The main aim of digital image scrambling

which is used as the pre-processing or post-processing in image information hiding

is to transform a meaningful image into a meaningless or disordered image in order to enhance the power to resist invalid attack and in turn enhance the security. This paper introduces the academic foundation of S-box that is usually applied to group cryptosystem with image information security as its background

and then presents a method of digital image scrambling based on S-box and discusses the periodicity of the arithmetic. The algorithm is proved to be efficient with experiments.