Abstract: By introducing the conversion function on ellipse angle, we use the method of shift matrix to achieve the simplification of ellipse problem. A very simple iterative formula is deduced on the tangent-delay for elliptic reflection, which is very useful for theoretical analysis. There exits a chaotic attractor when tangent delays one unit in TD-ERCS. The origin of the attractor and its stability are analyzed in theory. We find that the attractors in the circular and the elliptic cases are not entirely the same; the ellipse has two immobile lines, but only one of them is steady. We also find that, with the decrease of ellipse compression factor μ, the correlation of nearby iterative data is strengthened when the tangent-delay factor m is arbitrary. It means that in using the system for cryptography, the ellipse compression factor μ can not be too small, and the chaos system requires that it should not be too big, otherwise the degree of safety will be reduced.

Keywords: 
• chaos /
• tangent-delay /
• TD-ERCS /
• attractor