In spite of the research for a linear layer of Type-2 Generalized Feistel Network (Type-2 GFN) over more than 10 years, finding a good 32-branch permutation for Type-2 GFN is still a very hard task due to a huge search space. In terms of the diffusion property, Suzaki and Minematsu investigated the required number of rounds to achieve the full diffusion when the branch number is up to 16. After that, Derbez et al. presented a class of 32-branch permutations that achieves the 9-round full diffusion and they prove that this is optimal. However, this class is not suitable to be used in Type-2 GFN because it requires a large number of rounds to ensure a sufficient number of active S-boxes. In this paper, we present how to find a good class of 32-branch permutations for Type-2 GFN. To achieve this goal, we convert Type-2 GFN into a LBlock-like structure, and then we evaluate the diffusion property and the resistance against major attacks, such as differential, linear, impossible differential and integral attacks by an MILP. As a result, we present a good class of 32-branch permutations that achieves the 10-round full diffusion, ensures differentially/linearly active S-boxes of 66 at 19 round, and has the 18/20-round impossible differential/integral distinguisher, respectively. The 32-branch permutation used in WARP was chosen among this class.

MISTY1 is a 64-bit block cipher that has provable security against differential and linear cryptanalysis. MISTY1 is one of the algorithms selected in the European NESSIE project, and it has been recommended for Japanese e-Government ciphers by the CRYPTREC project. This paper shows that higher order differential attacks can be successful against 7-round versions of MISTY1 with FL functions. The attack on 7-round MISTY1 can recover a partial subkey with a data complexity of 254.1 and a computational complexity of 2120.8, which signifies the first successful attack on 7-round MISTY1 with no limitation such as a weak key. This paper also evaluates the complexity of this higher order differential attack on MISTY1 in which the key schedule is replaced by a pseudorandom function. It is shown that resistance to the higher order differential attack is not substantially improved even in 7-round MISTY1 in which the key schedule is replaced by a pseudorandom function.

Tweakable block cipher (TBC) is an extension of conventional block cipher. We study how to build a TBC based on generalized Feistel structure (GFS), a classical block cipher construction. While known dedicated TBC proposals are based on substitution-permutation network (SPN), GFS has not been used for building TBC. In particular, we take 64-bit GFS block cipher TWINE and try to make it tweakable with a minimum change. To find a best one from a large number of candidates, we performed a comprehensive search with a help of mixed integer linear programming (MILP) solver. As a result, our proposal TWINE is quite efficient, has the same number of rounds as TWINE with extremely simple tweak schedule.

MISTY1 is a 64-bit block cipher that has provable security against differential and linear cryptanalysis. MISTY1 is one of the algorithms selected in the European NESSIE project, and it has been recommended for Japanese e-Government ciphers by the CRYPTREC project. This paper reports a previously unknown higher order differential characteristic of 4-round MISTY1 with the FL functions. It also shows that a higher order differential attack that utilizes this newly discovered characteristic is successful against 6-round MISTY1 with the FL functions. This attack can recover a partial subkey with a data complexity of 253.7 and a computational complexity of 264.4, which is better than any previous cryptanalysis of MISTY1.

In this paper, we revisit related-key security of TWINE block cipher with 80-bit and 128-bit keys. Using an MILP-aided automatic search algorithm, we point out the previous evaluation of TWINE with a 80-bit key is wrong, and give a corrected evaluation result. Besides, we show a first security evaluation of TWINE with a 128-bit key in the related-key setting, which was infeasible due to the high computation cost in the original proposal.