New classes of quadratic bent functions in polynomial forms

We propose new classes of quadratic bent functions in polynomial forms, coefficients of which are from extension fields of F₂. Bentness of these functions is based on certain linearized permutation polynomials over finite fields of even characteristic, whose permutation properties are confirmed by virtue of arithmetics in skew-polynomial rings. This is the first time skew-polynomials over finite fields are used in studying quadratic bent functions.