On integral distinguishers of block ciphers based on generalized Feistel schemes

In 2002, L. Knudsen and D. Wagner introduced the integral cryptanalysis technique which has become the powerful tool to assess the security of block ciphers such as AES, PRESENT, DES, SIMON 32, CAMELLIA, KHAZAD, RECTANGLE, PRINCE, HIGHT. The main idea of the technique is based on construction of an integral distinguisher, which is used to recover some key bits. Many block ciphers are based on different generalizations of the Feistel scheme. In this paper, we have built the 3-round integral distinguisher for the PICARO block cipher, which is based on a generalized Feistel scheme. Non-bijective PICARO $s$-boxes as well as the expanding matrix are studied to check a propagation of the integral properties. We have also constructed integral distinguishers for some generalized Feistel schemes.