Spectral characterization of cryptographic Boolean functions satisfying the (extended) propagation criterion of degree l and order k

The (extended) propagation criterion was defined in cryptography in order to analyze the security of cryptographic components with respect to differential cryptanalysis. In this paper, we obtain the spectral characterization of functions satisfying the (extended) propagation criterion of degree l and order k. This important problem was left open since the introduction of these functions more than ten years ago.