Theorem to generate independently and uniformly distributed chaotic key stream via topologically conjugated maps of tent map (Q1955003)

Summary: We propose a theorem to generate chaotic key stream from topologically conjugated maps of a tent map. In this theorem, the condition for topological conjugation between a tent map and a class of chaotic maps is first determined. Then, the chaotic attractor of the maps is divided into \(2^n\) unequal subintervals, the chaotic orbit is sampled once in \(n\) time iteration, and, finally, the independently and uniformly distributed \(2^n\) phase key stream is obtained. The theoretical and numerical analyses show that the chaotic key stream generated by the proposed theorem successfully is independent and uniform, has a certain complex degree close to the maximum approximate entropy for \(2^{n}\) phase key stream, and satisfies the randomness requirement defined in NIST SP800-22. This theorem can be used in fields such as cryptography and numerical simulation.