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Entropy Mixing Networks: Enhancing Pseudo-Random Number Generators with Lightweight Dynamic Entropy Injection

Mohamed Aly Bouke, Omar Imhemmed Alramli, Azizol Abdullah, Nur Izura Udzir, Normalia Samian, Mohamed Othman, Zurina Mohd Hanapi

TL;DR

The paper addresses the need for high-quality randomness in cryptographic contexts by introducing the Entropy Mixing Network (EMN), a hybrid RNG that periodically injects entropy into a PRNG and securely mixes it with hashing. It proposes a comprehensive evaluation framework combining traditional statistics, advanced metrics, and visual analyses to assess randomness quality, predictability, and efficiency. EMN outperforms Python SystemRandom and MersenneTwister on key metrics, achieving a Chi-squared p-value of $0.9430$, entropy of $7.9840$ bits, and a predictability of $-0.0286$, at the cost of higher generation time ($0.2602$ s) due to entropy injection. The results indicate EMN's strong suitability for security-critical applications where randomness quality outweighs speed, and the framework itself offers a robust method for evaluating hybrid RNGs.

Abstract

Random number generation plays a vital role in cryptographic systems and computational applications, where uniformity, unpredictability, and robustness are essential. This paper presents the Entropy Mixing Network (EMN), a novel hybrid random number generator designed to enhance randomness quality by combining deterministic pseudo-random generation with periodic entropy injection. To evaluate its effectiveness, we propose a comprehensive assessment framework that integrates statistical tests, advanced metrics, and visual analyses, providing a holistic view of randomness quality, predictability, and computational efficiency. The results demonstrate that EMN outperforms Python's SystemRandom and MersenneTwister in critical metrics, achieving the highest Chi-squared p-value (0.9430), entropy (7.9840), and lowest predictability (-0.0286). These improvements come with a trade-off in computational performance, as EMN incurs a higher generation time (0.2602 seconds). Despite this, its superior randomness quality makes it particularly suitable for cryptographic applications where security is prioritized over speed.

Entropy Mixing Networks: Enhancing Pseudo-Random Number Generators with Lightweight Dynamic Entropy Injection

TL;DR

The paper addresses the need for high-quality randomness in cryptographic contexts by introducing the Entropy Mixing Network (EMN), a hybrid RNG that periodically injects entropy into a PRNG and securely mixes it with hashing. It proposes a comprehensive evaluation framework combining traditional statistics, advanced metrics, and visual analyses to assess randomness quality, predictability, and efficiency. EMN outperforms Python SystemRandom and MersenneTwister on key metrics, achieving a Chi-squared p-value of , entropy of bits, and a predictability of , at the cost of higher generation time ( s) due to entropy injection. The results indicate EMN's strong suitability for security-critical applications where randomness quality outweighs speed, and the framework itself offers a robust method for evaluating hybrid RNGs.

Abstract

Random number generation plays a vital role in cryptographic systems and computational applications, where uniformity, unpredictability, and robustness are essential. This paper presents the Entropy Mixing Network (EMN), a novel hybrid random number generator designed to enhance randomness quality by combining deterministic pseudo-random generation with periodic entropy injection. To evaluate its effectiveness, we propose a comprehensive assessment framework that integrates statistical tests, advanced metrics, and visual analyses, providing a holistic view of randomness quality, predictability, and computational efficiency. The results demonstrate that EMN outperforms Python's SystemRandom and MersenneTwister in critical metrics, achieving the highest Chi-squared p-value (0.9430), entropy (7.9840), and lowest predictability (-0.0286). These improvements come with a trade-off in computational performance, as EMN incurs a higher generation time (0.2602 seconds). Despite this, its superior randomness quality makes it particularly suitable for cryptographic applications where security is prioritized over speed.
Paper Structure (19 sections, 3 equations, 3 figures, 1 table, 1 algorithm)

This paper contains 19 sections, 3 equations, 3 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background
  3. The Proposed Framework
  4. Design Principles
  5. Algorithm Description
  6. Algorithm Implementation
  7. Evaluation Framework
  8. Chi-Squared Test.
  9. Entropy.
  10. Predictability.
  11. High-Frequency Performance.
  12. Results & Discussion
  13. Chi-Squared Statistic and p-value
  14. Entropy
  15. Predictability
  16. ...and 4 more sections

Figures (3)

  • Figure 1: Visual Metrics for EMN: (a) Heatmap of Correlation, (b) Power Spectrum Density, (c) Probability Mass Function, (d) Autocorrelation Function.
  • Figure 2: Visual Metrics for SystemRandom: (a) Heatmap of Correlation, (b) Power Spectrum Density, (c) Probability Mass Function, (d) Autocorrelation Function.
  • Figure 3: Visual Metrics for MersenneTwister: (a) Heatmap of Correlation, (b) Power Spectrum Density, (c) Probability Mass Function, (d) Autocorrelation Function.