Abstract:

 Perfect nonlinear functions are widely used in cryptography and algebra combinatorics. By using two known perfect nonlinear functions, a quadratic perfect nonlinear function over finite fields of odd characteristic was constructed based on determining the root of a linearized function.This quadratic function was proved to be inequivalent to x², and then an example was used to analyzed its inequivalence to x^ps+1.

Key words: perfect nonlinear function; almost perfect nonlinear function; CCZ-equivalence;EA-equivalence; linearized permutation