Constructions Of Boolean Functions With Good Cryptographic Properties And Their Applications In CDMA Systems

Boolean functions in cryptography are the key components of stream cipher algorithms and block ciphers algorithms,and their cryptographic properties are crucial to the security of the cryptographic systems.In the design of the security cryptographic systems,to resist various attacks,Boolean functions must satisfy a variety of cryptographic criteria,such as balanceness,high nonlinearity,correlation immunity and high algebraic immunity.In addition,due to their good properties,some Boolean functions are also employed in the design of CDMA spreading codes.Therefore,it is an important research topic to construct Boolean functions with various cryptography criteria.In the dissertation,both the Boolean functions with various cryptographic criteria and the high nonlinear resilient vectorial Boolean functions are constructed,and the assignment of CDMA spreading codes in the irregular graph are obtained by using the simulated annealing algorithms,the finite fields and the graph theory.The concrete results are as follows:(1)Generally speaking,various cryptographic criteria,such as the nonlinearity and the resiliency,need to be considered in the constructions of cryptographic Boolean functions.However,the Boolean functions that satisfy these criteria simultaneously are rare.The constructions based on the mathematical theory are difficult to trade off all these criteria.In order to solve this problem,the modified simulated annealing algorithms are employed to obtain the Boolean functions that satisfy the high nonlinearity,1-resiliency,optimal algebraic degree,optimal algebraic immunity and high resistance to fast algebraic attack.In short,these obtained functions achieve a good trade-off among various cryptographic criteria.(2)Usually,the high nonlinearity and the resiliency could not be achieved at the same time.Therefore,the constructions of vectorial Boolean functions that satisfy the high nonlinearity and the resiliency are a difficult problem.Based on the structure of the MaioranaMc Farland functions,two constructions of vectorial Boolean functions are proposed by employing the properties of disjoint linear codes and perfect nonlinear functions.It is shown that the constructed functions possess the resiliency and the high nonlinearity at the same time.(3)Semi-bent functions and Hadamard matrices could be used to construct the spreading codes in the CDMA systems.However,the CDMA systems could not employ the spreading codes to complete the normal communication without the proper assignment.In order to obtain the assignment of the CDMA spreading codes in the irregular graph,first,the assignment problem is transformed into the mapping problem in the irregular graph by using the graph theory;second,the hill-climbing,the tabu search and the simulated annealing algorithms are employed to solve the mapping problem and the appropriate assignment is obtained.Moreover,the running time of the three algorithms are also compared and the results show that the simulated annealing algorithms has a higher execution efficiency.