Dynamic Parameter-Control Chaotic System.

Area of Science:

• Chaos Theory
• Complex Systems
• Cryptography

Background:

• 1-D chaotic maps are fundamental in various scientific fields.
• Existing chaotic maps have limitations in diversity and parameter control.
• A need exists for generating a wider array of chaotic behaviors.

Purpose of the Study:

• To propose a general framework, the dynamic parameter-control chaotic system (DPCCS), for generating novel 1-D chaotic maps.
• To demonstrate the versatility of DPCCS by using existing chaotic maps as building blocks.
• To evaluate the performance and characteristics of the generated chaotic maps.

Main Methods:

• The DPCCS framework dynamically controls the parameter of a seed chaotic map using the output of a control chaotic map.
• Existing 1-D chaotic maps are utilized as both control and seed maps.
• Hardware implementation using Field-Programmable Gate Arrays (FPGAs) and a pseudo-random number generator (PRNG) were developed.

Main Results:

• DPCCS successfully generates a large number of new chaotic maps with unique properties.
• Generated chaotic maps exhibit increased sensitivity to initial states compared to their seed maps.
• The proposed PRNG based on DPCCS demonstrates excellent randomness properties.

Conclusions:

• DPCCS provides a simple yet effective method for creating diverse and complex chaotic maps.
• The framework facilitates straightforward hardware implementation, as shown by the FPGA design.
• The generated chaotic maps hold significant potential for advanced applications, particularly in PRNGs.