2025/09/30 by Skorski, Maciej, Soto, Francisco-Javier, Günlü, Onur
#Cryptography and Security (cs.CR) #FOS: Computer and information sciences #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.2509.26393
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 ℓ∞ and ℓ2 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.