  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.
