Unpredictability and robustness of chaotic dynamics for physical random number generation

Area of Science:

• Physics
• Information Security
• Applied Mathematics

Background:

• Physical random number generators (RNGs) are crucial for information security.
• Optical chaos, particularly in delay-feedback lasers, is a promising avenue for RNGs.
• Existing physical RNGs lack a robust theoretical foundation.

Purpose of the Study:

• To introduce a novel mathematical formulation for physical RNGs based on chaotic dynamics.
• To provide the first rigorous theoretical results for chaotic physical RNGs.
• To demonstrate the coexistence of fast generation and robustness in chaotic RNGs.

Main Methods:

• Development of a mathematical model for chaotic dynamics in physical RNGs.
• Application of ergodic theory, information theory, and statistical physics response theory.
• Rigorous analysis of the model to guarantee key RNG properties.

Main Results:

• A theoretical guarantee for the coexistence of fast random number generation and robustness.
• Demonstration of an inherent advantage of chaotic dynamics for physical RNGs.
• Establishment of a foundational theory for chaotic physical RNGs.

Conclusions:

• The proposed mathematical framework provides a rigorous foundation for chaotic physical RNGs.
• Chaotic dynamics offer a unique advantage for developing secure and efficient RNGs.
• This work paves the way for more advanced and reliable information security technologies.