LiNbO3-based Optical Physical Unclonable Functions with Optimised Cryptographic Entropy via Rare-Earth Co-doping: Analytical Model, NIST SP 800-22 Compliance, BER Analysis, Long-term Stability, and Security Comparison

<title>Abstract</title> <p>We address a fundamental problem in optical Physical Unclonable Function (PUF) design: the entropy-photorefraction trade-off in LiNbO3 single crystals, where MgO doping that suppresses photorefractive degradation simultaneously reduces cryptographic entropy by 20-25%. This problem has no solution in existing optical PUF literature. We propose rare-earth element (REE) co-doping as a decoupled solution: Er3+, Yb3+, Nd3+ ions substituting Li+ sites restore entropy via controlled ionic mismatch scattering without affecting photorefractive suppression. We derive an analytical entropy model H(c,T) calibrated against four experimental data points with zero residual error. Key calibrated result: 4 mol.% MgO + Er3+ + Yb3+ achieves H=95.8%, full NIST SP 800-22 compliance across −40 to +85°C, BER &lt; 10−20, and &gt;30 year projected lifetime. We report a previously unknown finding: standard 5 mol.% MgO fails NIST Uniqueness (D=44.08% &lt; 45%). Direct comparison with four optical PUF platforms from literature shows our approach uniquely combines full temperature range, 20+ year lifetime, NIST compliance, and ML resistance. An experimental verification programme (42 compositions, criteria V1-V5) is outlined.</p>