k-th order symmetric SAC boolean functions and bisecting binomial coefficients Original Research Article

The Strict Avalanche Criterion (SAC) and symmetry for Boolean functions are important properties in cryptographic applications. High order SAC was first studied by Forré. Based on bisecting binomial coefficients and S. Lloydʹs work, we describe a method to find kth order symmetric SAC functions (image). In this paper, we determine all the image n-variable functions for image, image. Also, for infinitely many n, we give some nontrivial binomial coefficient bisections. The existence of nontrivial bisections makes the problem to find all image functions very difficult.