The Theory Of Cellular Automata And It's Application In Cryptography

The basic theory of cellular automata, the ways how algorithms are designed based on cellular automata and the security of the algorithms have been discussed in this thesis. At first, some basic knowledge in stream cipher and cellular automata has been introduced; second, properties of one kind of cellular automata such as its periodicity, its topologies and the connection between its states have been deeply researched; third, the algorithms base on cellular automata and their security have been discussed; finally, I have implemented one simple cellular automata and one simple linear feedback shift register, and have analyzed the advantage and the disadvantage of cellular automata.The main results of this thesis are as follows:1. One kind of cellular automata has been researched. Its algebraic properties such as characters of states, periodicity, and topology have been deeply discussed.2. To the simple additive cellular automata, a method to compute its maximal cycle lengths has been presented.3. Many methods to designed stream cipher based on cellular automata and their security have been studied. How to designed stream cipher based on PCA has been studied.4. According to the property that all states of a certain cellular automata can build a permutation group, we can design block cipher based on this property.5. One simple cellular automata and one simple linear feedback shift register have been implemented. The result has shown that: CA compared with LFSR, its advantages is that it need little time, it is faster, and it is easy to implement.