Quadratic equations from APN power functions
We develop several tools to derive quadratic equations from algebraic S-boxes and to prove their linear independence. By applying them to all known almost perfect nonlinear (APN) power functions and the inverse function, we can estimate the resistance against algebraic attacks. As a result, we can show that APN functions have different resistance against algebraic attacks, and especially S-boxes with Gold or Kasami exponents have very weak resistance.
quadratic equations linear independence almost perfect nonlinear (apn) nonlinearity algebraic attack