difference with the tweak difference is used to make one blank round. Finally, we construct meet-in-the-middle distinguishers on 5-round QARMA-128 and QARMA-64, respectively. Therefore, the attack on QARMA4-128 is obtained by appending three rounds on the top of the distinguisher and two round on the bottom. Similarly, the attack on QARMA3-64 is obtained. Besides, this attack can be extended to attack on 9-round QARMA-64 without increasing the overall complexity. To the best of our knowledge, these are the first attacks on QARMA block ciphers including the outer whitening keys.