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arXiv · 2509.26393

Exact Bias of Linear TRNG Correctors -- Spectral Approach

Maciej Skorski·Francisco-Javier Soto·Onur Günlü
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Abstract

Using Fourier analysis, this paper establishes near-optimal security bounds for linear correctors commonly used in True Random Number Generators (TRNGs), expressed through code weight enumerators and input bias parameters. We provide the first near-tight bias characterization in total variation, by interpolating between optimal $\ell_\infty$ and $\ell_2$ norm results. Our bounds improve security assessments by an order of magnitude over previously known (overly conservative) estimates. Across $\sim $20,000 codes, we examine fundamental trade-offs between compression efficiency, cryptographic security, and hardware complexity. Achieving 80-bit security with 10\% input bias typically requires sacrificing more than 50\% of the code rate and incurs increased hardware cost. This quantifies the inherent cost of randomness extraction in hardware TRNG implementations.

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Maciej Skorski, Francisco-Javier Soto, Onur Günlü. 2026-05-21. Exact Bias of Linear TRNG Correctors -- Spectral Approach. https://arxiv.org/abs/2509.26393

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