Methods of Attacking Chaotic Encryption and Countermeasures Mohamed I. Sobhy and Alaa-eldin R. Shehata The Electronic Engineering Laboratory The University of Kent at Canterbury Canterbury Kent CT2 7NT, UK Phone +441227 823236 Fax +44 1227 456084 email: M.I.Sobhy@ukc.ac.uk Abstract: Methods of attacking chaotic encryption algorithms have been developed. These methods have been applied to all the published chaotic encryption systems and all these systems are broken in very short computer times. Counter measures have also been developed in order to make chaotic encryption secure. Several examples and results are given. 1. INTRODUCTION Many papers have been published describing chaotic encryption algorithms and analogue encryption systems [1-4]. None of the papers adequately discusses the problem of security or estimate the computational effort required to break the system. Almost all papers assume that the system security is derived from the fact that a cryptanalist does not know the encryption system and hence it is very difficult to attack it with knowledge of the ciphertext alone. Systems that derive their security in this way are not worth very much as sooner or later the system will be known. Worse still, is that the user will not be aware that the system has been known and all the messages sent will be easily attacked. In any encryption system one must assume that the cipher is well known but the message cannot be retrieved without the key used. This fact is well known to cryptographers but apparently not to researchers in chaotic systems. Most papers in chaotic encryption do not even identify the key. This lead to researchers in methods of attack to concentrate on processing the ciphertext alone without knowledge of the cipher itself [5-7]. In this paper we shall show that the first step in attack must be the determination of the system used. This can be done from processing the ciphertext. The second step is to build the system and minimise the output to obtain the key. These two processes are relatively easy to achieve especially that a ‘thumb print’ can be produced from the ciphertext to identify the chaotic system that produced it. The developed method has been applied to all published systems known to us and all of them have been broken with very little computational effort. The next question to be asked is ‘Does this mean that no chaotic encryption method is secure?’ To answer this question we introduced non-linear functions to change the system keys dynamically. In this case the method of attack requires knowledge of the non-linear functions used and all their parameters. So far we are unable successfully to attack such systems. 2. SYTEM IDENTIFICATION The first step of attack is to identify the chaotic system from the ciphertext. Chaotic time series possess a high level of information that point to the type of generating system. That information could be obtained by two ways: • Plotting the signal iterates. This is a plot of the signal versus a delayed version of itself. Several delay values could be used. For a discrete time series the delay is an integer larger than unity. This step produces a plot similar to a strange attractor and every chaotic system produces a different strange attractor. • The auto-correlation function of the time series is plotted. Again every chaotic system produces a different auto- correlation plot. From the above two relatively simple processes a ‘thumb print’ of the system is produced which when compared to already compiled library of plots, will identify the chaotic system used. Fig 1 Examples of iterates of chaotic signals produced by the Chua, Rössler, Lorenze and Van der Pol systems