A versatile mathematical function for generating stable and chaotic systems: A data encryption application

Being the generation of chaos through a practical function still a current challenge, here we present a new function called Tukmuky Jinma'any-Function (TJF), highly programable, that generates chaos for practical appli-cations. TJF provides complex behaviour with easy implementation, generating either periodic, quasi-periodic, weak, or strong chaotic trajectories. As an example of its applicability, we use this function as the entropy source of a symmetric encryption algorithm, using an image bitstream as test data with outstanding results, overcoming the drawbacks of previous chaos-based cryptosystems; e.g. the encryption uses strong keys and does not present gaps in its key space.