Generalized Maiorana–McFarland Construction of Resilient Boolean Functions With High Nonlinearity and Good Algebraic Properties

A new framework concerning the construction of small-order resilient Boolean functions whose nonlinearity is strictly greater than 2
^n-1
- 2
^[n/2]
is given. First, a generalized Maiorana-McFarland construction technique is described, which extends the current approaches by combining the usage of affine and nonlinear functions in a controllable manner. It is shown that for any given m, this technique can be used to construct a large class of n-variable (n both even and odd) m-resilient degree-optimized Boolean functions with currently best known nonlinearity. This class may also provide functions with excellent algebraic properties, measured through the resistance to (fast) algebraic attacks, if the number of n/2-variable affine subfunctions used in the construction is relatively low. Due to a potentially low hardware implementation cost, along with overall good cryptographic properties, this class of functions is an attractive candidate for the use in certain stream cipher schemes.