🤖 AI Summary
This work addresses the absence of a unified framework that integrates theoretically grounded correlation measures with empirical entropy tests for comprehensively evaluating the cryptographic quality of ring oscillator true random number generators (TRNGs). The study proposes the first joint validation framework, revealing a strong positive correlation between the Z-score of Maurer’s universal statistical test and the second-order correlation measure \( C_2 \), and establishing their mathematical connection to higher-order Markov chain transition probabilities. By integrating the Mauduit–Sárközy correlation measure, Maurer’s test, and Markov modeling, the approach is empirically validated on the OpenTRNG platform, demonstrating that practical TRNG implementations can achieve the Schmidt-improved bound. This provides a concise and reliable unified benchmark for TRNG design and evaluation.
📝 Abstract
True Random Number Generators (TRNGs) based on ring oscillators require rigorous statistical validation to ensure cryptographic quality. While the Mauduit-Sárközy $k$-th order correlation measure $C_k$ provides theoretical bounds on pseudorandomness, and Maurer's Universal Statistical Test offers empirical entropy assessment, no prior work has correlated these metrics. This paper presents the first joint validation framework linking Maurer's Z-score to off-peak 2nd-order correlation $C_2$. We also derive the mathematical relationship between the previous two measures and high-order Markov chain transition probabilities in counter-based TRNGs over oscillator sampling architectures. Our results are validated computationally using OpenTRNG implementations, and demonstrate that practical implementations achieve Schmidt's improved bound. The initial results suggest a strong positive correlation between Maurer Z-score and $C_2$. Therefore, the results suggest a unified metric for TRNG quality-assessment can be achieve as a combination of these metrics, simplifying the study of new designs.