| Summary: | This paper discusses the auto-correlation functions of <i>m</i>-bit random numbers obtained from <i>m</i> chaotic binary sequences generated by one-dimensional nonlinear maps. First, we provide the theoretical auto-correlation function of an <i>m</i>-bit sequence obtained by <i>m</i> binary sequences that are assumed to be uncorrelated to each other. The auto-correlation function is expressed by a simple form using the auto-correlation functions of the binary sequences. This implies that the auto-correlation properties of the <i>m</i>-bit sequences can be easily controlled by the auto-correlation functions of the original binary sequences. In numerical experiments using a computer, we generated <i>m</i>-bit random sequences using some chaotic binary sequences with prescribed auto-correlations generated by one-dimensional chaotic maps. The numerical experiments show that the numerical auto-correlation values are almost equal to the corresponding theoretical ones, and we can generate <i>m</i>-bit sequences with a variety of auto-correlation properties. Furthermore, we also show that the distributions of the generated <i>m</i>-bit sequences are uniform if all of the original binary sequences are balanced (i.e., the probability of 1 (or 0) is equal to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></semantics></math></inline-formula>) and independent of one another.
|
|---|