Generation of true random numbers with actively stabilized, low dimensional chaos

Author

Aidan Barton

Date of Award

2025

Document Type

Thesis

Degree Name

Master of Science in Engineering (MSE)

Department

Electrical and Computer Engineering

Committee Chair

Aubrey Beal

Committee Member

Ned Corron

Committee Member

Jonathan Blakely

Research Advisor

Aubrey Beal

Subject(s)

Random number generators, Entropy (Information theory), Chaotic behavior in systems

Abstract

True Random Number Generators (TRNGs) are heavily used and their design often relies on empirical validation from statistical test suites. Reliance solely on empirical observations to estimate entropy rates for cryptographic applications introduces risk, as accurately inferring long-term correlations demands prohibitively large datasets. Empirical validation of TRNGs must be supplemented by strong theoretical backing to justify estimated information theoretic quantities. We present an electronic, hardware TRNG scheme that produces a maximally random output guaranteed from first principles. This TRNG uses a pulse-width based hardware realization of an iterated map that produces physical entropy via low-dimensional chaotic dynamics. The simple dynamics of this source dictate a straight-forward method of bit extraction and permits direct computation of expected entropy rates. By constrast, TRNGs in recent literature often utilize extremely high dimensional chaotic systems or complex feedback for which this type of design and analysis is impossible. This TRNG implementation closely matches its theoretical properties and passes the NIST test suite with 100 million bits.

Recommended Citation

Barton, Aidan, "Generation of true random numbers with actively stabilized, low dimensional chaos" (2025). Theses. 792.
https://louis.uah.edu/uah-theses/792