Correlation Bounds and Markov Analysis for Ring-Oscillator TRNGs: A Joint Validation Framework
This provides a unified validation framework for cryptographic TRNG designers, though it appears incremental by combining existing metrics.
The paper tackles the problem of validating ring-oscillator true random number generators (TRNGs) by presenting the first joint framework linking Maurer's Z-score to off-peak 2nd-order correlation, and deriving mathematical relationships with high-order Markov chain probabilities. The results, validated computationally, show practical implementations achieve Schmidt's improved bound and suggest a strong positive correlation between these metrics.
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.