Lattice-Based Post-Quantum Access Control with Fair Resource Allocation via Convex Optimization

Abstract We present a lattice-based framework for post-quantum access control that integrates fairness-aware resource allocation without compromising cryptographic security. Building on the hardness of Learning with Errors (LWE) and Ring-LWE problems, we introduce a generalized lattice function combined with convex optimization to balance computational efficiency and equitable distribution of cryptographic resources. Formal analysis establishes convergence guarantees for fairness-aware allocation in large-scale systems. Empirical validation across blockchain networks, cloud storage, and smart grid datasets demonstrates a 41.3% reduction in fairness loss and a 39.7% improvement in resource retention accuracy compared with baseline lattice protocols. These results highlight the scalability and robustness of the proposed scheme, providing a mathematically grounded extension of lattice-based cryptography for secure and fair post-quantum infrastructures.