Cryptographical Boolean Functions Construction from Linear Codes

This paper presents an extension of the Maiorana-McFarland method for building Boolean functions with good cryptographic properties. The original Maiorana-McFarland construction was proposed to design bent functions. Then, it was extended in [1] to build highly nonlinear resilient functions. The classical construction splits the set of variables into two separate subsets. There, is proposed a decomposition of the whole working space into two complementary vector spaces. One of these spaces is considered as a linear code and its parameters assigns cryptographic properties to the constructed Boolean function. The cryptographical properties we are interested in are nonlinearity, resiliency and propagation properties. The obtained functions are linearly equivalent to those constructed by the traditional way. Thus, no improvement for affine invariant parameters such as nonlinearity is expected. On the other hand, for non affine invariant cryptographic parameters such as resiliency order or propagation order, better values are obtained.