Pseudorandom number generator based on the Bernoulli map on cubic algebraic integers

Area of Science:

• Number Theory
• Chaos Theory
• Cryptography

Background:

• Pseudorandom bit generators are crucial for simulations and secure communication.
• Existing generators like Mersenne Twister have limitations.
• Chaotic systems offer a potential source for high-quality randomness.

Purpose of the Study:

• To develop a novel pseudorandom bit generator based on chaotic dynamics.
• To address limitations of current pseudorandom number generators.
• To ensure unbiased seed selection and prevent sequence overlaps.

Main Methods:

• Utilizing chaotic true orbits of the Bernoulli map on real cubic algebraic integers.
• Developing a specific seed selection method for unbiased initial points.
• Analyzing the memory usage and growth of points on true orbits.

Main Results:

• The generator precisely simulates the Bernoulli map, producing ideal random binary sequences.
• A method for unbiased seed selection and overlap avoidance was established.
• Upper bounds for memory usage related to orbit point representation were determined.
• Extensive tests showed good statistical properties, outperforming Mersenne Twister MT19937.

Conclusions:

• The developed generator offers a high-quality alternative for pseudorandom binary sequence generation.
• The method provides a robust approach to seed selection, enhancing sequence reliability.
• This chaotic system-based generator demonstrates a promising advantage over established methods.