Discrete asymptotic deterministic randomness for the generation of pseudorandom bits

The deterministic randomness not only can become a dominant approach in exploring the relationship between chaos and randomness, but also can be associated with some famous number theoretical concepts and open problems in number theory. Compared with chaotic sequences, asymptotic deterministic randomness sequences have the characteristic of multi-value correspondence, which makes those sequences unpredictable in short steps. In this Letter, we will propose the definition of the discrete asymptotic deterministic randomness, and then analyze the dynamical characteristics such as maximum-period and multi-value correspondence. Referring to the NIST800-22 statistical test suite, we will present and discuss two examples of PRBGs based on DADR, from the point of view of FPGA design and randomness quality.