Digital noise produced by a non discretized tent chaotic map

摘要

This paper shows a digital electronic system that produces uniformly distributed binary sequences using the inverted tent chaotic map (ITCM) without the scaling and discretization processes. The proposed system has been developed considering a numerical representation of floating point with a 64-bit precision format according to the standard IEEE-754. The proposed system has four important advantages: (ⅰ) the produced binary sequences are uniformly distributed and they satisfy 10 randomness tests defined in the NIST 800-22SP guide, (ⅱ) the statistical behavior of the ITCM is not affected by the scaling and discretization processes; therefore, the chaotic map used is not modified, (ⅲ) the statistical behavior of the ITCM does not have stability islands inside the chaotic region, although its control parameter is changed, as it occurs with the logistic chaotic map and (ⅳ) the statistical behavior of the binary sequences is conducted by the control parameter and the skeleton of the bifurcation diagram of the ITCM, which can be considered as the security keys of the system.