Seven new block cipher structures with provable security against differential cryptanalysis

The design and analysis of block ciphers is an established field of study which has seen significant progress since the early l990s. Nevertheless, what remains on an interesting direction to explore in this area is to design block ciphers with provable security against powerful known attacks such as differential and linear cryptanalysis. In this paper we introduce seven new block cipher structures, named Feistel-variant A, B, CLEFIA and MISTY-EQ-variant A, B, C, D structures, and show that these structures are provably resistant against differential cryptanalysis. The main results of this paper are that the average differential probabilities over at least 2 rounds of Feistel-variant A structure and 1 round of Feistelvariant B structure are both upperbounded by p², while the average differential probabilities over at least 5 rounds of CLEFIA, MISTY-FO-vanant A, B, C and D structures are upperbounded by p⁴ + 2p⁵, p4, p⁴, 2p⁴ and 2p ⁴, respectively, if the maximum differential probability of a round F function is p. We also give provable security for the Feistel-variant A, B and CLEFIA structures against linear cryptanalysis. Our results are attamed under the assumption that all of components in our proposed structures are bijective. We expect that our results are useful to design block ciphers with provable security against differential and linear cryptanalysis. Copyright copy; 2008 The Institute of Electronics, Information and Communication Engineers.