  The need for fast and strong image cryptosystems motivates researchers to
develop new techniques to apply traditional cryptographic primitives in order
to exploit the intrinsic features of digital images. One of the most popular
and mature technique is the use of complex ynamic phenomena, including chaotic
orbits and quantum walks, to generate the required key stream. In this paper,
under the assumption of plaintext attacks we investigate the security of a
classic diffusion mechanism (and of its variants) used as the core
cryptographic rimitive in some image cryptosystems based on the aforementioned
complex dynamic phenomena. We have theoretically found that regardless of the
key schedule process, the data complexity for recovering each element of the
equivalent secret key from these diffusion mechanisms is only O(1). The
proposed analysis is validated by means of numerical examples. Some additional
cryptographic applications of our work are also discussed.
