Design and analysis of chaos based symmetric encryption systems

The security of digital data becomes more and more important due to the rapid development of the modern computer, networking and information technologies. Notably, the traditional encryption schemes fail to protect the multimedia data efficiently because of the special properties of multimedia data. To overcome this difficulty, researchers tried to develop special encryption schemes for multimedia data adopting some related nonlinear theories. The similarity between chaos and cryptography promoted the wide investigation on how to use chaotic systems to design secure and fast encryption schemes. A great number of chaos based encryption schemes have been proposed since 1990s. However, some new schemes have been found to be insecure from the viewpoint of cryptography, and some general recommendations have been drawn to facilitate the design of more secure encryption schemes. This thesis is concerned with the design and security analysis of chaos based symmetric encryption schemes. The security of the schemes against some common attack methods, such as brute-force attack, known/chosen-plaintext attack and differential attack, is investigated in detail with theoretical analyses and experimental verifications. In addition, some special design defects of the schemes are revealed and discussed. In this thesis, analyses the effects of chaotic system behaviors over cryptography systems depending on computational precision, when definite chaotic systems are used as pseudo random processes during cryptologic protocol design. While cryptologic designs use a finite set of integers as the workspace, chaotic systems use a set of real numbers. As a result, simulations of chaotic systems on digital computers suffer from truncation and round-off errors. In consequence, random behavior expected from chaos is replaced with periodical behavior which does not meet the confusion and diffusion requirements of the cryptologic designs. With these results, suitability of digital chaos in new cryptologic designs should be re-evaluated by the chaotic cryptology literature. Our contributions in this dissertation involve the following three aspects about digital chaos based cryptographic systems ciphers: experimental analyses of randomness properties of digital chaotic systems, cryptanalyses of chaos based cryptographic systems, and new designs of chaos based substitution boxes. The main achievements contained in this dissertation are as follows: ?Three different chaos based substitution box algorithm have been proposed. The performance of the proposed substitution box design has been compared to other chaos based substitution box designs and new designs have been demonstrated to provide a stronger substitution box design. ?A general attack scenario has been proposed for chaos based cryptographic systems. ?Security analyses of eleven different encryption algorithms have been done using proposed attack scenario. ?Experimental results show that logistic map, which are used as a source of randomness in many encryption algorithms, successfully pass the standard statistical tests, but its cryptographic randomness properties are worse than any standard random function.