From Chaos to Pseudorandomness: A Case Study on the 2-D Coupled Map Lattice

Area of Science:

• Chaos theory applications in digital communications.
• Pseudorandom number generation (PRNG).

Background:

• Secure digital communications rely on carefully chosen chaotic systems.
• Existing methods for chaotic PRNG often lack theoretical guarantees.
• Pseudorandom numbers are essential primitives for secure communication.

Purpose of the Study:

• To develop a theoretical approach for pseudorandom number generation using the 2D coupled map lattice (2D CML).
• To ensure the generated numbers meet stringent randomness criteria for secure applications.

Main Methods:

• Derivation of an analytical expression for the Lyapunov exponent (LE) spectrum of the 2D CML.
• Configuration of 2D CML parameters to achieve complex dynamic behavior.
• Development of an extraction algorithm (E) to "squeeze" uniform bits from system orbits.

Main Results:

• The derived LE spectrum allows for parameter configuration to ensure chaotic dynamics.
• The extraction algorithm E bounds the deviation of squeezed bits to 2^-z with z-bit precision.
• Generated pseudorandom bits pass NIST 800-22 and TestU01 test suites, demonstrating high quality and efficiency.

Conclusions:

• This research provides a theoretical foundation for applying 2D CML to secure communications.
• The proposed method offers an efficient way to generate high-quality pseudorandom numbers.
• The findings contribute to the advancement of chaos-based cryptography.