Construction of Perfect Nonlinear and Maximally Nonlinear Multi-Output Boolean Functions Satisfying Higher Order Strict Avalanche Criteria

We consider the problem of constructing perfect nonlinear multi-output Boolean functions satisfying higher order strict avalanche criteria (SAC). Our rst construction is an in nite family of 2-ouput perfect nonlinear functions satisfying higher order SAC. This construction is achieved using the theory of bilinear forms and symplectic matrices. Next we build on a known connection between 1-factorization of a complete graph and SAC to construct more examples of 2 and 3-output perfect nonlinear functions