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A Pseudorandom Number Generator Based on the Chaotic Map and Quantum Random Walks.
Wenbo Zhao1, Zhenhai Chang2, Caochuan Ma2
1School of Electronic Information and Electrical Engineering, Tianshui Normal University, Tianshui 741000, China.
Entropy (Basel, Switzerland)
|January 21, 2023
Summary
This study introduces a novel compound chaotic system and a pseudorandom number generator (PRNG). The system exhibits enhanced randomness and uniform output distribution, passing rigorous NIST tests for information security applications.
Area of Science:
- Dynamical Systems and Chaos Theory
- Information Security and Cryptography
Background:
- Existing chaotic systems often require enhancements for robust key space and output distribution.
- The need for high-quality pseudorandom number generators (PRNGs) is critical in modern information security.
Purpose of the Study:
- To construct a novel compound chaotic system with enhanced randomness and key space.
- To develop and evaluate a new pseudorandom number generator (PRNG) based on the proposed chaotic system.
- To assess the suitability of the PRNG for information security applications.
Main Methods:
- Construction of a surjective mapping satisfying Li-Yorke chaos.
- Application of a perturbation algorithm using high-dimensional chaos to enhance randomness.
- Design of a composition algorithm combining quantum random walks with chaotic system outputs.
- Evaluation of the compound chaotic system using time series complexity, autocorrelation, and output frequency distribution.
- Testing the PRNG using NIST SP 800-22 test suites.
Main Results:
- The compound chaotic system demonstrated complex dynamic behavior, high randomicity, unpredictability, and uniform output distribution.
- The proposed PRNG successfully passed all NIST SP 800-22 tests.
- The system's key space was effectively expanded through parameter and input perturbation.
Conclusions:
- The developed compound chaotic system offers superior randomness and output characteristics compared to conventional systems.
- The proposed PRNG is a viable and effective tool for applications in the information security field.
- The integration of chaos theory and quantum principles provides a promising avenue for advanced cryptographic solutions.
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