Pseudo-random number generator based on asymptotic deterministic randomness

Abstract

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

Statistical independence in nonlinear maps coupled to non-invertible transformations

“…(1) presents fundamental differences with the previously known chaotic systems. This phenomenon is called "deterministic randomness" [18,[24][25][26][27][28]. A very interesting development in the study of "deterministic randomness" has been the construction of the so-called Lissajous maps [24][25][26][27][28].…”

“…Given some conditions for z and b, the Lissajous maps have been shown to produce exactly the return maps that are generated by the random processes defined by Eq. (1) [24][25][26][27][28]. Consider the following particular example:…”

“…, N, the mth return map represents a perfect Lissajous figure. The sequence generated by this system is unpredictable in N steps [28]. When b → ∞, this system is equivalent to the process y n = cos[2π z n ] [28].…”

“…Recently the theory of functions and dynamical systems that can produce unpredictable time-series has been a very active area of research [15][16][17][18][19][20][21][22][23][24][25][26][27][28]. Some of these works are based on ideas as the following.…”

“…(1) are the solutions to several classes of chaotic maps [15][16][17][18][19][20][21][29][30][31][32][33][34][35]. Several dynamical systems have been proposed to generate similar dynamics [17][18][19][20][21][22][23][24][25][26][27][28]. In the present Letter we will investigate the higher-order correlations of nonlinear maps coupled to noninvertible transformations.…”