Integral cryptanalysis of the BSPN block cipher

In this paper, we investigate the application of integral cryptanalysis to the Byte-oriented Substitution Permutation Network (BSPN) block cipher. The BSPN block cipher has been shown to be an efficient block cipher structure, particularly for environments using 8-bit microcontrollers. In our analysis, we are able to show that integral cryptanalysis has limited success when applied to BSPN. A first order attack, based on a deterministic integral, is only applicable to structures with 3 or fewer rounds, while higher order attacks and attacks using a probabilistic integral were found to be only applicable to structures with 4 or less rounds. Since a typical BSPN block cipher is recommended to have 8 or more rounds, it is expected that the BSPN structure is resistant to integral cryptanalysis.