Biblio

Random number generators (RNGs) has an extensive application area from cryptography to simulation software. Piecewise linear one-dimensional (PL1D) maps are commonly preferred structures used as the basis of RNGs due to their theoretically proven chaotic behavior and ease of implementation. In this work, a skew-tent map based RNG is designed by using the chaotic sampling method in TSMC 180 nm CMOS process. Simulation data of the designed RNG is validated by the statistical randomness tests of the FIPS-140-2 and NIST 800-22 suites. The proposed RNG has three key features: the generated bitstreams can fulfill the randomness tests without using any post processing methods; the proposed RNG has immunity against external interference thanks to the chaotic sampling method; and higher bitrates (4.8 Mbit/s) can be achieved with relatively low power consumption (9.8 mW). Thus, robust RNG systems can be built for high-speed security applications with low power by using the proposed architecture.

Chaotic dynamics is widely used to design pseudo-random number generators and for other applications, such as secure communications and encryption. This paper aims to study the dynamics of the discrete-time chaotic maps in the digital (i.e., finite-precision) domain. Differing from the traditional approaches treating a digital chaotic map as a black box with different explanations according to the test results of the output, the dynamical properties of such chaotic maps are first explored with a fixed-point arithmetic, using the Logistic map and the Tent map as two representative examples, from a new perspective with the corresponding state-mapping networks (SMNs). In an SMN, every possible value in the digital domain is considered as a node and the mapping relationship between any pair of nodes is a directed edge. The scale-free properties of the Logistic map's SMN are proved. The analytic results are further extended to the scenario of floating-point arithmetic and for other chaotic maps. Understanding the network structure of a chaotic map's SMN in digital computers can facilitate counteracting the undesirable degeneration of chaotic dynamics in finite-precision domains, also helping to classify and improve the randomness of pseudo-random number sequences generated by iterating the chaotic maps.