The XSL attack relies on first analyzing the "internal design" of a cipher then deriving a system of quadratic simultaneous equations. These systems of equations are typically very large, for example 8000 equations with 1600 variables for the 128-bit AES. Several methods for solving such systems are known. In the XSL attack, a specialized algorithm, termed XSL (eXtended Sparse Linearization), is then applied to solve these equations and compute the key.