LiNbO3-based Optical Physical Unclonable Functions with Optimised Cryptographic Entropy via Rare-Earth Co-doping

We present a comprehensive theoretical study of LiNbO3-based optical Physical Unclonable Functions (PUFs) with entropy optimisation through combined MgO and rare-earth element (REE) co-doping. The core challenge -- the entropy-photorefraction trade-off -- is addressed by introducing REE ions as controlled random scattering centres. We derive an analytical entropy model H(c,T), calibrate it against experimental data, and evaluate compositions against NIST SP 800-22 metrics, Bit Error Rate (BER), long-term degradation H(t), and ML attack resistance. The optimal composition -- 4 mol.% MgO + 0.55 mol.% Nd3+ + 0.35 mol.% Yb3+ -- achieves +18.6% entropy gain, full NIST compliance across -40 to +85C, BER < 10^-22, entropy retention of 95.6% after 20 years, and superior ML attack resistance versus silicon Arbiter PUFs. An experimental verification programme covering 42 compositions is outlined.