We develop several tools to derive linear independent multivariate equations from algebraic S-boxes. By applying them to maximally
nonlinear power functions with the inverse exponents, Gold exponents, or Kasami exponents, we estimate their resistance against
algebraic attacks. As a result, we show that S-boxes with Gold exponents have very weak resistance and S-boxes with Kasami
exponents have slightly better resistance against algebraic attacks than those with the inverse exponents.
Keywords Algebraic Attack - S-boxes - Boolean Functions - Nonlinearity - Differential Uniformity