Correlation Bounds and Markov Analysis for Ring-Oscillator TRNGs: A Joint Validation Framework

TL;DR

This paper introduces a joint validation framework linking theoretical correlation measures and empirical entropy tests for ring-oscillator-based TRNGs, supported by mathematical derivations and computational validation, aiming to unify TRNG quality assessment.

Contribution

It establishes the first correlation between Maurer's Z-score and second-order correlation, deriving their relationship with Markov chain models for TRNGs, and validates these findings computationally.

Findings

Strong positive correlation between Maurer Z-score and C2

Practical implementations meet Schmidt's improved bound

Unified metric for TRNG quality assessment proposed

Abstract

True Random Number Generators (TRNGs) based on ring oscillators require rigorous statistical validation to ensure cryptographic quality. While the Mauduit-S\'ark\"ozy $k$-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.