An approach to generate the pseudorandom-bit sequence from the asymptotic deterministic randomness system is proposed in this Letter. We study the characteristic of multi-value correspondence of the asymptotic deterministic randomness constructed by the piecewise linear map and the noninvertible nonlinearity transform, and then give the discretized systems in the finite digitized state space. The statistic characteristics of the asymptotic deterministic randomness are investigated numerically, such as stationary probability density function and random-like behavior. Furthermore, we analyze the dynamics of the symbolic sequence. Both theoretical and experimental results show that the symbolic sequence of the asymptotic deterministic randomness possesses very good cryptographic properties, which improve the security of chaos based PRBGs and increase the resistance against entropy attacks and symbolic dynamics attacks. PACS number(s): 05.45.-a

In this paper, we consider a symbolic dynamic method, based on going athwart the coupled map lattices, to estimate unknown initial conditions of nonlinear dynamical system from the given symbolic vector sequence. It is proved that any value taken from the interval IN will converge to the initial conditions with the iteration of athwart-coupled map lattices function, and an initial condition detection method from symbolic vector sequence is presented. Both theoretical and experimental results show that the estimation method can establish one-to-one correspondence between the initial conditions of coupled map lattices and their symbolic vector sequence; therefore this technique appears to be ideally suited for information estimation.

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