Paper 2025/503 Original: eprint.iacr.org/2025/503 ↗

Max Bias Analysis: A New Approach on Computing the Entropy of Free Ring-Oscillator

Abstract

This work introduce a new approach called Max bias analysis for the entropy computation of structures of Free Ring Oscillator-based Physical Random Number Generator. It employs the stochastic model based on the well-established Wiener process, specifically adapted to only capture thermal noise contributions while accounting for potential non-zero bias in the duty cycle. Our analysis is versatile, applicable to combinations of multiple sampled Ring Oscillator (RO) filtering by any function. The entropy computation takes as inputs the parameters of the thermal stochastic model and delivers directly a proven bound for both Shannon entropy and min-entropy to fulfill AIS31 and NIST SP 800-90 B. As an example, we apply the new methodology on an enhanced structure of TRNG combining several free-running Ring Oscillators filtered by a vectorial function built from a linear error correcting code that optimizes the functional performance in terms of [entropy rate/silicium area used] and that maintains the mathematical proof of the entropy lower bound as simple as possible.