Using Fourier analysis, this paper establishes exact security bounds for linear extractors in True Random Number Generators (TRNGs). We provide the first near-optimal total variation security characterization by interpolating between optimal $\ell_{\infty}$ and $\ell_2$ norm results, expressed through code weight enumerators and input bias parameters. Our bounds improve security assessments by an order of magnitude over previous approximations. By scanning ~20,000 codes, we reveal fundamental trade-offs between compression efficiency and cryptographic security. For instance, we show that achieving 80 bits of security can require sacrificing more than 50\% of the code rate when correcting 10\% input bias. Our bounds enhance security evaluation of TRNG post-processing schemes and quantify the inherent cost of randomness extraction in hardware implementations.

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