Analysis Of A Symmetric Encryption Algorithm Based On Dimension Cellular Automata And The Period Distribution Of CA

It is well known that the traditional encryption method has become more difficult tosubstantially increase safety and efficiency of encryption. Therefore, researchers try tointroduce some new methods and theories to develop new encryption algorithm. Withthe development of artificial intelligence and other related technologies, manyintelligent computer methods have been applied in the fields of encryption. To searchthe intelligent computing on the encryption has become a new research direction.Cellular Automata (CA) is an important artificial life sciences research tools andtheoretical branch. CA theory in the field of encryption application has become a newhotspot.The purpose of this thesis is analysis of a symmetric encryption algorithm based onthe dimension cellular automata and the period distribution of CA. This thesis focuseson two problems: one is the analysis of the period distribution based on differentdimension of the Cellular Automata, and the other is that a symmetric encryptionalgorithm is designed based on periodic CA. Futthermore, we study on the influence ofthe encryption security between different dimensions of CA, which is directly motivatedby the in-depth research of the first problem.For the first problem, we respectively analyze the period of one-dimensional andtwo-dimensional CA under the rule of170N. By using the method of matrix, CA’sGOE(Gardens of Eden) under the rule of170N is solved. Set CAm×nbe a2D CA by rule170N(see1D CA as CA1×n), B be a configuration of the CA. If there exists an invertiblematrix P and Q such that the PP (S)Q is a diagonal matrix (E0), where E is identitymatrix, and0is zero matrix, the B is a GOE of CAm×nonly if there exsits a andThen the number of GOE is derived, therefore we can compute the transient length τand the great lap length γ to obtain the period of CAm×nand period distribution.For the second problem, the use of CA in encryption algorithm is due to thepeculiarity that the number can be expressed by CA and also by binary system, and bothof those two systems have the discreteness on state and space. Through to the firstquestion discussion,we can get that CA1×8is perodical under the rule170N with theperiod of14. By converting the plaintext into a binary stream, we regard the stream as anumber of one-dimensional CAs to be encrypted. The secret key is the collection of all the CAs state transition. Meanwhile, CA3×8that under the rule170N is periodical withthe period of28. Based on these properties, we construct a new secure image encryptionalgorithm which coupled toggle encrypts every bit plane of the image with periodictwenty-eight2D CA. Let the set of each CA’s iteration numbers be the key, then thedecryption is the inverse process of encryption. Simulation results show that theproposed algorithm has the advantages of high sensitivity, simple hardwareimplementation, large key space, and high efficiency.