Stream Cipher Algorithm Based On Chaotic Dynamical Systems

In this paper, a new stream cipher algorithm based on Lorenz chaotic system is designed. Since the security of stream cipher depends on the randomness of key sequence and the intensity of the initial key, first we analyze sensitiveness of Lorenz chaotic system to initial conditions and parameters, and non-periodicity and pseudo-randomness of the chaotic sequence generated by Lorenz chaotic system. The optimum domain of initial values and parameters is obtained. Then based on it, the algorithm is designed. Since Lorenz chaotic system is a three-dimension dynamic system, we use the operation of one-time three bytes while doing iteration, which increase not only the processing speed, but also the period and randomness of the key sequence. And we improve the algorithm with Logistic chaotic system, which increase further the security of the algorithm. Among the algorithmic design, the corresponding solution to the problems of transforming from the real sequence to binary sequence and precision in the chaotic stream cipher is put forward, and more efficient algorithm and better randomness of key sequence are obtained. By using the text file and BMP file, the experiment shows our algorithm comes up to the expectation. At the precision of 64 bits, even if a variable in the initial key has a minute difference about 10-15, any information about the original plaintext can't be obtained. The security of the algorithm is analyzed from the randomness, linear complexity of the chaotic sequence and the intensity of initial key. The results show the randomness of the key sequence pass the frequency test, sequential test, poker test, autocorrelation test, runs test, etc. And the total level is better than the binary sequence generated by the PRNG of Delphi 7.0, Logistic chaotic system and RC4, the linear complexity comes up to the expectation, the initial key has very strong intensity. Under the condition of the precision of p bits and regardless of the absolute value less than , the space of initial key is about , the entropy of system is about (5p+20)/6, which comes up to the demand of the security at the sense of modern cryptology. Moreover, this algorithm can be implemented very easily in software, and has a good prospect in the fields of secret communication and information security.