Refracted Light Interaction in Turbulent Bubbling Water (RLITBW): A Macroscopic Fluid-Optic Entropy Source

Nirjhar Debnath; Dwaipayan Datta; Kousik Dasgupta

cs.ETApr 14, 2026

Refracted Light Interaction in Turbulent Bubbling Water (RLITBW): A Macroscopic Fluid-Optic Entropy Source

Authors: Nirjhar Debnath, Dwaipayan Datta, Kousik Dasgupta

Organizations: Department of Computer Science and Engineering, Kalyani Government Engineering College, Kalyani, 741253, India

Abstract

The demand for high quality, unpredictable random numbers is a fundamental requirement in cryptography, stochastic simulation, and optimization. While pseudo-random number generators (PRNGs) are computationally efficient, their deterministic nature limits their suitability for security-critical applications. True random number generators (TRNGs), although physically grounded, often rely on expensive quantum or tightly controlled electronic phenomena. This paper introduces a low-cost, macroscopic TRNG based on Refracted Light Interaction in Turbulent Bubbling Water (RLITBW). The proposed system exploits compound classical chaos arising from multiphase fluid dynamics and time-varying optical refraction. A physical-mathematical model is developed to describe the cascade of non-linear processes from stochastic bubble nucleation and turbulent ascent to chaotic optical path scrambling that collectively amplify microscopic uncertainties into measurable entropy.The raw optical signal is digitized and processed using a provably secure entropy-conditioning pipeline based on Toeplitz universal hashing, followed by deterministic cryptographic expansion. The chaotic nature of the physical source is empirically validated using phase-space reconstruction, Lyapunov exponent estimation, autocorrelation analysis, and entropy metrics. The conditioned output successfully passes the full NIST SP 800-22 statistical test suite and nonlinear dynamical measures including Lyapunov exponents and sample entropy. Beyond statistical validation, the generated randomness is applied to population-based optimization algorithms, demonstrating practical usability as a replacement for conventional PRNGs. Finally, deployment architectures and scalability considerations are discussed, positioning RLITBW as an accessible, reproducible, and economically viable entropy source for real-world systems.

Figures & tables

Symbol	Description	Symbol	Description
$\rho_{w}$	Density of water	$n_{w}$	Refractive index of water
$\rho_{a}$	Density of air	$n_{a}$	Refractive index of air
$\rho$	Fluid density in Navier–Stokes equations	$\theta_{w}$	Refraction angle in water
$g$	Acceleration due to gravity	$\theta_{a}$	Refraction angle in air
$\sigma$	Surface tension coefficient	$\Psi(\mathbf{u},t)$	Optical intensity at sensor plane
$d$	Diameter of air orifice	$\Psi_{0}(\mathbf{u}_{0})$	Incident irradiance

Table 1: Variables, symbols, and mathematical notation used in the RLITBW physical–mathematical model.

Figure 2: Schematic representation of the experimental setup (illumination, bubbling column, and single-element light sensor).

Figure 3: Schematic representation of how a bubble (at an instantaneous time) can alter the directions of incoming light rays from the bottom of the apparatus. Here the bubble is shown as a sphere but in real its surface always moves and thus do not keep a fixed geometry.

Figure 4: Time-series of raw light intensity measurements captured from the RLITBW system. The signal exhibits irregular, aperiodic fluctuations arising from the combined effects of turbulent bubble dynamics and optical path scrambling, forming the basis for subsequent entropy extraction and statistical validation.

Figure 5: Phase-space reconstruction of the RLITBW sensor signal using time-delay embedding. The plot shows the sensor intensity $x(t)$ versus its delayed version $x(t+\tau)$ , where $\tau$ is the embedding delay. The resulting non-periodic, structured geometry indicates deterministic chaotic dynamics with sensitive dependence on initial conditions, supporting the suitability of the underlying physical process as an entropy source.

Figure 6: Autocorrelation of the raw sensor signal, showing a rapid drop to zero, indicating high unpredictability.

Statistical Test	P-VALUE	PROPORTION	Result
Frequency	0.739918	10/10	PASS
BlockFrequency	0.350485	10/10	PASS
CumulativeSums (Forward)	0.534146	10/10	PASS
CumulativeSums (Backward)	0.350485	10/10	PASS
Runs	0.122325	10/10	PASS
LongestRun	0.739918	10/10	PASS

Table 2: NIST SP 800-22 Test Results for 10x 1M Bit Sequences

Figure 7: Histogram showing the frequency distribution of P-values from the NIST tests. The relatively flat and uniform spread is consistent with the behavior of a true random source.

Panel of Figure 8 — Figure 8: Statistical validation of randomness using P-value distribution analysis.

