High-dimensional Arnold inverse transformation for multiple images scrambling

Abstract

The traditional scrambling technology based on the low-dimensional Arnold transformation (AT) is not able to assure the security of images during the transmission process, since the key space of the low-dimensional AT is small and the scrambling period is short. Actually, the Arnold inverse transformation (AIT) is also a good image scrambling technique. The high-dimension AIT used in the image scrambling, can solve the shortcomings of low-dimensional geometric transformation, have good image scrambling effect, and achieve the purpose of image encryption, which enriches the theory and application of image scrambling. Taking account that an image has location space and colour space, the high-dimensional AIT for image scrambling improves the anti-attack ability of image scrambling since the combination of the location space coordinates and the colour space component is very flexible. We investigated the property and application of AIT with five- or six-dimension in the digital images scrambling. Specifically, we proposed the theory of n-dimensional AIT. Our investigations show that the technology in larger key space has good effects on scrambling and has a certain application value.