Multidimensional zero-correlation linear cryptanalysis of the block cipher KASUMI

The block cipher KASUMI, proposed by ETSI SAGE more than 10 years ago, is widely used for security in many synchronous wireless standards nowadays. For instance, the confidentiality and integrity of 3G mobile communications systems depend on the security of KASUMI. Up to now, there are a great deal of cryptanalytic results on KASUMI, however, its security evaluation against the recent zero-correlation linear attacks is still lacking. In this paper, combining with some observations on the FL, FO and FI functions, we select some special input/output masks to refine the general 5-round zero-correlation linear approximations and propose the 6-round zero-correlation linear attack on KASUMI. Moreover, under the weak keys conditions that the second keys of the FL function in round 2 and round 8 have the same value at 1st to 8th and 11th to 16th bit-positions, we expand the attack to 7-round KASUMI(2-8). These weak keys take 1/2 of the key space. The new zero-correlation linear attack on the 6-round needs about 2 encryptions with 2 known plaintexts and 2 memory bytes. For the attack under weak keys conditions on the last 7 round, the data complexity is about 2 known plaintexts, the time complexity is about 2 encryptions and the memory requirements are about 2 bytes.