Figure 9: Scatter plot visualization of test results. Top: P-values for all executed tests indexed sequentially; all points lie above the $\alpha=0.01$ failure threshold. Bottom: Detailed scatter plot for the 148 Non-Overlapping Template sub-tests, demonstrating a random spread of P-values.

Function	Algorithm	Description	PRNG		TRNG
			Mean	Std	Mean	Std
Ackley	CMA-ES	Covariance Matrix Adaptation Evolution Strategy	3.99e–15	0.00e+00	4.11e–15	6.37e–16
	L-SHADE	Success-History Adaptive Differential Evolution	8.27e–03	4.02e–03	7.41e–03	3.99e–03
	SPSO	Standard Particle Swarm Optimization	1.398	1.033	1.570	0.936
Rastrigin	CMA-ES	Covariance Matrix Adaptation Evolution Strategy	6.268	4.322	6.467	4.919
	L-SHADE	Success-History Adaptive Differential Evolution	3.389	1.461	7.766	2.589

Table 3: Combined optimization results for all benchmark functions and algorithms. Each entry reports the mean and standard deviation of the final objective value over multiple independent runs (lower is better).

Figure 10: Overall deployment architecture of the proposed system. Multiple RLITBW fluid–optic sensors generate independent raw bitstreams, which are processed by a local backend consisting of a universal-hash extractor (Toeplitz) and a stream or block cipher (ChaCha20/AES). The intermediate high entropy seeds are separately stored in a server-side entropy buffer, and client systems obtain randomness through a lightweight authenticated API or service endpoint.

Architecture	Cost	Complexity	Entropy Source
QRNG	Very High	High	Quantum Optics
FPGA Ring Osc.	Medium	High	Timing Jitter
Chaotic Circuits	Low–Mid	Medium	Nonlinear Voltage
RLITBW	Very Low	Low	Fluid–Optic Chaos

Table 4: Comparison of RLITBW with Existing TRNG Technologies

Neuromorphic Pseudo-Random Number Generators with a Low Power Hardware Implementation
Sep 30, 2026Jafar Shamsi, Navid Akbari, Sonia Sennik +2Spiking Neural Networks Neuromorphic Computing
Hotchkiss Brain Institute, University of Calgary, Calgary, Canada · Biomedical Engineering, University of Calgary, Calgary, Canada · Electrical and Software Engineering, University of Calgary, Calgary, Canada +2
Reproducible AI Requires Reproducible Randomness
Sep 22, 2026Anthony Bertrand, Tom Schmitt, Engelbert Mephu Nguifo +1ML Reproducibility Scientific Reproducibility
UCA, LIMOS · UCA · LIMOS, UCA +1
Blind PRNG Hijacking: An Undetectable Integrity-Preserving Attack Against LLM Watermarking
May 27, 2026Ziyang You, Huilong He, Xiaoke Yang +1LLM Security LLM Watermarking
Fujian Provincial Key Laboratory of Automotive Electronics and Electric Drive, School of Electronic, Electrical and Physics, Fujian University of Technology, Fuzhou 350118, China · School of Humanities, Fujian University of Technology, Fuzhou 350118, China · Institute of Applied Physics and Materials Engineering, University of Macau, Macau 999078, China

Sep 30, 2026J/K move · Enter open · S save

Neuromorphic Pseudo-Random Number Generators with a Low Power Hardware Implementation

Jafar Shamsi, Navid Akbari, Sonia Sennik, Aaron Gruber+1

Hotchkiss Brain Institute, University of Calgary, Calgary, Canada · Biomedical Engineering, University of Calgary, Calgary, Canada · Electrical and Software Engineering, University of Calgary, Calgary, Canada+2

Spiking Neural Networks Neuromorphic Computing

Open paper AskPDF arXiv

Pseudo-random number generation often requires trade-offs among quality, power consumption, and bandwidth to produce unpredictable sequences of numbers. The brain, on the other hand, efficiently generates unpredictable output complex network dynamics occurring in a high-dimensional state. This state, which is hypothesized to be chaotic, relies on the balance between excitation and inhibition. Here, we investigated if computational models of these chaotic balanced states can be harnessed for Neuromorphic Pseudo-Random Number Generators (NPRNGs) in low power hardware. We successfully constructed a balanced spiking neural network model consisting of leaky-integrate-and-fire neurons that could be readily implemented in low power FPGAs and used as a NPRNG. The prototyped NPRNG consumed 3.24 mW during operation and produced pseudo-random numbers at 120kbps. In both hardware and software instantiations, NPRNGs produce high-quality random numbers as validated by standard metrics for testing RNG quality.

Abstract

Explore similar work

Neuromorphic Pseudo-Random Number Generators with a Low Power Hardware Implementation

Reproducible AI Requires Reproducible Randomness

Blind PRNG Hijacking: An Undetectable Integrity-Preserving Attack Against LLM Watermarking