Upper Bounds for the Probability of Differential Characteristics of Five Block Cipher Constructions Functions

Block ciphers have the main role in the communication and information security and also electronic and cyber defense. A secure block cipher must be resistant against the known attacks, such as the differential cryptanalysis. Kim et al. presented seven block cipher constructions with provable security against          differential cryptanalysis in 2008, which can be used to design the block ciphers. In this paper, for five of the seven mentioned block cipher constructions, the upper bounds on the probability of differential       characteristics have been presented. This has been done using an automated differential cryptanalysis     approach based on linear programming. This approach formally introduced by Mouha et al. in 2011, was used for the analysis of several block ciphers.  Using the Mouha et al.’s approach, it is shown that the      five-round differential characteristics of the constructions have the upper bound p 4 which are approvable in comparison with the upper bounds of the differentials obtained by Kim et al. where p is the differential probability of the round function used in the constructions.