Machine Learning-Assisted Selection of Algebraic Structures for Post-Quantum Cryptographic Systems: A Multi-Objective Computational Optimization Model

The transition to post-quantum cryptography creates a mathematical decision problem in which security strength, algebraic structure, key and ciphertext sizes, execution time, memory demand, implementation complexity, and side-channel resilience must be considered simultaneously. This paper develops a machine learning-assisted multi-objective computational framework for ranking candidate algebraic structures and parameter configurations for post-quantum cryptographic deployment. The framework combines a normalized utility model, feasibility constraints, Pareto dominance, and supervised learning. A reproducible simulation study with 2,400 synthetic candidate configurations representing lattice-, code-, hash-, multivariate-, and group-based families is used to demonstrate the methodology without presenting the simulated values as implementation benchmarks. Random Forest, Gradient Boosting, and Support Vector Machine classifiers are compared using a stratified 70:30 train-test split and five-fold cross-validation. On the held-out test set, Gradient Boosting achieved an accuracy of 0.901, F1-score of 0.869, and ROC-AUC of 0.968, while five-fold cross-validation produced a mean ROC-AUC of 0.960. Security strength was the dominant predictor in permutation analysis, but side-channel resilience, algebraic dimension, key size, memory demand, and decapsulation time also contributed to the selection boundary. A Pareto analysis identified 25 non-dominated feasible configurations in the simulated design space. The proposed model provides a transparent mathematical mechanism for combining cryptographic constraints with data-driven classification and can be adapted to measured benchmark datasets as they become available. The principal contribution is therefore methodological: it gives a reproducible bridge between computational algebra, multi-criteria optimization, and machine learning for cryptographic parameter selection.