A novel shift-multiply framework for one-dimensional chaotic map

This paper introduces a shift-multiply framework to generate one-dimensional (1-D) chaotic maps using a combination of two 1-D chaotic maps (called seed maps). On the basis of conventional 1-D chaotic map, its iteration algorithm is improved which enhances the ability of anti-dawning. Simulations show that the proposed chaotic maps have more parameters and greater chaotic range than current seed maps. It also has good initial-value sensitivity, correlation, and balance performance. It is a good candidate in the DSSS (direct sequence spread spectrum) underwater communication system.