Abstract
FUTURE, recently proposed in AFRICACRYPT 2022, is a lightweight Substitution Permutation Network (SPN) based block cipher with 10 rounds. In this paper, we propose two attack algorithms on FUTURE, both based on biclique structure. The first algorithm uses a biclique structure that is constructed at the ciphertext side between the output state of round 10 (i.e., the ciphertext) and the output state of round 6. The time and memory complexities of the attack are 2125.8875 and 232, respectively, while the maximum data complexity is upper bounded by 248. We further improve upon the attack complexity by introducing one more biclique between the output state of round 6 and the output state of round 2. In the improved attack algorithm, by targeted partitioning and sub-partitioning of the keyspace and by using the biclique structures, a valid key, plaintext, and ciphertext triplet can be obtained for the cipher with time and memory complexities 2125.5365 and 232, respectively, while the maximum data complexity is upper bounded by 248. This is the first work that shows the susceptibility of full round FUTURE under a biclique-based cryptanalysis technique. The second approach is novel in the sense that it uses multiple biclique structures instead of a single biclique structure as used in usual biclique attacks, and thus reduces the time complexity by a factor of 0.22 over the first attack.