(untitled) (Contemporary Mathematics, 2025)
Quantum computing threatens mainstream cryptosystems that rely on integer factorization and discrete-logarithm hardness assumptions. Although Post-Quantum Cryptography (PQC) and biometric authentication have each progressed rapidly, few solutions fuse their respective advantages. We present an AI-enhanced post-quantum two-tier authentication framework that unifies cryptographic robustness with adaptive, behaviour-based biometrics. Tier 1 uses conventional factors-passwords and static biometrics-to establish a baseline identity. Tier 2 then acquires dynamic emotional cues from facial expressions, speech prosody and physiological signals, which are continuously analysed by deep-learning models. The resulting emotion signatures are bound to the credential stream via a lattice-based chameleon hash and signed with the CRYSTALS-Dilithium scheme, yielding strong resistance to spoofing, coercion and quantum adversaries. Simulation results show a True Acceptance Rate of 95.7% and a False Acceptance Rate of 2.1% under targeted adversarial attacks. These findings demonstrate that coupling emotion-aware AI biometrics with PQC primitives can deliver adaptive, quantum-resilient authentication for next-generation digital infrastructure.