On the Cryptographicmeasures and Chaotic Dynamical Complexity Measures

Pseudorandom binary sequences are widely applied to the various engineering domains such as biology system control, spread spectrum communications and cryptography [1-3]. Particularly, the security of cryptographic systems is strongly contingent on the pseudorandomness of the key stream [3]. Depending on the cryptography application, a sequence is required to present many properties so as to be considered as pseudorandom. The linear complexity and nonlinear complexity of a sequence s are both important cryptographic measures. The linear complexity is defined as the length of the shortest linear feedback shift register (LFSR) that generates s, which has already been widely studied for several decades [4-9]. The nonlinear complexity is defined as the length of the shortest feedback shift register (FSR) that generates s. On the contrary, it has not been studied to the same extent [10-15].