| Cryptography is the kernel of the secure communication and information security. From the foundation of modern cryptography, all of the countries in the world have been looking for the self-dependent techniques of the cryptography to ensure the information security of the country and society, thus guarantee their benefits and gains. In the exploration of the self-dependent techniques of the cryptography, the Cellular Automata (CA) is viewed as the most potential of the kernel technique in the self-dependent techniques of the cryptography by its simple, regular and high parallel processing architecture which is suitable of VLSI implementation and its complicated dynamic properties. These make it more suitable for the applications in cryptography, and it becomes the most potential of the kernel technique in the independent research of the cryptography.In the research of the doctoral period, the author has taken part in the projects of the "New Algorithm of the Cipher" and "New Architecture of the Cryptography" to research the applications of the CA in Cryptography. The focuses of the research are the theory of CA, the various models and the architecture of the CA applied to Cryptography, and the main contributions include of the analysis of the state transition diagram of CA, the pseudo-random number/sequence generations based on CA, the symmetry ciphers based on CA, the HASH functions based on CA, and etc..Several valuable and important results which bring forth new ideas are achieved and listed as follows:7. In the study of additive CA, we obtain the isomorphism of the rules 90/150 additive CA and its corresponding linear 90/150 CA under the condition that the linear 90/150 CA has irreducible polynomial, which is the most important conclusion in the application of rules 90/150 additive CA.Based upon the conclusion of the isomorphism of the additive 90/150 CA and its corresponding linear 90/150 CA with irreducible polynomial, we bring forth several models of pseudo-random number/sequence generation which includes: pseudo-random number/sequence generation based on autonomy determinate CA, pseudo-random number/sequence generation8. based on autonomy programmable CA, pseudo-random number/sequence generation based on heteronomy determinate CA, pseudo-random number/sequence generation based on heteronomy programmable CA, and pseudo-random number/sequence generation based on the combination of and/or/xor of CA. 9. From the properties of invertible CA, the unaffected group property of CA by its input boundary, and the isomorphism of the additive 90/150 CA and its corresponding linear 90/150 CA with irreducible polynomial, we put forward the model of symmetry encipher based on the reversible CA.10. Based upon the entropy maximization of output sequences and the inverse iterations theory of the toggle rule of CA, we bring up a model of symmetry encipher.11. For rules 60/102/204 linear CA, the conditions of group property are derived. We also illustrated the conditions for which states transition diagram have equal cycle length from the viewpoint of matrix equation, and bring forward a symmetry cipher model based on it, which extended the former conclusions of S. Nandi.12. Based upon the characteristic polynomial of cellular automata, we analyzed a CA of rule 90 which can be used as the multi to one map iteration function of HASH function, the conditions of rule 90 CA to be the Two Predecessor Single Attractor (TPSA) CA are obtained. And we also demonstrated that the 90 linear CA and its corresponding additive CA are also isomorphic, which bring a large family of additive CA of rule 90 with Two Predecessor Single Attractor (TPSA).Contrasted to the other methods such as LFSR, the most potent of CA is the architecture which adapted to the VLSI implementation, and the System on Chip (SoC) is the idea implementation of the cipher algorithm, this makes the applications of CA in cryptography not only can simplify the design of cipher system, but also has the performance advantages. These make the...
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