Algebraic Attack to SMS4 and the Comparison with AES

SMS4 is a 128-bit block cipher, which is used in the WAPI standard in China. This paper examines algebraic attacks on SMS4 over two different fields, that is, GF(2) and GF$(2^8),$ respectively. With regards to this, we first describe the SMS4 as systems of quadratic equations over the two different fields, and then estimate the computational complexities of XL algorithm for solving the two equations systems. Further, we compare resistances of SMS4 with that of AES against algebraic attacks, and as a result the SMS4 cipher seems robuster than AES.