General Design Rules for Chaos-Based Encryption Systems
K. Kelber, Wolfgang Schwarz · 2005
During the past decade a large number of chaos-based encryption systems has been suggested and investigated. Several of these systems are not suitable for cryptographic applications as they are cryptographically weak. In this paper some general design rules for chaosbased encryption systems are derived based on strenghts and weaknesses of already suggested systems. To demonstrate the importance of each design rule an example system which does not obey this rule is given and its weakness is shown. 1. Motivation and objective of the work During the past decade a large number of chaos-based encryption systems has been suggested and investigated (e.g. [1, 2, 3]). The idea behind is to use complex dynamics but simple mathematical descriptions and algorithms of chaotic systems for the purpuse of encryption. So the design of these systems has generally be done on symbol level and not as in classical cryptography on bit level. This approach has some general limitations concerning the cryptographic strength of the designed systems as pointed out in [4]. On the other hand for applications like encryption of image and audio data cryptographical requirements are often not so strong as for other applications. But the amount of data to process is very large and thus for classical cryptosystems the computational effort might be very high. Therefore the scope of this paper is to derive some general design rules for chaos-based encryption systems according to strengths and weaknesses of already suggested systems. These design rules shall help to reduce or even to avoid cryptographical weaknesses of chaos-based encryption systems. Signals of (analogue) chaotic circuits are often not exactly reproducible due to inevitable small changes in initial conditions or system parameters. As for most applications an exact recovery of the original data is required here considerations are focused on discrete-time encryption systems. To show the importance of each design rule the following example systems are used: System E1: Image Encryption Scheme Based on 3D Chaotic Baker Map [3, 5] key generation 2D to 3D 3D to 2D 3D Baker map diffusion 128 bit user key input image WxH output image WxH k ,k 5 6 k ,k 3 4 k ,k 1 2 No. of rounds