A Hybrid Algebraic Cryptographic Strength Index and Machine Learning Model for Predicting the Security of Algebraic Structures

Michael Nsikan John. (2026). A Hybrid Algebraic Cryptographic Strength Index and Machine Learning Model for Predicting the Security of Algebraic Structures. Ktrend - International Journal of Data Science and Machine Learning (IJDSML), 1(1), 1-15. https://doi.org/10.5281/zenodo.20651402 

The choice of algebraic structure is a central problem in modern cryptography, especially in the transition from classical public-key schemes to quantum-resistant security models. Classical cryptographic systems such as RSA and elliptic curve cryptography are strongly connected to number theory, finite groups, conjugacy behavior, bilinear maps, and discrete logarithm assumptions; however, there is still no generally accepted data-driven framework for predicting the cryptographic strength of algebraic structures before deployment. This paper proposes a new hybrid modelling framework called the Algebraic Cryptographic Strength Index (ACSI), combined with supervised machine learning, for predicting whether a finite or computationally represented algebraic structure is suitable for cryptographic use. The framework transforms group-theoretic, character theoretic, elliptic-curve, bilinear, lattice, and number-theoretic invariants into a structured feature space. A simulated dataset of 12,000 algebraic structures was generated using mathematically motivated constraints derived from conjugacy classes, centralizer ratios, derived length, monomial character indices, elliptic curve security margins, RSA modulus complexity, bilinear pairing depth, and lattice hardness. Four models were trained and evaluated: Random Forest, Gradient Boosting, Support Vector Machine, and Neural Network. The Neural Network achieved the best overall accuracy of 78.86% and ROC-AUC of 87.49%, while Gradient Boosting and Random Forest provided more interpretable feature-importance patterns. The results suggest that lattice hardness, elliptic curve security margin, small cancellation score, conjugacy density, and character-codegree entropy are among the most influential predictors. The study contributes a reproducible mathematical-data-science framework for algebraic cryptographic suitability prediction and opens a pathway for explainable machine learning in post-quantum cryptographic structure selection.