Modelling 1/f Noise in TRNGs via Fractional Brownian Motion

• URL: http://arxiv.org/abs/2410.14205v3
• Date: Wed, 28 May 2025 20:37:50 GMT
• Title: Modelling 1/f Noise in TRNGs via Fractional Brownian Motion
• Authors: Maciej Skorski,
• Abstract summary: Security of random number generators is not fully understood due to complex $1/falpha$ phase noise.<n>We introduce fractional Brownian motion as a comprehensive theoretical framework, capturing power-law spectral densities from white to flicker frequency noise.
• Score: 1.3053649021965603
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Security of oscillatory true random number generators remains not fully understood due to insufficient understanding of complex $1/f^\alpha$ phase noise. To bridge this gap, we introduce fractional Brownian motion as a comprehensive theoretical framework, capturing power-law spectral densities from white to flicker frequency noise. Our key contributions provide closed-form tractable solutions: (1) a quasi-renewal property showing conditional variance grows with power-law time dependence, enabling tractable leakage analysis; (2) closed-form min-entropy expressions under Gaussian phase posteriors; and (3) asymptotically unbiased Allan variance parameter estimation. This framework bridges physical modelling with cryptographic requirements, providing both theoretical foundations and practical calibration for oscillator-based TRNGs.

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