On integral distinguishers of Rijndael family of ciphers

The Rijndael family of ciphers was designed by Daemen and Rijmen for the AES competition. Let each member be Rijndael _b, where b ∈ {128, 160, 192, 224, 256} denotes the block size. The current AES standard is Rijndael ₁₂₈, for key sizes of 128, 192, and 256 bits. This paper treats the integral cryptanalysis of Rijndael _b, notably for b ∈ {160, 192, 224, 256}. Integral cryptanalysis (in its basic form, first known in folklore as the Square attack) is unique for the Rijndael context because it was first applied to the Rijndael predecessor Square. Integral attacks were also the only and best known attacks on reduced round Rijndael found by its designers and explicitly described within its specification document.